International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
1
THU: 28-12-2017 Hall Sec Poster (01) ( 1 )
 01:15 : 02:45

MPH - 1 EG Assoc.Prof. A. Mahdy mahdy4@yahoo.com

115
Mixed convection flow of a nanofluid containing gyrotactic microorganisms along a vertical wedge in porous media
A. Mahdy

 Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

ABSTRACT
The main objective of the present paper is to examine the case of mixed convection flow due to gyrotactic microorganisms from an isothermal vertical wedge embedded in a porous medium saturated with a nanofluid. In this pioneering study, the simplest possible boundary conditions are considered, namely those in which the temperature, the nanoparticle fraction and the density of motile microorganisms are constant along the wall of the wedge. The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing, and anticipated improved stability of the nanofluid. Upon the Oberbeckâ€“Boussinesq approximation and non-similarity transformation, the nonlinear model equations are obtained and tackled numerically numerically by using the R.K. Gill and shooting methods to obtain the dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms together with the reduced Nusselt, Sherwood and motile microorganism numbers. The bioconvection parameters strongly influence the heat, nanoparticle volume fraction and motile microorganism transport rates. In the absence of bioconvection, the results are compared with the existing data in the open literature and found to be in very good agreement.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
2
THU: 28-12-2017 Hall Sec Poster (01) ( 2 )
 01:15 : 02:45

MPH - 4 DZ Dr. Berrehail Mounira Berrehail1936@yahoo.fr

115
Class of invariants for a time dependent linear potential
mounira berrehail , benamira farid

 2 Département des Sciences de la matière, Université de Bordj Bou Arreridj Bordj Bou Arreridj 43000, Algeria Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Constantine 1, Constantine 25000, Algeria

ABSTRACT
General solution of the one-dimensional Schrödinger equation in presence of a time-dependent linear potential is reconsidered in the context of Lewis-Riesenfeld and unitary transformation approaches. Three invariant operators are constructed as limiting cases of a general Hermitian quadratic invariant and their instantaneous eigenfunctions are obtained. Then the corresponding solutions of Schrödinger equation for each invariant operator are derived. These solutions include all known solutions of the system. Furthermore, it is shown how different solutions can be related to each other.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
3
THU: 28-12-2017 Hall Sec Poster (01) ( 3 )
 01:15 : 02:45

MPH - 5 EG Dr. Rania El- tantawy rania_eltantwy@yahoo.com

115
VISCOELASTIC STRESSES OF NONLINEAR ROTATING FUNCTIONALLY GRADED SOLID AND ANNULAR DISKS WITH GRADUALLY VARYING THICKNESS
M.N.M. Allam , R. Tantawy , A. Yousof , A.M. Zenkour

 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Department of Mathematics, Faculty of Science, Damietta University, Damietta 34517, Egypt Department of Mathematics, Faculty of Science, Damietta University, Damietta 34517, Egypt Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

ABSTRACT
Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
4
THU: 28-12-2017 Hall Sec Poster (01) ( 4 )
 01:15 : 02:45

MPH - 14 EG Ms. Afaf hatem Syam Ah_syam2015@yahoo.com

115
Concomitants of order statistics And record values from general farlie-gumble-morgenestern type bivariate- generalized exponential distribution
H. M. Barakat , E. M. Nigm , A. H. Syam

 Departement of mathematics-faculty of science- zagazig university Departement of mathematics-faculty of science- zagazig university Higher Technological Institute 10th of Ramadan city

ABSTRACT
We introduce BKb-fgm type bivariate generalized exponential distribution. Some distribution properties of concomitants. Of order statistics as well aas record values for this family are studied. Recurrence. Relations between the momeents of concomitants are obtained. Some of these recurrence relations were not published before even for morgenestern type bivariate distributions. Morever, most of paper results are extended To arbitrary distributions (see remark 3.1)
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
5
THU: 28-12-2017 Hall Sec Poster (01) ( 5 )
 01:15 : 02:45

MPH - 22 EG Dr. Tarek El-shahat el_shahat@yahoo.com

115
Entanglement of thermal states of two-qutrit states with Long-Range Interaction.
A. R. Mohammed. , T. M. El-Shahat

 Math. Dept., Faculty of Science, Al-Azhar University, 71524, Assiut, Egypt. Math. Dept., Faculty of Science, Al-Azhar University, 71524, Assiut, Egypt.

ABSTRACT
We investigate the effect of the long-range interaction (LRI) with an inverse-square function on the thermal entanglement in anisotropic two-qutrit Heisenberg XYZ system with Dzyaloshinskii- Moriya (DM) interaction in the presence of the external magnetic eld, using Negativity and Measurement-Induced Disturbance (MID) to quantify entanglement. The temperature and mag- netic eld dependence of the thermal entanglement in this system for this interaction are discussed. Our results indicate that, when the LRI type interactions exist, there is a rich conduct dependent between spins on the interaction strength, temperature, DM interaction and magnetic eld. In addition, we conclude that sudden death is displayed at the critical distance of the entangle- ment. We nd that for less than a critical distance there are entanglement plateaus dependent upon the distance between spins. Furthermore it, we will make obvious comparison between the measurement-induced disturbance (MID) and negativity for this model. we will discover that MID is more robust than thermal entanglement against temperature T.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
6
THU: 28-12-2017 Hall Sec Poster (01) ( 6 )
 01:15 : 02:45

115
Piezoelectric FGPM Rotating Hollow Variable Thickness Disc in Hygrothermal Envairoment
M.N.M. Allam , R. Tantawy , A. Yousof

 Mathematics department, Faculty of science, Mansoura University, Mansoura, 35516 Egypt Mathematics department, Faculty of science, Damietta University, Damietta, 34517 Egypt Mathematics department, Faculty of science, Damietta University, Damietta, 34517 Egypt

ABSTRACT
a semi-analytical solution for a functionally graded piezoelectric rotating disc with variable thickness is presented. There are pressure on the boundary surface, uniform distribution of hygrothermal effect and electric potentials difference between the inner and outer surface. All material properties of the disc assumed to be a function in the radial direction. Some cases of boundary conditions are presented. At last, numerical results are carried out and discussed. The values used in this study are arbitrary chosen to demonstrate the hygrothermal effect on FGPM with variable thickness.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
7
THU: 28-12-2017 Hall Sec Poster (01) ( 7 )
 01:15 : 02:45

MPH - 24 EG Dr. Ali Abu-Bakr alibakrm@yahoo.com

115
Mathematical modeling of Hyperthermia in a system of interaction ferromagnetic particles
Ali F. Abu-Bakr , Andery Yu. Zubarev

 Mathematics department, Faculty of Science, Menoufia university, Egypt Theoretical and Mathematical Phyiscs department, Institute of Natural Science and Mathematics, Ural Federal University

ABSTRACT
Hyperthermia is the method of heating materials with the help of micro- or nano- sized magnetic particles embedded in them. The essence of this effect is that the medium with particles is placed in an alternating magnetic field. The speed and degree of heating of the particles can be regulated by the strength and frequency of the applied field. Hyperthermia refers to the heating of organs or tissues to temperatures ranging from 42°C to 46°C where it causes the death of cancer cells [1,2]. In this work, we employ an interparticle interaction of magnetic nanoparticles model based on a system of nonlinear differential equations of rotation equations and stokes equations under the influence of rotation magnetic field. Computer simulation has been used to solve this system numerically and investigate of magnetic hyperthermia in the cell of tumor. The results show that the interparticle interaction under rotating magnetic field can significantly increase the heat production as compared with the calculations in the model of the interparticle interaction in linearly oscillating magnetic field. References [1] R.E. Rosensweig. Heating magnetic fluid with alternating magnetic field. Journal of Magnetism and Magnetic Materials, 252, (2002), Pp. 370–374. [2] A.Yu. Zubarev, L. Iskakova and A.F. Abu-Bakr, Magnetic hyperthermia in solid magnetic colloids, Physica A, 467, (2017), Pp. 59–66.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
8
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 1 )
 04:00 : 04:15

MPH - 2 NG Dr. Mohammed Abdulhameed amohd@fptb.edu.ng

115
MHD electroosmotic micro-pump of non-Newtonian fluids through micro-channel
Mohammed Abdulhameed

 Federal Polytechnic Bauchi, Nigeria

ABSTRACT
This problem deals with steady driven pressure flow and heat transfer of electro-magnetohydrodynamic micro-pump of third grade fluids between two micro-parallel plates embedded in a porous medium. The effect of thermal radiation and electro-kinetic have been taken into account. The flow forced by the Lorentz force, produced by the interaction of a vertical magnetic field and an externally horizontal imposed electrical field, is assumed to be unidirectional and one dimensional. Based upon the velocity field, the thermally fully developed heat transfer with radiation effect are analyzed by taking the viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. Analytical solutions corresponding to the fluid velocity and temperature distribution are obtained in series forms, in the assumption that the non-Newtonian viscoelastic parameter has small values. The effects of permeability of the porous medium K, the dimensionless electrical strength parameter H, Hartmann number Ha, non-Newtonian parameter Lamda, constant pressure P, thermal radiation Nr and non-dimensional parameter Brinkman number gamma1 on the velocity and temperature are investigated graphically and discussed in detail.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
9
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 2 )
 04:15 : 04:30

MPH - 3 NG Mr. Mohammed Salisu Chimo moallahyidi@gmail.com

115
Analytical study of chemically reactive Rivlin-Ericksen viscoelastic fluid in a circular tube
Mohammed Salisu Chimo , Mohammed Abdulhameed , Sagir Mahmud Abdullahi

 Federal Polytechnic Bauchi, Nigeria Federal Polytechnic Bauchi Federal Polytechnic Bauchi

ABSTRACT
This problem deals with the influence of chemically reactive Rivlin-Ericksen viscoelastic fluid in a circular tube with no thermal convection. The fluid starts heat generation because of its reactive nature of chemically viscoelastic fluid which set up free convection currents inside the tube. The governing equations are modelled using the fully developed flow conditions. Analytical algorithm based on the modefied homotopy perturbation method (HPM), incorporating the He's polynomial and combined with the Laplace transform is implemented in time and space with the second grade constitutive model for the viscoelastic liquids. Explicit analytical expressions for the transient state as well as the steady state for velocity field and temperature field have been derived. These solutions are written as the sum between the permanent solutions and the transient solutions. The algorithm is validated against the classical solution of this problem for reactive viscous fluid results. The nature of the wall shear stress and Nusselt number engendered due to the flow are determined. The results also indicate that it takes longer to attain steady-state in the case of molten polymer than water and air.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
10
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 3 )
 04:30 : 04:45

MPH - 6 NG Dr. Abdulsalam Ya'u Gital yidi76@yahoo.com

115
Effects of the fractional order on nanoparticles in Blood flow through the stenosed artery
Dr. Abdulsalam Ya'u Gital

 Abubakar Tafawa Balewa University Bauchi, Nigeria

ABSTRACT
In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. , and are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to and nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
11
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 4 )
 04:45 : 05:00

MPH - 7 EG Assoc.Prof. Abdallah A. Nahla a.nahla@science.tanta.edu.eg

115
Atomic population inversion of the asymmetric atom-atom interaction and SU(1,1) quantum system
Abdallah A. Nahla , M.M.A. Ahmed

 Department of Mathematics, Faculty of Science, Tanta University, Egypt. Department of Mathematics, Faculty of Science, Al-Azhar University, Egypt.

ABSTRACT
A model of the asymmetric two two-level atoms interacting with the SU(1,1) quantum system is presented. The rotating wave approximation (RWA) and the atom-atom interaction are considered in the Hamiltonian operator. The time-dependent wave function for asymmetric case is obtained analytically via solving the Schrodinger equation. Initially, the SU(1,1) quantum system prepared in the Perelemov coherent state and two atoms are in superposition states. Therefore, the atomic population inversion is obtained and discussed for different values of model parameters such as initial atomic angles, Perelomov coherent parameter, the Bargmann index and the detuning parameters. We note that the quantum system is sensitive to the variation in both the Perelomov coherent parameter and the Bargmann index. Moreover, there are non-classical characteristics of the proposed system in the presence the detuning parameters.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
12
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 5 )
 05:00 : 05:15

MPH - 8 EG Dr. Sara Abdelsalam sara.abdelsalam@bue.edu.eg

115
A theoretical study of variable magnetic field with endoscope effect on peristaltic blood flow of Prandtl nanofluid having TiO2 nanoparticles
Sara Abdelsalam , Muhammed Bhatti

 The British University in Egypt Shanghai University

ABSTRACT
In this article, we have studied the variable magnetic field and endoscope effects on peristaltic blood flow of nanofluid containing TiO2 nanoparticles through a porous annulus. The Prandtl fluid model is taken into account for the present flow. The mathematical modeling comprises the temperature, continuity, nanoparticle concentration, and equations of motion which are further simplified by taking a long peristaltic wave and creeping flow regime. The obtained highly nonlinear partial differential equations are solved using homotopy perturbation scheme. The inclusion of the pertinent parameters is discussed mathematically and graphically for the pressure rise, friction forces, temperature profile, and concentration profile. The trapping phenomenon is also investigated with the help of contours. Results show that the maximum velocity distribution exists near the centre of the annulus, whereas the average time flow boosts the velocity profile.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
13
THU: 28-12-2017 Hall[A] Oral - Sec01 ( 6 )
 05:15 : 05:30

115
Exact Solution of the N-dimensional Radial Schrödinger Equation via Laplace Transform Method with the Modified Extended Cornell Potential
M. Abu-Shady , T. A. Abdel-Karim , E. M. Khokha

 Department of Mathematics, Faculty of Science, Menoufia University, Shebin El- Kom Egypt Department of Mathematics, Faculty of Science, Menoufia University, Shebin El- Kom Egypt Department of Basic Science, Modern Academy for Engineering and Technology, Cairo, Egypt

ABSTRACT
The exact solution of N- dimensional radial Schrödinger equation with the modified extended Cornell potential has been obtained using the Laplace transform (LT) method. The energy eigenvalues and the corresponding wave functions for any state have been determined. The eigenvalues for some special cases of the modified extended Cornell potential have been derived. We have investigated the present results to calculate the mass spectra of heavy quarkonium systems such as charmonium, bottomonium and the meson in comparison with the experimental data and with the other studies. The present results have been improved in comparison with other recent studies and have shown a good agreement with the experimental data.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
14
FRI: 29-12-2017 Hall[A] Oral - Sec04 ( 1 )
 08:45 : 09:00

MPH - 10 BH Prof. Nasser Metwally Nmetwally@gmail.com

115
Quantifying and teleporting Fisher Information for accelerated two-qubit system
Nasser Metwally

 Math. Dept., college of Science, P. O. Box 32038 Kingdom of Bahrain, University of Bahrain

ABSTRACT
The quantum Fisher information of an accelerated two qubit system is discussed, where the analytical solution which consists of three different parts is derived. We show that, the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. Fisher information is employed to estimate the states' parameters. Although the precision of estimating the state's parameters decreases as the acceleration increases, it can be maximized at certain values of the Unruh acceleration. Moreover, the contribution of the three different parts on the total Fisher information is investigated. Additionally, quantum Fisher information is introduced as a measure of estimating the quantity of the teleported information between two users, where only one of them is accelerated. The estimation degree depends on Unruh acceleration, the used single mode approximation (within/beyond), the type of encoded information (classic/quantum) in the teleported state, and the entanglement of the initial communication channel. The estimation degree of the parameters can be maximized if the partners teleport classical information.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
15
FRI: 29-12-2017 Hall[A] Oral - Sec04 ( 2 )
 09:00 : 09:15

MPH - 11 EG Assoc.Prof. A. Mahdy mahdy4@yahoo.com

115
Buongiorno's nanofluid model for mixed convection flow over a vertical porous wedge with convective boundary conditions
A. Mahdy

 Mathematics Departement, Faculty of Science, South Valley University

ABSTRACT
An exploring of the state of mixed convection flow due to an isothermal vertical wedge submersed in saturated porous medium utilize Buongiorno’s nanofluid paradigm is the master intention of our research. In this pioneering investigation, Buongiorno’s nanoﬂuid model that comprises the effects of both of Brownian motion and thermophoresis is employed. The paradigm takes regard the case when the nanoﬂuid particle fraction on the boundary layer is passively rather than actively controlled. The wall of the wedge is submersed in a uniform porous medium and the convective boundary condition has been employed over the wedge wall. Upon the Oberbeck–Boussinesq approximation and non-similarity transformation, the nonlinear set equations are obtained and tackled numerically by using the R.K. Gill and shooting method. A parametric study of the entire flow regime is procured to clarify the effects of the controlled parameters such as: wedge angle parameter ( ), buoyancy ratio parameter ( ), mixed convection parameter ( ), Biot number ( ), Brownian motion parameter ( ), thermophoresis parameter ( ) and Lewies number ( ); the results are likened with the available data in the open literature and detected to be in very good harmonizing. The eminent lineaments of the achieved outcome have been construed and depicted.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
16
FRI: 29-12-2017 Hall[A] Oral - Sec04 ( 3 )
 09:15 : 09:30

MPH - 12 EG Dr. Tarek El-shahat el_shahat@yahoo.com

115
Dynamics of entanglement and non-classicality features of a single-mode nonlinear Jaynes-Cummings model intensity-dependent coupling
Tarek M. Elshahat

 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

ABSTRACT
In this paper, we study the interaction between a Four-level atom and a quantized single-mode field with "intensity-dependent coupling" involving two-photon processes in a "Kerr medium". The Four-level atom is considered to be in a $\lambda$-type configuration. Using the generalized (nonlinear) Jaynes-Cummings model, the exact analytical solution of the wave function for the considered system under particular condition, has been obtained when the atom is initially in the superposition state and the field is in a coherent state. By using some particular condition, the $\lambda$-type Four-level reduced to $\Xi$-type three level atom, Then, we study the amount of entanglement of the generated entangled states using the field entropy,purity and Fidelity. Moreover, we evaluate a few of their non-classical properties such as momentum increment, momentum diffusion, Mandel $Q$-parameter, mean photon number, Normal squeezing and establish their non-classicality features.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
17
FRI: 29-12-2017 Hall[A] Oral - Sec04 ( 4 )
 09:30 : 09:45

115
Electro-osmotic flow of non-Newtonian biofluids through wavy micro-concentric tubes
Kh. S. Mekheimer , R. E. Abo-Elkhair , A. M. A. Moawad

 Mathematical Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt Mathematical Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt Mathematical Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

ABSTRACT
Most of the bio-fluids are non-Newtonian fluid with complex flow behavior, for instances the human blood and DNA sample are shear thinning fluids (Jeffery model). The Electrokinetic transport of such fluids by micro-peristaltic pumping has been interested in biomedical engineering and other of medical technology. This kind of fluid transport requires more elegant mathematical models and numerical simulations. Motivated by these developments, the present article analyzed the simultaneous effects of an electric double layer and a transverse magnetic field on peristaltic transport of Jeffrey fluid as blood flow model. We select it as a constitutive relation to describe electroosmotic flow located in the gap between two coaxial horizontal pipes. Under low Reynolds number, long wavelength and Debye linearization approximations, the Poisson-­Boltzmann equation together with the governing partial differential equations for mass and momentum are derived with appropriate boundary conditions. The expressions for electric potential, stream function, axial velocity, shear wall stress, and axial pressure gradient have been obtained. Pressure rise and frictional force per wavelength have been evaluated numerically and discussed briefly. Our computational evidence that the electric potential is an increasing function of the thickness of the electrical double layer (EDL). Also, axial flow is accelerated with the adding electric field and decelerated with opposing electric field. Finally, bolus size is reduced as the axial external electric field change its direction from adding to opposing direction.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
18
FRI: 29-12-2017 Hall[A] Oral - Sec04 ( 5 )
 09:45 : 10:00

MPH - 15 EG Dr. shaimaa fathey shaimaafathey2012@yahoo.com

115
Peristaltic flow of micropolar fluid with nanoparticles through porous medium under the effects of heat absorption, chemical reaction and wall properties

 Al-Azhar University

ABSTRACT
In the present analysis we have discussed the effects of heat absorption, chemical reaction and wall properties on peristaltic flow of micropolar nanofluid through a porous medium. The fundamental equations of the motion are first modulated and then simplified under the assumptions of long wavelength and low Reynolds number. The exact solutions have been calculated for the velocity and the microrotation velocity, while the governing equations of energy and nanoparticles equations are solved analytically using homotopy perturbation method. In the end, graphical results are discussed to illustrate the effects of various physical parameters of the problem on these distributions.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
19
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 1 )
 04:00 : 04:15

MPH - 16 EG Ms. Amany Elgarawany dr_newten90@yahoo.com

115
A Theoretical Study Of The Effect Of A Laser Mode With Different Coherent Angles On The Motion Of Atomic Vapors
Aly M. Abourabia , Amany Z. Elgarawany

 Department of Mathematics-Faculty of Science-Menoufiya University. Shebin-El kom 32511.Egypt Department of Computer Science-Higher Institute Of Computer and Management Sciences-Integrated Thebes Institutes-1st Maadi Corniche, Cairo 11434.Egypt

ABSTRACT
We follow theoretically the motion of the sodium atoms in vapor state under the influence of a laser mode in (1 + 1) D, which is achieved via different optical filters. In the Dirac interaction representation, the equations of motion are represented via the Bloch form, together with the Pauli operators to find the elements of the density matrix of the system. The immergence of the principle of coherence in varying the angles of the laser mode, permits to evaluate the average force affecting the atoms acceleration or deceleration, accordingly the corresponding velocities and temperatures are investigated. The atomic vapor is introduced in a region occupied by a heat bath presented by the laser field, such that the state of the atomic vapor is unstable inside the system due to the loss or gain of its kinetic energy to or from the laser field. This instability is studied through finding the eigenvalues of the system's entropy. Resorting to the assumption of Boten, Kazantsev and Pusep, who issued a coupling between the mean numbers of photons in terms of time, allows the evaluation of the rate of entropy production of the system under study. A set of figures illustrating the dynamics of the problem is presented.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
20
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 2 )
 04:15 : 04:30

MPH - 17 EG Prof. Hamad Yehia hyehia@mans.edu.eg

115
LAGRANGIAN VERSUS HAMILTONIAN FORMALISMS IN CERTAIN PROBLEMS OF DYNAMICS

 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

ABSTRACT
It is commonly believed that Lagrangian and Hamiltonian equations for a given mechanical system are equivalent. We show that, even in case of mathematical equivalence, the Lagrangian description has certain advantages. This is related to the fact that in a given set of generalized coordinates, Lagrange’s equations are unique, although the Lagrangian itself is not unique, due to possible gauge transformations. On the other hand, neither the Hamiltonian nor Hamilton’s equations are unique for a given mechanical system. This difference is essential in inverse problems of physical importance, when integrable Hamiltonians are constructed from the solution of an integrability requirement. Physical characteristics of the system are mostly disguised in the Hamiltonian form. Examples are given from dynamics of a 3-D system with a symmetry, involving a particle or a rigid body about a fixed point.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
21
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 3 )
 04:30 : 04:45

MPH - 18 EG Dr. Ahmed Kamal ahmed.abunab@yahoo.com

115
The concentration distribution surrounded the growing of gas bubbles in the bio tissues
A. K. Abu-Nab , S. A. Mohammadein

 Mathematics Department, Faculty of science, Menoufia University, Shebin El-Koom Egypt Mathematics Department, Faculty of science, Tanta University, Tanta, Egypt

ABSTRACT
The concentration distribution around growing gas bubble in the blood and bio tissues of divers who ascend to surface too quickly is obtained by Mohammadein and Mohamed model [12] for variant and constant ambient pressure through the decompression process. The mathematical model describing this problem consists of four main equations: mass, convective diffusion, Fick's and Laplace’s equations. The mathematical model is solved analytically to obtain the concentration distribution around a growing gas bubble in biotissues. The growth of gas bubble is affected by initial concentration difference ∆C_0, diffusivity of gas in tissue , the constant K_d at decompression, surface tension , initial void fraction . The relation between the growth of gas bubble and time is obtained from the definition of the concentration distribution around a growing gas bubble in biotissues. The relation between the growth of gas bubble and time is studied under the effect of two different values of initial void fraction , critical bubble radius . The present model is compared with Mohammadein and Mohammed model [12].
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
22
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 4 )
 04:45 : 05:00

MPH - 19 EG Mr. Mahmoud-SifedDin Taha msifeddin.taha@eng.asu.edu.eg

115
Solution to Pauli-Schrodinger Equation in Discrete 1 and Continuum 3 Dimensions with Application to Valence Electrons of Silicon

 Faculty of Engineering, Ain Shams University, Cairo, Egypt Faculty of Engineering, Ain Shams University, Cairo, Egypt Faculty of Engineering, Ain Shams University, Cairo, Egypt

ABSTRACT
Many-electron solution to Schrodinger Equation is hard to be put in closed form in terms of single-electron solution. Many perturbation theories and methods, including Linked Cluster by Sinanoglu and Coupled Cluster by Cizek, aimed to formulate a means to such a solution. Mostly spinless electrons were addressed by these methods at first to simplify the problem. Using the simplest form of Configuration Interaction and Brillouin-Wigner Perturbation Theory we present a formulated method for constructing the many-electron solution to Pauli-Schrodinger Equation. Spatial and Spin symmetry and asymmetry variation are addressed here. New Physics-relying and Mathematics-simplifying concepts are proposed here to provide a viable finite Energy wavefunction tracing. Silicon valance electron states are presented as an application of our theoretical formulation.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
23
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 5 )
 05:00 : 05:15

MPH - 20 EG Mr. Mahmoud-SifedDin Taha msifeddin.taha@eng.asu.edu.eg

115
Numerical Method to Calculate Electron and Phonon Density of States Functions from 3D Brillouin Zone Energy Dispersion and Application to Silicon

 Faculty of Engineering, Ain Shams University, Cairo, Egypt Faculty of Engineering, Ain Shams University, Cairo, Egypt Faculty of Engineering, Ain Shams University, Cairo, Egypt

ABSTRACT
The number of allowed states within the range of energy permitted for the Electrons and the Phonons per unit volume, typically known as Density of States Functions, is an important parameter for electrons out of their Thermal Equilibrium. Usually these functions are needed for current calculation along the energy range but the particle energy are modeled against the inverse space wave vector. Numerical Method depending on contour tracing of particle energy in the 1st Brillouin Zone is presented here. Comparison to approximate formula based on the effective mass of electrons in Silicon is shown. These functions are essential mathematical component to our Full-band Monte Carlo Method for bulk and device conductivity that is presented elsewhere.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Physics.
24
FRI: 29-12-2017 Hall[A] Oral - Sec08 ( 6 )
 05:15 : 05:30

MPH - 21 EG Dr. Tarek El-shahat el_shahat@yahoo.com

115
Description of Two Three-level Atoms-Field Interaction via Quantized Caldirola-Kanai Hamiltonian
M. K. Ismail , T. M. El-Shahat , A.-S. F. Obada

 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt. Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt. Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt

ABSTRACT
The system of two Λ-type three-level atoms and a quantized single-mode cavity field was proposed, where the Hamiltonian of the field is performed based on the Caldirola-Kanai damping Hamiltonian. An analytical description of such system was presented. Some of nonclassical features of such system were discussed, such as quantum entanglement, sub-Poissonian statistics and Quadrature fluctuation. Here, the effects of damping parameter, initial atomic states on the evolution of Linear entropy and the nonclassical features were considered for such system. In addition, some of quantum properties was studied via Mandel parameter. It was found that the damping parameter and initial atomic states play central roles in the evolution of the Linear entropy and nonclassicality evolution of the particle.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
25
THU: 28-12-2017 Hall Sec Poster (01) ( 1 )
 01:15 : 02:45

STA - 4 IN Dr. Manmath Lohgaonkar mhlohgaonkar@gmail.com

115
An Intuitionistic Fuzzy Approach to Solve Multi-objective Transportation Problem
Manmath Haridasrao Lohgaonkar , Vijay Narkhede

 Shri Chhatrapati Shivaji College Shrigonda, India Joint Director, Higher Education Pune, India

ABSTRACT
The aim of this paper is to develop a new concept of optimization technique using Atanassov’s intuitionistic fuzzy sets (IFS), to solve multi-objective transportation problem. It refers to a special class of vector minimum linear programing problem in which the constraints are of equality type and all the objectives are conflict with each other. All the methods either generate a set of non-dominated solutions or find a compromise solution. In this paper, we use a special type of linear and non-linear membership functions to solve the multi-objective transportation problem. It gives an optimal compromise solution. In addition, numerical example is also presented to illustrate the methodology.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
26
THU: 28-12-2017 Hall Sec Poster (01) ( 2 )
 01:15 : 02:45

STA - 10 EG Dr. Nourhan Rakha nourhankhalil266@yahoo.com

115
A new class of bivariate distributions including the bivariate normal distribution, with applications
H. M. Barakat , O. M. Khaled , N. Khalil. Rakha

 Dept. of Math. Faculty of Sci. Zagazig University, Zagazig, Egypt. Dept. of Math., Faculty of Sci. Port said University, Port Said, Egypt. Physics and Engineering Math. Dep., Faculty of Engineering, Port Said University, Port Said, Egypt.

ABSTRACT
In this paper we introduce a new method to add two shape parameters to any baseline bivariate distribution function (df) to get a more felixable generalized family of the bivariate df'. Through the additional parameters we can fully control the type (by controlling the skewness and kurtosis) of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution. The statistical properties of this family is studied. Moreover, we compared this family with some competitors important generalized families of bivariate df's. To motivate the use of the new suggested family, we present a successful example of real data, concerning the air pollution.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
27
THU: 28-12-2017 Hall Sec Poster (01) ( 3 )
 01:15 : 02:45

STA - 18 EG Ms. Naeima elkhader naeima_nesr@yahoo.com

115
A new extended mixture skew normal distribution,with applications

 Department of Mathematics-Faculty of Science-Zagazig University-Zagazig-Egypt. Faculty of Science, Alexandria University, Alexandria, Egypt Current address: Faculty of Science, Alexandria University, Alexandria, Egypt- Permenant address: Department of Statistics Faculty of Science- Benghazi University-Benghazi-Libya

ABSTRACT
The stable symmetric family of distribution functions (df’s) is a family that contains the reverse of every df belonging to it. It is revealed that this family is capable of describing many types of statistical data. We show that the mixture of the skew normal distribution and its reverse, after adding a location parameter to the skew normal distribution, and adding the same location parameter with different sign to its reverse, is stable symmetric family that contains all the possible types of df’s and it has a very remarkable wide range of the indices of skewness and kurtosis. To motivate the use of the new suggested family, we present a successful example of real data.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
28
THU: 28-12-2017 Hall Sec Poster (01) ( 4 )
 01:15 : 02:45

115
Estimation in Step Partially Accelerated Life Tests for KIW Model Using Progressive Type-II Censoring

 Mathematics Department, Faculty of Science, A1-Azhar University, Nasr-City (11884), Cairo, Egypt

ABSTRACT
In this article, based on progressively type-II censored schemes under step-stress partially accelerated life test model, the maximum likelihood, Bayes, and two parametric bootstrap methods are used for estimating the unknown parameters of the Kumaraswamy inverse Weibull distribution and the acceleration factor. Asymptotic confidence interval estimates of the model parameters and the acceleration factor are also evaluated by using Fisher information matrix. The classical Bayes estimators cannot be obtained in explicit form, so Markov chain Monte Carlo method is used to tackle this problem, which allows us to construct the credible interval of the involved parameters. Finally, analysis of a simulated data set has been also presented for illustrative purposes.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
29
THU: 28-12-2017 Hall[B] Oral - Sec02 ( 1 )
 04:00 : 04:15

STA - 2 EG Prof. Ahmed Elsayed atabl181@yahoo.com

115
Modeling Correlated Missing Data
Ahmed Mohamed Mohamed El-Sayed

 High Institute for Specific Studies Department of Management Information Systems Nazlet Al-Batran, Giza, Egypt.

ABSTRACT
Missing data have occurred in longitudinal studies. Missing data may reduce the performance of confidence intervals, reduce statistical power and increase the standard errors. This paper provides a new model for arising the effect of missing data, which are considered also as correlated binary data, on the correlated binary variables. Depending on serial dependence, we formulate the model using Markov properties for the correlated missing data. The alternative quadratic exponential form are employed for the correlated binary variables. The logit functions are used for modeling the missing data. The vectorized generalized linear models have used with five cases of correlated missing data associated with covariates. The simulation study is investigated, using "bindata" and "VGAM" packages in R program, to indicate the effect of missing data on the regression model comparing with the model without missing data.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
30
THU: 28-12-2017 Hall[B] Oral - Sec02 ( 2 )
 04:15 : 04:30

STA - 3 EG Prof. Ahmed Abd Ellah ahmhamed@hotmail.com

115
New Applications to Evaluate the Prediction Intervals with Maple
Prof. A. H. Abd Ellah

 Al Baha University, Faculty of Science, Mathematics Department, Al Baha, P.O. Box.(1988), KSA.

ABSTRACT
In these paper we use new applications to evaluate prediction intervals. In this article, we study the problem of predicting future records (two-sample prediction) based on progressive type-II censoring with random removals, were the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds Prediction. Bayesian point prediction under symmetric and symmetric loss functions are discussed. The maximum likelihood (ML) prediction intervals using "plug-in" procedure for future records are derived. An example is discussed to illustrate the application of the results under this censoring scheme.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
31
THU: 28-12-2017 Hall[B] Oral - Sec02 ( 3 )
 04:30 : 04:45

STA - 5 NG Mr. Sagir Mahmud Abdullahi sagirmahmudabdullahi@gmail.com

115
Factors Contributing To Students’ Poor Performance in Mathematics at West African Examination Council (WAEC) and National Examination Council (NECO) in Bauchi State, Nigeria

 Federal Polytechnic Bauchi, Nigeria Federal Polytechnic Bauchi

ABSTRACT
This paper describes the prevailing academic scenarios of senior secondary schools in Bauchi state with special references to students’ poor performance in mathematics. The research instruments used to collect data was the questionnaire which had both close ended and open ended questions. Correlation and regression analyses were used and analyzed the data. Investigation of prevailing education scenario revealed wide variations of academic environment, managerial statuses of the school (school-based factors), teacher-related factors as well as students' related factors seem to be major factors influencing academic performance as they were found out to be positively correlated with students' poor performance. These include students' negative attitude toward mathematics, fear and anxiety of mathematics, inadequately qualified teachers, poor teaching methods, inadequate teaching materials, and inadequate supervision of teachers by the authority, overcrowded classes were some of the causes of poor performance in mathematics in the study area. The study also revealed that students attributed their failure mainly to lack of material resources, poor teaching methods, bad teacher behavior and poor grounding in the subject at lower levels as well as their fear of the subject. It is anticipated that the findings of this study will give curriculum developers new insights into emerging issues on performance and influence the Ministry of Education on policy formulation. The Ministry of Education should embark on serious in-service training for mathematics teachers, frequent supervision, and inspection by proper authorities.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
32
THU: 28-12-2017 Hall[B] Oral - Sec02 ( 4 )
 04:45 : 05:00

STA - 6 JO Dr. Hazem Al-Mofleh almof1hm@cmich.edu

115
The Normal- Generalized Hyperbolic Secant distribution: Properties and Applications
Hazem Al-Mofleh

 Tafila Technical University, Tafila 66110, Jordan

ABSTRACT
In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized hyperbolic secant distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Renyi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
33
THU: 28-12-2017 Hall[B] Oral - Sec02 ( 5 )
 05:00 : 05:15

STA - 8 EG Dr. Mahmoud Ragab mahmoud.ragab@bue.edu.eg

115
Sorting Processes : An Analysis with Different Sampling Strategies
Mahmoud Ragab

 Mathematics Department, Faculty of Science, Al Azhar University, Nasr City,11884 Cairo, Egypt

ABSTRACT
Sorting data is one of the most important problems that play an important rule in many applications in operations research and computer science. Many sorting algorithms are well studied but the problem is not to find a way or algorithm to sort elements, but to find an efficiently way to sort elements. The output is a stream of data in time. We are interested in this flow of data. For the performance of such algorithms, there has been little research on their stochastic behavior and mathematical properties. In this paper we study the mathematical behavior of some different versions sorting algorithms. We also discuss the corresponding running time using some different strategies.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
34
FRI: 29-12-2017 Hall[B] Oral - Sec05 ( 1 )
 08:45 : 09:00

STA - 9 IN Dr. Hemant Umap umaphemant@gmail.com

115
Fuzzy Inventory Model For Deteriorating Items
HEMANT UMAP

 Yashavantrao Chavan Institute of Science, Satara.(M.S.), India.

ABSTRACT
In this paper the total cost and optimum order quantity are obtained in fuzzy sense for deteriorating items and especially considering demand being dependent on selling price and frequency of advertisement. Function principle method is used for defuzzification. Also the median rule is applied to find the optimum Economic Order Quantity [EOQ] and shortage quantity. Solution procedure is illustrated by a numerical example. The sensitivity analysis of the optimum solution with respect to the changes in the different parameter values is also discussed.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
35
FRI: 29-12-2017 Hall[B] Oral - Sec05 ( 2 )
 09:00 : 09:15

STA - 11 EG Dr. Nourhan Rakha nourhankhalil266@yahoo.com

115
New classes of bivariate distributions including the bivariate normal distribution, with applications
H. M. Barakat , O. M. Khaled , N. Khalil. Rakha

 Dept. of Math. Faculty of Sci. Zagazig University, Zagazig, Egypt. Dept. of Math., Faculty of Sci. Port said University, Port Said, Egypt. Physics and Engineering Math. Dep., Faculty of Engineering, Port Said University, Port Said, Egypt.

ABSTRACT
In this paper we introduce a new method to add two shape parameters to any baseline bivariate distribution function (df) to get a more felixable family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's and possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some competitors important generalized families of bivariate df's via real data examples.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
36
FRI: 29-12-2017 Hall[B] Oral - Sec05 ( 3 )
 09:15 : 09:30

STA - 12 EG Dr. Ayman Abd-Elrahman ayman275@aun.edu.eg

115
Reliability Estimation under Type-II Censored Data from The Generalized Bilal Distribution: comparison between Bayesian and classical approaches
Ayman M. Abd-Elrahman

 Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt.

ABSTRACT
The main object of this article is the estimation of the unknown population parameters and reliability function for the generalized Bilal model under Type-II censored data. Both maximum likelihood and Bayesian estimates are considered. In the Bayesian framework, although we have discussed mainly the squared loss function, any other loss function can easily be considered. A Gibb’s sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute the Bayes estimates and also to construct their corresponding credible intervals with the help of two different importance sampling techniques. A simulation study is carried out to examine the accuracy of the resulting Bayesian estimators and compare them with the corresponding maximum likelihood estimates. Application to a real data set is considered for the sake of illustration.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
37
FRI: 29-12-2017 Hall[B] Oral - Sec05 ( 4 )
 09:30 : 09:45

STA - 13 JO Dr. Hazem Al-Mofleh almof1hm@cmich.edu

115
Type II Exponentiated Half Logistic Generated Family of Distributions with Applications
Hazem Al-Mofleh , M. Elgarhy , Ahmed Z. Afify

 Tafila Technical University, Tafila 66110, Jordan Department of Mathematical Statistics, Burraydah colleges, Qassim, KSA. Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Cairo, Egypt. Department of Statistics, Mathematics and Insurance, Benha University, Egypt.

ABSTRACT
A new family of distributions called type II exponentiated half logistic is introduced and studied. Four new special models are presented. Some mathematical properties of the new family are studied. Explicit expressions for the moments, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Parameter estimation of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
38
FRI: 29-12-2017 Hall[B] Oral - Sec05 ( 5 )
 09:45 : 10:00

115
Estimating the Modified-Weibull Parameters in Presence of Step-Stress Partially Accelerated Life Testing
Mohamed A. W. Mahmoud , Rashad M. EL-Sagheer , Amr M. Abou-Senna

 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt Mathematics Department, Faculty of Engineering, Shoubra, Benha University, Cairo, Egypt

ABSTRACT
Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of each item under normal condition follows the modified-Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are considered. The likelihood equations are to be solved numerically to obtain the maximum likelihood estimates. Based on normal approximation to the asymptotic distribution of maximum likelihood estimates, the approximate confidence intervals for the parameters are derived. It is difficult to get explicit form for Bayes estimates, so Markov chain Monte Carlo method is used to solve this problem, which gives us flexibility to construct the credible intervals the for the parameters. Lindley approximation is also being discussed to obtain Bayes estimators. Finally, an illustrative example and simulation studies are being considered.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
39
FRI: 29-12-2017 Hall[B] Oral - Sec09 ( 1 )
 04:00 : 04:15

STA - 17 EG Mr. islam elhusseiny islam_elhusseiny@yahoo.com

115
Concomitants of Order statistics and record values from FGM Type Bivariate-Generalized Exponential Distribution
H. M. Barakat , E. M. Nigm , M.A. Alawady , I. A. Husseiny

 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

ABSTRACT
We introduce the successive iterations in the original FGM type bivariate-generalized exponential distribution. Some distributional properties of concomitants of order s- tatistics as well as record values for this family are studied. Recurrence relations between single as well as product moments of concomitants are obtained.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
40
FRI: 29-12-2017 Hall[B] Oral - Sec09 ( 2 )
 04:15 : 04:30

STA - 19 EG Dr. Esraa Abo Zaid eabozaid31@yahoo.com

115
Asymptotic Distributions of Record Values under Exponential Normalization
H.M.Barakat , E.M.Nigm , E. O. Abo Zaid

 Professor of Mathematical Statistics Zagazig University Faculty of Science Mathematics Department Professor of Mathematical Statistics Zagazig University Faculty of Science Mathematics Department Assistant Professor -High Institute of Engineering and Technology Zagazig

ABSTRACT
In this article we study the limit distribution of the record values under non- linear normalization which have called as exponential norming. The corresponding limit laws are called as e-max stable laws. Moreover, we will study the domain of attraction criteria for these types of limit laws.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
41
FRI: 29-12-2017 Hall[B] Oral - Sec09 ( 3 )
 04:30 : 04:45

STA - 21 EG Prof. Ahmed Tarabia a_tarabia@yahoo.com

115
Alternative analysis of a fluid queue driven by Markovian queue
A.M.K Tarabia , Ali H.El Baz , Abdulaziz M. Darwiesh

 Mathematics Department-Faculty of Science-Damietta University-Egypt Mathematics Department-Faculty of Science-Damietta University-Egypt Mathematics Department-Faculty of Science-Damietta University-Egypt

ABSTRACT
In this paper, we consider a fluid queue with an infinite buffer capacity which is both filled and depleted by fluid at constant rats. These rats are uniquely determined by the number of customers in an M/M/1/N queue with constants arrival and service rates. An alternative approach to obtain analytical expression for the joint stationary distribution of the buffer level and the state of M/M/1/N queue is given. Through our approach we obtain the determinant of a tridiagonal matrix in terms of the roots of Chebychev's polynomial of second kind. Moreover, we illustrate the effectiveness of the derived formula through graphs and numerical discussion.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Mathematical Statistics.
42
FRI: 29-12-2017 Hall[B] Oral - Sec09 ( 4 )
 04:45 : 05:00

STA - 16 EG Mr. Atef Hashem dr_afh2010@yahoo.com

115
Inference on a New Distribution Under Progressive-Stress Accelerated Life Tests Based on Progressively Hybrid Censored Data with Binomial Removals
Saralees Nadarajah , Alaa H. Abdel-Hamid , Atef F. Hashem

 aSchool of Mathematics, University of Manchester, Manchester Faculty of Science, Beni-Suef University Faculty of Science, Beni-Suef University

ABSTRACT
A new distribution called geometric-Poisson-Rayleigh distribution is proposed based on failures of a parallel-series system. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other six distributions. The progressive-stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the new distribution. It is assumed that its scale parameter satisfies the inverse power law such that the stress is a non-linear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type-I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear-exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed and numerical computations are carried out to compare the performance of the implemented estimation methods
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
43
THU: 28-12-2017 Hall Sec Poster (01) ( 1 )
 01:15 : 02:45

NAM - 10 EG Assoc.Prof. Bothina El-sobky bothinaelsobky@yahoo.com

115
A penalty method with trust-region mechanism for nonlinear bilevel optimization problem
Bothina Elsobky , Yousria Abo-Elnaga

 Department of Mathematics, Faculty of Science, Alexandria University, Egypt. Department of basic science, Higher Technological Institute, Tenth of Ramadan City , Egypt

ABSTRACT
We present a penalty method with trust-region technique for nonlinear bilevel optimization problem in this paper. This method follows Dennis, El-Alem, and Williamson active set idea and penalty method to transform the nonlinear bilevel optimization problem to unconstrained optimization problem. This method maybe simpler than similar ideas and it does not need to compute a base of the null space. A trust-region technique is used to globalize the algorithm. Global convergence theorem is presented and applications to mathematical programs with equilibrium constraints are given.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
44
THU: 28-12-2017 Hall Sec Poster (01) ( 2 )
 01:15 : 02:45

NAM - 11 EG Assoc.Prof. Bothina El-sobky bothina_elsobky@alexu.edu.eg

115
Generation of Pareto optimal solutions for multi-objective optimization problems via a reduced interior-point algorithm
Bothina Elsobky , Yousria Abo-Elnaga

 Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Egypt. Department of basic science, Higher Technological Institute, Tenth of Ramadan City , Egypt

ABSTRACT
In this paper, a reduced interior-point algorithm is introduced to generate a Pareto optimal front for multi-objective constrained optimization (MOCP) problem. A weighted Tchebychev metric (WTM) approach is used together with achievement secularizing function approach to convert (MOCP) problem to a single-objective constrained optimization(SOCO) problem. An active-set technique is used together with a Coleman-Li scaling matrix to find the solution of (SOCO)problem. A decrease interior-point method is used to compute Newton’s step by solving a smaller dimension system. A Matlab implementation of the proposed algorithm was used to solve three cases and application. The results showed that the algorithm out perform some existing methods in literature. The results, by using our suggested approach to benchmark problems are promising when compared with well-known algorithms. Also, our outcomes recommend that our calculation may be superior relevant for comprehending real-world application problems.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
45
THU: 28-12-2017 Hall Sec Poster (01) ( 3 )
 01:15 : 02:45

NAM - 14 DZ Prof. HAIOUR MOHAMED haiourmohamed@gmail.com

115
L∞–error Estimate for an Approximation of asystem of Parabolic Variational Inequalities
HAIOUR MOHAMED , Salah Boulaaras , Mohamed Amine Bencheikh Le Hocine

 LANOS Laboratory, Department of Mathematics, Faculty of Sciences, Badji Mokhtar University, Annaba, Algeria Department of Mathematics, Colleague of Science and Arts, Al-Ras, Al-Qassim University, Kingdom Of Saudi Arabia Department of Mathematics and Computer Science, Tamanghesset University Center, Sersouf, Tamanghesset , Algeria;

ABSTRACT
In this paper, a system of parabolic quasi-variational inequalities relevant to the management of energy production with mixed boundary condition was considered where a quasi-optimal of error estimate on uniform norm was proved, by using theta scheme combined with Galerkin method. Furthermore, an asymptotic behavior result in the same norm was proved. Taking into consideration the discrete stability properties.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
46
THU: 28-12-2017 Hall[C] Oral - Sec03 ( 1 )
 04:00 : 04:15

NAM - 1 NG Mr. Kabiru Muhammad kabiru98@gmail.com

115
PERFORMANCE ANALYSIS OF TWO MODIFIED BROYDEN LIKE METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

 Department of Statistics, Kano State Polytechnic, Kano Nigeria. Department of Statistics, Kano State Polytechnic, Kano Nigeria Department of Statistics, Kano State Polytechnic, Kano Nigeria.

ABSTRACT
Abstract: In this paper an analysis on the performance of two modified Broyden method is presented: Broyden – like Method (BLM) and Trapezoidal Broyden Method (TBM) . Four test problems with standard initial points were used to compare the performance of the two methods in terms of CPU time and Number of Iterations. Numerical results have shown that there is little difference between the two methods in terms of Number of Iterations. Further analysis using performance indices has also shown that TBM is superior to BLM in terms of CPU time.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
47
THU: 28-12-2017 Hall[C] Oral - Sec03 ( 2 )
 04:15 : 04:30

NAM - 2 EG Dr. Tamer Kasem tamaero@yahoo.com

115
NOVEL WENO ALGORITHMS USING UNDIVIDED DIFFERENCES
Tamer Heshmat Mohamed Aly Kasem

 Cairo University, Faculty of Engineering

ABSTRACT
A new smoothness indicator (SI) for the high order weighted essentially non oscillatory (WENO) method is introduced. The new SI formula is based on undivided differences (UD), but they improve the original UD WENO scheme by keeping the formal order of accuracy. The new algorithm is tested and compared with the classical WENO algorithm based on total variations. The advantages of the new scheme are clarified.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
48
THU: 28-12-2017 Hall[C] Oral - Sec03 ( 3 )
 04:30 : 04:45

NAM - 3 EG Prof. Nasser Sweilam nsweilam@sci.cu.edu.eg

115
Comparative Studies for Solving the General Nonlinear Klein Gordon Model
Nasser Hassan Sweilam , Seham AL-Mekhlai , Anan O. Albalawi

 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt Department of Mathematics, Faculty of Education, Sana'a University, Sana'a, Yemen. Department of Mathematics, Faculty of Science, Shaqra University, Riyadh, Saudi Arabia

ABSTRACT
In this talk, Different numerical techniques are used to study the general nonlinear Klein-Gordon Model. Integer, Fractional, and variable order Klein-Gordon models are introduced. The nonstandard weighted average finite difference method is used to study the proposed model problems. The stability condition and the error estimates of the proposed method are presented. Comparative studies are done. The numerical results are compared with both the explicit standard finite difference method and the nonstandard finite difference method. It is found that the stability regions are bigger using the nonstandard weighted average finite difference method.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
49
THU: 28-12-2017 Hall[C] Oral - Sec03 ( 4 )
 04:45 : 05:00

NAM - 4 EG Prof. Waleed Abd-Elhameed walee_9@yahoo.com

115
Spectral tau Algorithm for Solving a Class of Fractional Optimal Control Problems via Jacobi Polynomials
Youssri H. Youssri , Waleed M. Abd-Elhameed

 Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt

ABSTRACT
This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
50
FRI: 29-12-2017 Hall[C] Oral - Sec06 ( 1 )
 08:45 : 09:00

NAM - 7 EG Dr. onefrist62@yahoo.com

115
الرياضه العدديه وتطورها العقلي لمواجه مشكله صعوبات التعلم الرياضي
احمد الرفاعي فتحي النحراوي

 وزاره الشئون الاجتماعيه

ABSTRACT
مشكله صعوبات التعلم يمكن لبعض المسائل في التحليل العددي أن تحل بشكل دقيق عن طريق خوارزمية ما ويسمى هذا النوع من الخوارزميات "طرقا مباشرة" : مثالها الاختصار الغاوسي لحل جمل المعادلات الخطية وطريقة التبسيط (طريقة سيمبلكس) في البرمجة الخطية. وهناك ظاهره كبيره في صعوبات التعلم الرياضيه
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
51
FRI: 29-12-2017 Hall[C] Oral - Sec06 ( 2 )
 09:00 : 09:15

NAM - 8 EG Ms. Hanaa Eldidamony hanaa.eldidamony@gmail.com

115
ADVANCED APPROACH FOR MULTI-OBJECTIVE FRACTIONAL PROGRAMMING PROBLEMS
E.A.Youness , N.A.El-Kholy , H.A.Eldidamony

 Faculty of Science, Tanta University, Tanta, Egypt Faculty of Science, Tanta University, Tanta, Egypt Higher Technological Institute, 10th of Ramadan city, Egypt

ABSTRACT
In this paper, a new approach for finding all efficient solutions for multi-objective fractional programming problems is presented. This approach based on solving auxiliary problems, one of them to obtain minimizing the numerator and the other maximizing the denominator. Illustrative examples are presented to clarify the obtained results.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
52
FRI: 29-12-2017 Hall[C] Oral - Sec06 ( 3 )
 09:15 : 09:30

NAM - 9 EG Dr. Samah El-kholy samahelkholy77@yahoo.com

115
Discrete spline Numerov method for solving Swift-Hohenberg equation
W. K. Zahra , S. M. Elkoly

 Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt and 2Department of Mathematics, Basic and Applied Sciences School, Egypt-Japan University of Science and Technology, New Borg El-Arab City, Alexandria, 21934, Egypt. Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh Univ., Egypt

ABSTRACT
Discrete spline function based method is developed to solve the time fractional Swift-Hohenberg equation in the sense of Riemann Liouville derivative. Via Fourier method, the developed method is unconditionally stable. Two schemes are acquired, these schemes are verified to be convergent of order two and four. Numerical results are demonstrated for various values of fractional Brownian as a function of time and also the standard motion to confirm the applicability and the theoretical results.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
53
FRI: 29-12-2017 Hall[C] Oral - Sec06 ( 4 )
 09:30 : 09:45

NAM - 12 EG Ms. Eman Fares eman.fares@pua.edu.eg

115
On the location of a constrained k-tree facility in a tree network with unreliable edges
Abdallah W . Aboutahoun , Eman Fares

 (ِِAssoc. Prof.) Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt (ِِِAssistant teacher)Department of Basic Science, Faculty of Engineering, Pharos University, Alexandria, Egypt

ABSTRACT
Given a tree network T with n vertices where each edge has an independent operational probability, we are interested in finding a subtree with at most k leaves and with a diameter of at most l which maximizes the expected number of nodes that are reachable from the selected subtree by operational paths. An efficient algorithm is presented for finding a (k, l) – tree core of T. Examples are provided to illustrate the algorithm.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.
54
FRI: 29-12-2017 Hall[C] Oral - Sec06 ( 5 )
 09:45 : 10:00

NAM - 13 EG Assoc.Prof. Abdallah Aboutahoun tahoun44@yahoo.com

115
Bicriteria Tree-Shaped Facility Location Problem on a Tree Network with Median and Center Objectives

 Associative Prof., Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

ABSTRACT
As an extension of classical facility location models in network, the problem of locating a tree-shaped facility in a tree network is considered. We consider the minisum criterion in which the sum of the distances from all the vertices of the tree network to the facility is minimized and the minimax criterion in which the distance from the facility to the farthest vertex in the tree network is minimized. Using single criterion does not capture all essential elements of a location problem. An efficient algorithm is developed which generate the set of all Pareto-optimal subtrees in the objective space. Examples are provided to illustrate the algorithm
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
55
FRI: 29-12-2017 Hall Sec Poster (02) ( 1 )
 01:15 : 02:45

115
A decision mathematical model for selection production strategy
Prof/ Gamal M. Nawara , Dr/ M. Mansour , Dr/ Ghada M. Abdel Salam

 Industrial Engineering Department,Zagazig University, Cairo, Egypt Industrial Engineering Department,Zagazig University, Cairo, Egypt Industrial Engineering Department,Zagazig University, Cairo, Egypt

ABSTRACT
Developing supply chain strategy plays an essential role to retain competition among companies. This paper investigates the decision about which items to make to stock and which ones to make to order based on a mathematical model minimize the difference between the costs of the two approaches. The production environment is characterized by multiple activities such as purchasing, manufacturing, subassembly, and finished assembly. Through some numerical experiments the effect of different demand quantitates, customer delivery time and capacity limit are identified. The analysis provides an insight into the relationship between the supply chain costing and the strategic decision making.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
56
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 4 )
 04:45 : 05:00

DSA - 2 EG Dr. Amira Salem amerasalem5@yahoo.com

115
Effects of Slip Velocity and Hall Currents on Peristaltic Transport of Bingham-Papanastasiou Fluid with Heat Transfer
Nabil T.M. Eldabe , Hamida M. Shawky , Amira S. Awaad

 Mathematics Department, Faculty of Education, Ain-Shams University. Department of Mathematics, Faculty of Science (Grils), AL- Azhar University. Department of Mathematics, Faculty of Science (Grils), AL- Azhar University.

ABSTRACT
In this work, we investigated the effects of slip boundary condition and Hall currents on peristaltic motion of a non-Newtonian fluid which is obeying Bingham-Papanastasiou model, with heat transfer taking into account the thermal radiation and heat generation, through an asymmetric channel. This phenomena is modeled mathematically by a system of governing equations which are continuity, momentum and heat equations. These equations are solved analytically under low Reynolds number condition and long wavelength approximation. The stream function and temperature distribution are obtained as functions of physical parameters of the problem. The effects of the parameters on these solutions are discussed numerically and illustrated graphically through a set of figures. It is found that the physical parameters played important roles to control the velocity and temperature distribution.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
57
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 5 )
 05:00 : 05:15

DSA - 3 EG Prof. Elmetwally Elabbasy emelabbasy@mans.edu.eg

115
On the Solutions of a System of Difference Equations
Elmetwally M. M. Elabbasy , Hamdy A. El-Metwally

 Math. Dept. Faculty of Science, Mansoura University Math. Dept. Faculty of Science, Mansoura University

ABSTRACT
In this paper, we investigate the dynamical behavior of the positive solutions of the following system of difference equations u_{n+1}=((au_{n})/(b+cv_{n-1}^{p})) ,v_{n+1}=((dv_{n})/(e+fw_{n-1}^{q})) ,w_{n+1}=((gw_{n})/(h+Iu_{n-1}^{r})) where the initial conditions u_{-i},v_{-i},w_{-i} (i=0,1,2,3) are non-negative real numbers and the parameters a,b,c,d,e,f,g,h,I,p,q,r, are positive real numbers, by extending some results in the literature.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
58
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 6 )
 05:15 : 05:30

DSA - 6 KE Mr. Titus Orwa torwa@strathmore.edu

115
Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria
Titus Okello Orwa , Rachel Waema Mbogo , Livingstone Luboobi

 Strathmore University Strathmore University Strathmore University

ABSTRACT
Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world’s population at risk of malaria infection. The infectious protozoan disease is endemic in tropical and subtropical regions, with an estimated 212 million new cases and 429,000 malaria-related deaths in 2015. An in-host mathematical model of malaria that describes the dynamics and interactions of malaria parasites with the host’s liver cells, the red blood cells and macrophages is reformulated. By a theoretical analysis, an in-host basic reproduction number R_0 is derived. The disease free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveal that the erythrocyte invasion rate β_r , the average number of merozoites released per bursting infected erythrocyte K and the proportion of merozoites that cause secondary invasions at the blood phase ζ, are the most influential parameters in determining the malaria infection outcomes. Numerical results show that intervention during malaria infection should focus on minimizing the density of and the rates of merozoite invasion on healthy erythrocytes at the blood stage.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
59
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 7 )
 05:30 : 05:45

DSA - 4 EG Prof. Hamdy El-Metwally eaash69@yahoo.com

115
DYNAMICS OF A NON-AUTONOMOUS DIFFERENCE EQUATION
Hamdy A. El-Metwally , Elmetwally M. M. Elabbasy , Amna Eshtiba

 Faculty of Science, Mansoura University Faculty of Science, Mansoura University Faculty of Education, Tripoli University, Libya

ABSTRACT
In this paper we investigate the boundedness, the periodicity character and the global behavior of the positive solutions of the difference equation x_{n+1}=a_{n}+((x_{n}^{p})/(x_{n-1}^{p})), n=0,1,..., where {a_{n}} is a sequence of nonnegative real numbers and the initial conditions x₋₁,x₀ are arbitrary positive real numbers.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Dynamical Systems and Applications.
60
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 8 )
 05:45 : 06:00

DSA - 5 KE Ms. Purity Ngina pngina@strathmore.edu

115
Modelling Optimal control of in-host HIV Dynamics using different control strategies
Purity Ngina , Dr. Rachel Waema , Prof. Livingstone S. Luboobi

 Strathmore University, Kenya Strathmore University, Kenya Strathmore University, Kenya

ABSTRACT
HIV is a major cause of deaths especially in Sub-Sahara Africa. In this paper an in-vivo deterministic model of differential equations is presented and analyzed for HIV dynamics. Optimal control theory is applied to investigate the key roles played by the various HIV treatment strategies. In particular, we wish to establish the optimal strategies for controlling the infection using three treatment regimes as the system control variables. We apply the Pontryagin’s maximum principle in characterizing the optimality control, which is then solved numerically by applying the Runge-Kutta forth order scheme. The numerical results indicate that an optimal controlled treatment strategy would ensure significant reduction in viral load and also in HIV transmission. It is also evident from the results that protease inhibitor plays a key role in virus suppression; this is not to underscore the benefits accrued when all the three drugs regimes are used in combinations.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
61
FRI: 29-12-2017 Hall Sec Poster (02) ( 1 )
 01:15 : 02:45

115
New Adaptive Method to Speed Up Training of Back Propagation Algorithm
Zahraa Elsayed Mohamed , Elsadek Hussien Ibrahim

 Zagazig University, Faculty of Science, Zagazig, Egypt High Institute of Engineering and Technology Al-Obour, Zagazig, Egypt

ABSTRACT
Using Back Propagation (BP) algorithm in training of multilayer feedforward networks is a very effective learning approach. It finds the best weights of Artificial Neural Network (ANN) by computing the weight change. There are many drawbacks of BP algorithm but the main problems are slow training and reaching local minima easily. Through the last years, a lot of algorithms were proposed to improve and modify the BP algorithm. Overcoming these problems requires adding new parameters as learning rate and momentum. In this research, a new adaptive BP algorithm is proposed by introducing a new function for adaptive learning rate and adaptive momentum which depends on the error gradient at every layer. In the learning samples, the simulation results mention the convergence action of proposed algorithm. Comparing with classic BP algorithm, the proposed algorithm gives better convergence rates and finds a good solution efficiently. Three popular benchmark classification problems are used to explain the improvement in convergence rates.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
62
FRI: 29-12-2017 Hall Sec Poster (02) ( 2 )
 01:15 : 02:45

CSC - 4 EG Mr. mahmoud atef ma7moud.aatef@gmail.com

115
Performance Analysis of Some Ad hoc Routing Protocols AODV, DSR and OLSR under Certain Conditions as Speed, Network Density and Packet Size
Zahraa E. Mohamed , Mahmoud Atef

 Faculty of Science, Mathematics Department, Zagazig University, Zagazig, Egypt High Institute for Engineering & Technology – Al-Obour, Cairo, Egypt

ABSTRACT
MANET is a collection of mobile nodes which are independent, self-organization and self-configuration where each node communicates with other nodes by a multi-hops manner and can move arbitrarily without any infrastructure or central control. This paper aims to analysis and compare the performance of three ad hoc routing protocols namely: AODV, DSR and OLSR vs. three different variables parameters using OPNET 17.5 simulations. Furthermore, this study focuses on comparing the main features of these protocols and evaluated the performance of these protocols. We studied the effect of nodes density, mobility speed and data packet size on the performance of these protocols based on the rate of file transfer protocol (FTP) with medium load traffic. The results in all simulations decided that the performance of OLSR protocol is better than both of them AODV and DSR in terms of end to end delay and data dropped, Whereas the performance AODV protocol is the best in terms of throughput and also DSR protocol has the lowest network load. As, we concluded that each protocol has different effect with respect to the environment conditions and considered metrics, including the average throughput, network load, end-to-end average delay, and data dropped. The results are shown that OLSR protocol can be more suitable choice in a large density networks compared to AODV and DSR.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
63
FRI: 29-12-2017 Hall Sec Poster (02) ( 3 )
 01:15 : 02:45

CSC - 7 EG Dr. Wael Fawaz wael_fawaz@hotmail.com

115
Implementation of the particle swarm optimization algorithm for solving the JSSP using parallel MATLAB
Wael M.F. Abdel-Rehim

 Faculty of computers and information, Suez University, Egypt.

ABSTRACT
In this study, we implement a Particle Swarm Optimization (PSO)-based method in parallel by using a parallel MATLAB with one, two, three, and four threads to solve the Job-Shop Scheduling Problem (JSSP). The resulting parallel PSO algorithm is evaluated by applying it to some job shop benchmark problems. The obtained results indicate that implementing PSO in parallel is an effective method for the JSSP that significantly increases the speedups especially for large-scale problems.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
64
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 1 )
 04:00 : 04:15

CSC - 2 EG Mr. Hammam Alshazly hammam.alshazly@sci.svu.edu.eg

115
Binary versus non-binary visual features representations: a comparative study
Hammam A. Alshazly , M. Hassaballah , Abdelmgeid Amin Ali

 Faculty of Science, South Valley University, Qena, Egypt Faculty of Computers and Information, South Valley University, Luxor, Egypt Faculty of Computers and Information, Minia University, El Minia, Egypt

ABSTRACT
Many computer vision applications rely on detecting a set of salient image features, then representing the neighborhood of each feature point by a feature vector for further processing. In this paper, we introduce a comparative study between the two main categories of representing the feature neighborhood: binary and non-binary. We highlight their differences under various image conditions using image datasets that have geometric and photometric transformations and different scene types. In addition, we illustrate when to pick a specific representation scheme based on the application needs or the distortions exist in the images.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
65
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 2 )
 04:15 : 04:30

115
Self-Stabilization Deterministic Cluster-Based Skip List Protocol for Peer to Peer Systems
Ahmed A. A. Gad-ElRab , T. A. A. Alzohairy , Khaled A. A. Khalf-Allah

 Department of Mathematics, Faculty of Science Al-Azhar University - Cairo, Egypt Department of Mathematics, Faculty of Science Al-Azhar University - Cairo, Egypt Department of Mathematics, Faculty of Science Al-Azhar University - Cairo, Egypt

ABSTRACT
Self-stabilization is one of the most important concepts used to build an overlay network which is a logical layer that used to manage and manipulate the information and data of a dynamic distributed systems as Peer-to-Peer (P2P) system. In P2P system the topology of the network is continuously changing by joining and leaving peers at any time. Stabilization ensures that P2P system is a persistently running system with a countless number of peers which communicate with each other and every peer has a partial view of the network. In this paper, the algorithms of Deterministic Cluster-Based Skip List protocol for dynamic distributed system (CBSL) stability will be analyzed and proved by using self-stabilization methods such as linearization, correctness and connectivity, and the ability to extend CBSL to a ring
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Computer Science.
66
FRI: 29-12-2017 Hall[C] Oral - Sec10 ( 3 )
 04:30 : 04:45

CSC - 5 EG Ms. Reda Mohammed reda.mohamed@sci.svu.edu.eg

115
Predicting and Analysis of Students' Performance Using data mining Techniques
Reda Mohammed , Nahla F. Omran , Abdelmgeid A. Ali

 Faculty of Science, South Valley University, Qena, Egypt Faculty of Science, South Valley University, Qena, Egypt Faculty of Computers and Information, Minia University, Al Minia, Egypt

ABSTRACT
Educational database holds on massive amount of data and it is increasing rapidly. Data mining provides effective techniques for discovering useful knowledge and pattern from students' data. The discovered patterns can be used to understand many problems in the educational field. This paper proposes a framework to predict the performance of first year bachelor’s students in computer science course. Decision Tree, Naïve Bayes, and Multilayer Perceptron classification methods are applied to the students’ data using the Weka Data Mining tool to produce the best prediction model of the students’ academic performance. We conduct experiments that detect the best model among the used techniques and compute models' accuracy. The extracted knowledge from prediction model will be utilized to recognize and profile the student to decide the students' level of success in the first semester.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
67
FRI: 29-12-2017 Hall[D] Oral - Sec07 ( 1 )
 08:45 : 09:00

115

 Damietta University

ABSTRACT
The purpose of this paper is to extend the notations of the compatibility and orthogonality of tripotents in a Jordan triple system to that of quadripotents in a Jordan quadruple system. We provide the necessary and sufficient condition for the compatibility of quadripotents in a Jordan quadruple system. Moreover, we refine the Peirce decomposition of Jordan quadruple systems to be with respect to a system of orthogonal quadripotents and get the multiplication rules of the Peirce spaces. We also study the relation between minimal and primitive quadripotents in a Jordan quadruple system. Finally, we show that from any Jordan quadruple system with a quadripotent, we can define a Jordan algebra.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
68
FRI: 29-12-2017 Hall[D] Oral - Sec07 ( 2 )
 09:00 : 09:15

ALG - 4 EG Dr. wajih ashraf syedwajihashraf@gmail.com

115
EPIMORPHICALLY PRESERVED HETEROTYPICAL SEMIGROUP IDENTITIES
WAJIH ASHRAF

 ALIGARH MUSLIM UNIVERSITY, INDIA

ABSTRACT
It is shown that a particular classes of heterotypical semigroup identities whose both sides contain repeated variables and are preserved under epis in conjunction with all seminormal identities using Isbell's Zigzag Theorem.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
69
FRI: 29-12-2017 Hall[D] Oral - Sec07 ( 3 )
 09:15 : 09:30

ALG - 5 EG Prof. Abdelrahman Heliel Heliel9@yahoo.com

115
Finite groups with certain kind of subgroups weakly c-supplemented

 Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt

ABSTRACT
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hg ≤ H for every g belongs to G. A subgroup H of G is called weakly c-supplemented in G if G has a subgroup K such that G = HK and H∩K is an H-subgroup in G. In this talk, we investigate the structure of finite groups by means of weakly c-supplemented subgroups. Some recent results about supersolvability of finite groups are generalized to a saturated formation containing the class of all supersolvable groups.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
70
FRI: 29-12-2017 Hall[D] Oral - Sec07 ( 4 )
 09:30 : 09:45

ALG - 5 EG Assoc.Prof. Emam Emam eg_emom@yahoo.com

115
An Operation on Intuitionistic Fuzzy Matrices
E.G.Emam

 Department of Mathematics,Faculty of Science, Zagazig University

ABSTRACT
In this paper, we define an operation on the intuitionistic fuzzy matrices called the Gödel implication operator as an extension to the definition of this operator in the case of ordinary fuzzy matrices due to Sanchez and Hashimoto. Using this operator, we prove several important results for intuitionistic fuzzy matrices. Particularly, some properties concerning pre-orders, sub-inverses, and regularity . We concentrate our discussion on the reflexive and transitive matrices. This studying enables us to give a largest sub-inverse and a largest generalized inverse for a reflexive and transitive intuitionistic fuzzy matrix. Also, we obtain an idempotent intuitionistic fuzzy matrix from any given one .
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
71
FRI: 29-12-2017 Hall[D] Oral - Sec07 ( 5 )
 09:45 : 10:00

ALG - 6 EG Dr. Susan El-Deken sfdeken@hotmail.com

115
EXTENSIONS OF HOMOGENEOUS SEMILOCAL RINGS I
SUSAN F. EL-DEKEN

 Department of Mathematics Faculty of Science, Helwan University Ain Helwan, 11790, Helwan, Egypt

ABSTRACT
A ring R with Jacobson radical J(R) is a homogeneous semilocal ring if R/J(R) is simple artinian. In this paper, we study the transfer of the property of being homogeneous semilocal from a ring R to the formal power series ring R[[x]], the skew formal power series ring R[[x, α]] and the Hurwitz series ring HR. The results of the paper generalize those proved for commutative local rings. We also consider finite centralizing extensions proving that if the ring of matrices M n (R) is a homogeneous semilocal ring, then so is R. More generally, if e is an idempotent of a homogeneous semilocal ring S, then eSe is homogeneous semilocal.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
72
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 1 )
 04:00 : 04:15

ALG - 7 EG Ms. Asmaa Naser asmaanaser99@yahoo.com

115
Non-commutative Unique Factorization Rings with Zero Divisors
M. H. Fahmy , A. M. Hassanian , A. Naser

 Math. Dept., Fac. of Sci., Al-Azhar Univ., Nasr city (11884), Cairo, Egypt. Math. Dept., Fac. of Sci., Al-Azhar Univ., Nasr city (11884), Cairo, Egypt. Math. Dept., Fac. of Women, Ain Shams Univ., Nasr city (Fax:24157804), Cairo, Egypt.

ABSTRACT
It was shown by Galovich that if R is commutative UFR with identity, then the set of non-units in R is nilpotent, and R is local. In this paper we extend Galovich's results in non-commutative UFR.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
73
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 2 )
 04:15 : 04:30

ALG - 8 EG Ms. sarah Kamal El-Din sarakamal81@yahoo.com

115
Mohamed H. Fahmy , Sabria Atallah , Abdel-Rahman Hassanein , Sarah Kamal El-Din

 Prof. of Math. Math. Dept., Faculty of Science, Al-Azhar University, Cairo, Egypt. Prof. of Math. Math. Dept., Faculty of Science(Girls), Al-Azhar University, Cairo, Egypt. Prof. of Math. Math. Dept., Faculty of Science, Al-Azhar University, Cairo, Egypt. Ass.teacher. of Math. Math. Dept., Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt.

ABSTRACT
This paper is two folded. One consider a well known series of generalization of domains such as reduced, symmetric, reversible,...,dedekind finite. The other consider the extension of those rings by their radicals, concentrating on prime and Jacobson radicals. We study their structure and deduce by examples that such rings are not related.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
74
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 3 )
 04:30 : 04:45

ALG - 9 EG Assoc.Prof. Mohammed Abuelhassan Saleem abuelhassan@yahoo.com

115
Weierstrass points of order one on smooth septic curves
Mohammed A. Saleem , Waleed Khaled Elshareef

 Sohag University, Egypt. Sohag University, Egypt.

ABSTRACT
Weierstrass points on an algebraic curve C of genus g≥2, as well as their generalizations to higher orders, are of fundamental importance in analyzing the properties of C. For example, one can use them to construct projective embeddings for moduli spaces of curves. Moreover, they form an important invariant of a curve which is of particular use for the study of automorphisms. In [ ], the authors studied the geomtric classifications of the Weierstrass points of ordre on smooth projective plane septic curves but this classification was not complete. The goal of this paper is to find all the candidates for the 1-Weierstrasss points on smooth projective plane septic curves and to investigate the geometry of such points. The paper contains a variety of examples that illustrate and enrich the subject.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
75
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 4 )
 04:45 : 05:00

ALG - 10 EG Dr. Ahmed Ageeb ahmadageb@yahoo.com

115
EXTENSIONS OF VON NEUMANN LOCAL RINGS
SUSAN F. EL-DEKEN , A. AGEEB

 Department of Mathematics, Faculty of Science Helwan University, Ain Helwan, 11790, Helwan, Cairo, Egypt Department of Mathematics, Faculty of Science Al-Azhar University, Nasr City, 11884, Cairo, Egypt

ABSTRACT
This paper introduces an extension of von Neumann local rings (called EVNL-ring). Among other results, we show that Zn is an EVNL-ring for all integers n > 1; the direct product of EVNL-rings is an EVNL-ring and the class of EVNL-rings coincides with the class of C-rings. Also, we study the case when a formal power series ring is an EVNL-ring.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
76
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 5 )
 05:00 : 05:15

ALG - 11 EG Ms. Zeinab Mohammed Ahmed zeinabmahran88@yahoo.com

115
An algorithm for the shortest distance path for a graph
H. El- zohny , Afaf Abd El kadr , Z. Mohammed

 Al Azhar university Al Azhar university Al Azhar university

ABSTRACT
In this article we determine the shortest distance path algorithm between any two distinct vertices for a given graph.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
77
FRI: 29-12-2017 Hall[D] Oral - Sec11 ( 6 )
 05:15 : 05:30

ALG - 13 EG Ms. Bsmaa EL gamudi basmagamudi@gmail.com

115
Rigid rings with involution
Usama A. Aburawash , Bsmaa M. ELgamudi , Muna E. AbdUlhafed

 Faculty of Science-Alexandria University Faculty of Science-Alexandria University Faculty of Science-Alexandria University

ABSTRACT
Working in the category of rings with involution, we introduce the property of *-rigid and α-*-rigid for *-rings. These new *-rings generalize that of rigid and α-rigid *-rings, respectively. We show also that α-rigid *-rings are α-*-rigid, α-*-reversible and α-*-Armendariz *-rings. Moreover, we give sufficient conditions for α-*-rigid, α-*-reversible and α-*-Armendariz *-rings to be α-rigid. Furthermore, We show that the properties of *-rigid, α-*-rigid, α-*-reversible and α-*-Armendariz are extended to its polynomial *-ring R[x], Laurent polynomial *-ring R[x, x-1], localization (S-1)R of R to S, Ore *-ring Q and Dorroh extension D(R,Z). Finally, we show that if a *-ring R is α-*-Armendariz then the skew polynomial R[x,α] is *-Baer (*-reversible) if and only if R is so.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Algebra and applications.
78
SAT: 30-12-2017 Hall Sec Poster (03) ( 1 )
 01:15 : 02:45

ALG - 1 EG Mr. Usama Wadie pasotier@gmail.com

115
Usama's Method for solving linear systems of algebraic equations.

 an engineer of computer and automatic control-faculty of engineering ,Ain_shams university.

ABSTRACT
This document gives My new method for solving linear systems of algebraic equations. I gave the name Usama's method for My Method where I introduced it in the last conference (ICMTD 2015). Usama's method contains equations and rules. Usama's method is more easy than Cramer's rule, where it produces an explicit formula for the solution ,but with less arithmatic operations. and also Usama's method is more easy than Gaussian elimination for producing the solution for the unique solution's linear systems, but without much division operations,where there is only one division operation.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
79
FRI: 29-12-2017 Hall Sec Poster (02) ( 1 )
 01:15 : 02:45

TGA - 3 EG Mr. Abdelmohaymen Mohammed Abdulaziz Fawaz Mr.abdelmohymen_fawaz@yahoo.com

115
A research on the fifth case of the triangulation cases
Abdelmohaymen Mohammed Abdulaziz Fawaz

 Mathematics teacher at Al-Azhar Al-Sharif

ABSTRACT
This research aims to conclude a fifth case of the cases of congruent triangles, the case of the equal triangles in the area. As we know, if the triangles are identical, then they are equal in space and vice versa is not always true. So this research is focused on the situation in which the equal triangles in the area are to be congruent and the required conditions, for them, to get matched. After the study mentioned in the research, and with the availability of some elements, I was able to get to the text of the fifth case of the cases of congruent triangles which states: “The two equal triangles correspond to the area if a rib and an angle match in one of the triangles with their counterparts in the other triangle”
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
80
SAT: 30-12-2017 Hall[A] Oral - Sec12 ( 1 )
 08:45 : 09:00

TGA - 1 EG Dr. M Elsafty elsafty010@yahoo.co.uk

115
Attributes priority arrangement of cancellations in the life insurance using rough set
M. A. Elsafty , H. M. Elkhawaga , A.M.Kozae

 Department of Mathematics and Statistics, Faculty of Science, Taif University Department of Statistics and Mathematics and Insurance, Tanta University, Egypt Department of Mathematics, Faculty of Science, Tanta University, Egypt

ABSTRACT
In this paper, we present a new method to rough set attributes priority arrangement of cancellations in the life insurance, the number of canceled documents on the rise plus they oscillatory also in rates of cancellations in constant fluctuation which requires searching in the problem of cancellations of these documents where, these cancellations affect negatively the results of the Egyptian life insurance operations of insurance companies. This paper also aims to identify the most important variables that affect the rates of cancellations and so as to reach solutions that lead to reducing the number of canceled documents by using the Rough Model. The research also aims to use the Rough model to identify the determinants of cancellations in the life insurance of the Egyptian insurance market, so as to reach solutions that lead to reducing the number of canceled policies and find solutions to them. Our findings proved that the most important factors that affect the document cancellation in the Egyptian life insurance policies are; policy premiums, insurance period and age of policyholders respectively.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
81
SAT: 30-12-2017 Hall[A] Oral - Sec12 ( 2 )
 09:00 : 09:15

TGA - 2 EG Prof. Fathi Khedr khedrfathi@gmail.com

115
Results on generalized fuzzy soft topological spaces
F.H. Khedr , S.A. Abd El-Baki , M.S. Malfi

 Assiut University Assiut University Assiut University

ABSTRACT
In this manuscript, the concept of a generalized fuzzy soft point is introduced and some of its basic properties are studied. Also, the concepts of a generalized fuzzy soft base (subbase) and a generalized fuzzy soft subspace are introduced and some important theorems are established. Finally, we study the relationship between fuzzy soft set, intuitionistic fuzzy soft set, generalized fuzzy soft set and generalized intuitionistic fuzzy soft set are investigated.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
82
SAT: 30-12-2017 Hall[A] Oral - Sec12 ( 3 )
 09:15 : 09:30

TGA - 4 EG Assoc.Prof. Heba Mustafa dr_heba_ibrahim@yahoo.com

115
Soft rough approximation operators via ideal with application in decision making
Heba Ibrahim Mustafa

 Faculity of science Zagazig University

ABSTRACT
Theories of soft sets and rough sets are two different approaches to vagueness. They can be combined to form a powerful mathematical tool for dealing uncertain problems. Soft rough set introduced by Feng[7] is the connection between these approaches and it is the generalization of rough set with respect to the soft approximation space. This paper extend soft rough approximation model by defining new soft rough approximation operators via ideal. When the ideal is the least ideal of $\wp(U)$, these two approximations coincide. We present the essential properties of new opertors via ideal and supported by illustrative examples. The notion of soft rough equal relations via ideal is proposed and related examples are examined. We also show that rough set via ideal [26] can be viewed as a special case of soft rough set via ideal, and these two notions will coincide provided that the underlaying soft set is a partition soft set. We obtain the structure of soft rough set via ideal, gives the structure of topologies induced by soft set and an ideal. Moreover, an example containing a comparative analysis between rough sets via ideal and soft rough sets via ideal is given. We show that soft rough approximation via ideal could provide a better approximation than rough set via ideal. Finally application of data reduction are done and an algorithm of multi-attribute decision making based on soft rough sets via ideal is given.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
83
SAT: 30-12-2017 Hall[A] Oral - Sec12 ( 4 )
 09:30 : 09:45

TGA - 5 EG Assoc.Prof. Fawsia Sleim fsleim@yahoo.com

115
A multi-set function
Fawsia Sleim

 Faculity of science Zagazig university

ABSTRACT
In this paper, we study the cartesian product of two multi-sets and some of its properties . Also we study the multi-set function and some of its properties and define the image and the inverse image of multi- sets and study of some properties .We study the multi-order relation ,multi-increasing ( decreasing ) function ,and the multi-topological ordered spaces and some of m - separation axioms of multi-topological spaces
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
84
SAT: 30-12-2017 Hall[A] Oral - Sec12 ( 5 )
 09:45 : 10:00

TGA - 6 EG Assoc.Prof. Heba Mustafa dr_heba_ibrahim@yahoo.com

115
On modified Soft rough sets on a complete atomic Boolean lattice
Heba

 Zagazig University

ABSTRACT
Soft set theory and rough set theory are treated as mathematical approaches to deal with uncertainty. They are combined together by F.Feng et al. In[ ], we introduce the notion of soft rough sets on a complete atomic Boolean lattice as a generalization of soft rough sets. In this paper, we strengthen the concept of soft rough on a complete atomic Boolean lattice by defining the concept of MSR sets on a complete atomic Boolean lattice. In this model, some properties which were not satisfied in soft rough sets on a complete atomic Boolean lattice can be proved. Finally, the notion of lower and upper MSR-approximations of soft sets on a complete atomic Boolean lattice is studied.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
85
SAT: 30-12-2017 Hall[A] Oral - Sec15 ( 1 )
 04:00 : 04:15

TGA - 7 EG Assoc.Prof. Fawsia Sleim fsleim@yahoo.com

115
SMOOTH HESITANT FUZZY TOPOLOGICAL SPACES
Fawsia

 Zagazig university

ABSTRACT
In this paper, we define the basic concepts of hesitant fuzzy sets and smooth hesitant fuzzy topologies in $\hat{S}$ostak sense. We study and investigate some properties of smooth hesitant fuzzy topological spaces. Moreover, we introduce the concepts of smooth hesitant closure and smooth hesitant interior of a fuzzy hesitant set and obtain some of their structural properties.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
86
SAT: 30-12-2017 Hall[A] Oral - Sec15 ( 2 )
 04:15 : 04:30

TGA - 8 EG Dr. Abd El Fattah El Atik aelatik55@yahoo.com

115
On nano pre-I-open sets and a decomposition of nano I-continuity
Abd El Fattah A. El Atik , Arafa A. Nasef

 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt Department of Physics and Engineering Mathematics, Faculty of Engineering Kafrelsheikh University, Egypt.

ABSTRACT
In this paper, we introduce and study the notion of nano pre-I-open sets which is properly placed between nano openness and nano preopenness regardless the nano topological ideal. Also, we show that the class of near pre-I-open sets is properly places between the classes of nano I –open and nano preopen sets. We give a decomposition of nano I-continuity by proving that a function f(X,τ,I)→(Y,σ) is nano I-continuous if and only if it is nano I-continuous and nano *-I-continuous .
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
87
SAT: 30-12-2017 Hall[A] Oral - Sec15 ( 3 )
 04:30 : 04:45

TGA - 9 EG Mr. mohammed atef matef1993@yahoo.com

115
New Types of separation axioms on Graphs
Abd El Fattah A. El Atik , Mohammed atef

 Department of mathematics, Faculty of Science, Tanta University. Department of mathematics, Faculty of Science, Menoufia University.

ABSTRACT
The focus of this article is to define a new definition of the neighborhood which is built on the choice of the distance between two vertices. A comparison between these types of results from a new formed topologies and neighborhoods is discussed. Through the edges between vertices in any graph, we introduce a new class of separation axioms called graph separation axioms. Also, we study the connections between these graph separation axioms.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
88
SAT: 30-12-2017 Hall[A] Oral - Sec15 ( 4 )
 04:45 : 05:00

TGA - 10 EG Mr. haytham ashraf haytham.ali88@yahoo.com

115
Magnetic curves of spherical images in Euclidean space
H. S. Abdel-Aziz , M. Khalifa Saad , Haytham. A. Ali

 Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt. Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt. Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt.

ABSTRACT
In the theory of curves, a magnetic field generates a magnetic flow whose trajectories are curves, called magnetic curves. In the present paper, magnetic curves which corresponding to killing magnetic fields of spherical indicatrices for a regular curve in Euclidean 3-space are obtained. These curves are magnetic curves of the tangent, principal normal and binormal spherical indicatrices. Especially, for the tangent indicatrix of a regular curve, TT , NT and BT -magnetic curves are characterized. Furtheremore, some theorems and important results are given. Finally, we introduce an example to illustrate our main results with figures.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Topology & Geometry and Applications
89
SAT: 30-12-2017 Hall[A] Oral - Sec15 ( 5 )
 05:00 : 05:15

TGA - 11 EG Dr. Salah Ali salahelgendi@yahoo.com

115
Linear one form deformation of sprays
Salah Gomma Ahmed Ali Elgendi

 Faculty of Science - Benha University

ABSTRACT
In this paper, the linear one form deformation of a flat spray is investigated. The metrizability of the deformation spray is characterized. New projectively flat Reimannain metrics are obtained. These new metrics are not, generally, isometric to the Klein metric via affine transformations. New Finsler solutions for Hilbert's fourth problem are constructed. Various examples are studied.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
90
SAT: 30-12-2017 Hall[B] Oral - Sec13 ( 1 )
 08:45 : 09:00

FUA - 1 EG Dr. Mohaned Abdalla m.abdallah@sci.svu.edu.eg

115
Operational formulae of the generalized hypergeometric matrix functions and related matrix polynomials
M. Abdalla , H. Abd-Elmageedb , M. Abul-Ez

 Dept. of Math., Faculty of Science, South Valley University, Qena 83523, Egypt. Dept. of Math., Faculty of Science, South Valley University, Qena 83523, Egypt. Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

ABSTRACT
The aim of this article is to present an overview of the modern de- velopments around the theme of multivariable hypergeometric matrix functions (MHMFs). Operator representations of multivariable hy- pergeometric functions and certain classes of orthogonal matrix poly- nomials are established here by a new technique.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
91
SAT: 30-12-2017 Hall[B] Oral - Sec13 ( 2 )
 09:00 : 09:15

FUA - 2 EG Dr. Mohaned Abdalla m.abdallah@sci.svu.edu.eg

115
On the matrix versions of Srivastava's triple hypergeometric functions
M. Abdalla

 Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

ABSTRACT
This paper deals with the study of the Srivastava's triple hypergeometric matrix functions. The convergent properties, an integral representation of these functions and contiguous function relations are obtained. Some results coming from operating the differential operator on Srivastava's triple hypergeometric matrix functions are established. Moreover a solution of certain partial differential equation are given.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
92
SAT: 30-12-2017 Hall[B] Oral - Sec13 ( 3 )
 09:15 : 09:30

FUA - 3 EG Dr. Mohaned Abdalla m.abdallah@sci.svu.edu.eg

115
Some results on Appell hypergeometric matrix functions
H. ABD-ELMAGEED , M. ABUL-EZ , Z. KISHKA , A. ABDEL RADY

 Department of Mathematics Faculty of Science South Valley University Qena 83523 Egypt Department of Mathematics Faculty of Science Sohag University Sohag 82524 Egypt Department of Mathematics Faculty of Science Sohag University Sohag 82524 Egypt Department of Mathematics Faculty of Science South Valley University Qena 83523 Egypt

ABSTRACT
In this paper we have established result for the Appell's hypergeometric matrix functions. An integral representation of these functions, generating functions and reduction formulas are derived here. Furthermore, certain relations are obtained by acting a diﬀerential operator to Appell matrix functions arguments have also been discussed.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
93
SAT: 30-12-2017 Hall[B] Oral - Sec13 ( 4 )
 09:30 : 09:45

FUA - 4 EG Dr. Sahar Mohamed Ali Abou Bakr saharm_ali@yahoo.com

115
FIXED POINT AND CONVERGENCE THEOREM FOR GENERALIZED ϕ WEAK CONTRACTIONS AND {a; b; c; r} GENERALIZED CYCLIC CONTRACTIONS IN QUASI METRIC SPACES
Sahar Mohamed Ali Abou Bakr

 Ain Shams University, Faculty of Science, Department of Mathematics, Cairo, Egypt.

ABSTRACT
We prove the existence of only one common fixed point of two mappings, in particular; proves the existence of unique fixed point of some generalized contraction, introduces new type of {a, b, c; r} generalized cyclic contraction, proves the existence of unique fixed point of such mappings; all are defined on complete quasi metric spaces, and then establishes a convergence theorem for a sequence of fixed points of a sequence of generalized cyclic contractions to the unique fixed point of a given generalized cyclic contraction S. This research extends and generalizes results previously proved.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
94
SAT: 30-12-2017 Hall Sec Poster (03) ( 1 )
 01:15 : 02:45

FUA - 5 DZ Dr. Hakima BOUHADJERA b_hakima2000@yahoo.fr

115
MORE GENERAL COMMON FIXED POINT THEOREMS UNDER A NEW CONCEPT

 Laboratory of Applied Mathematics Badji Mokhtar-Annaba University P.O. Box 12, 23000 Annaba, Algeria

ABSTRACT
A general common fixed point theorem for two pairs of weakly subsequentially continuous mappings (recently introduced) satisfying a significant estimated implicit function is proved. An extension of this results thereby obtained. Our results assert the existence and uniqueness of common fi xed points in several cases.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
95
SAT: 30-12-2017 Hall Sec Poster (03) ( 2 )
 01:15 : 02:45

FUA - 9 EG Mr. Dhyaa Abdalhassan Mohan dhyaa.mohan79@gmail.com

115
Some Properties of Certain Subclasses of Analytic Functions Defined by using An Integral Operator
A. H. Hassan , D. A. Mohan

 Faculty of Science, Zagazig University, Zagazig 44519, Egypt Faculty of Science, Zagazig University, Zagazig 44519, Egypt

ABSTRACT
In this paper, by using the subordination principle we introduce and study new subclasses of analytic functions with negative coefficients defined on the open unit disk. We obtain numerous sharp results including (for example) coefficient estimates, distortion theorem, radii of starlikeness and convexity. Moreover, we deduce some results according to the modified Hadamard product of functions belonging to these subclasses.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
96
SAT: 30-12-2017 Hall Sec Poster (03) ( 3 )
 01:15 : 02:45

FUA - 10 EG Dr. Taha Yassen taha_hmour@yahoo.com

115
Quaternion-Valued Functions and Lacunary Series Expansions in Hyperholomorphic $F^{\alpha}_{G}(p,q,s)$ Spaces
Mohamed Abdelrahman Ahmed , Alaa Kamal Mohamed , Taha Ibrahim Yassen Moursy

 Professor of Mathematics, Faculty of Science - Assiut University- Egypt Port Said University, Faculty of Science, Department of Mathematics,Port Said, Egypt Port Said University, Faculty of Science, Department of Mathematics,Port Said, Egypt

ABSTRACT
The purpose of this paper is to define a new class of hyperholomorphic functions, the so called $F^{\alpha}_{G}(p,q,s)$ Spaces. For this class we obtain characterizations by ${\mathcal{B}}^{\alpha}$ spaces. Moreover, we characterize the hyperholomorphic $F^{\alpha}_{G}(p,q,s)$ functions by the coefficients of certain lacunary series expansions in Clifford analysis.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
97
SAT: 30-12-2017 Hall Sec Poster (03) ( 4 )
 01:15 : 02:45

FUA - 12 EG Dr. Ahmed M. Zidan zidan.math90@azhar.edu.eg

115
Fixed Point Theorems in Weak Quasi Partial Metric Spaces and it's Application
A. M. Zidan , M. A. Barakat

 Department of Mathematics, Faculty of Science, Al-Azhar University, Assuit branch, Egypt. Department of Mathematics, Faculty of Science, Al-Azhar University, Assuit branch, Egypt.

ABSTRACT
We present a New generalized fixed point theorems in weak quasi partial metric spaces for cyclic compatabl contraction . Our result extend some known results duo to Barakat et.al. [1]. Also, in order to illustrate our results, we present the study about the existence and uniqueness of solutions of the functional equation.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
98
SAT: 30-12-2017 Hall[B] Oral - Sec16 ( 1 )
 04:00 : 04:15

115
A NEW GENERALIZED S-ALGORITHM VIA ADMISSIBLE APPROACH TO COMMON FIXED POINTS OF GENERAL-TYPE CONTRACTION MAPPINGS
Ali Mohamed Saddeek , Sayed Attia Ahmed

 Department of Mathematics, Faculty of Science, Assiut University, Assiut , Egypt Department of Mathematics, Faculty of Science, Assiut University, Assiut , Egypt,,,Umm Al Qura University, Jamoum University College, Makka, Saudi Arabia

ABSTRACT
In this paper, a new generalized S-algorithm in terms of admissible and generalized admissible mappings for approximating common fixed points of three mappings satisfying general contraction type conditions is introduced and its strong convergence is proved in uniformly convex Banach spaces. The results improve and generalize the main results of several authors.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
99
SAT: 30-12-2017 Hall[B] Oral - Sec16 ( 2 )
 04:15 : 04:30

FUA - 7 EG Dr. Alaa Hassan alaahassan@zu.edu.eg

115
A Novel Subclasses of Bi-Univalent Analytic Functions Defined by Using Q-Calculus
A. H. Hassan

 Department of Mathematics, Faculty of Science, Zagazig University

ABSTRACT
In this paper, by using the q-derivative we introduce certain generalized subclasses of normalized (f(0)=f'(0)-1=0) bi-univalent analytic functions. For functions belonging to the subclass under investigation, we ﬁnd estimates on the Maclaurin coeffcients |a_2| and |a_3|. Some earlier results are improved and some special cases are pointed out.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
100
SAT: 30-12-2017 Hall[B] Oral - Sec16 ( 3 )
 04:30 : 04:45

FUA - 11 EG Dr. Alaa Hassan alaahassan@zu.edu.eg

115
Further Properties of Certain Class of Analytic Functions Associated with Bessel-Type Operator
A. H. Hassan

 Faculty of Science, Zagazig University

ABSTRACT
In this paper we investigate some subordination properties of certain linear operator associated with the well-known Bessel functions. Also, we investigated some estimates and sufficient starlike conditions of certain subclass of univalent functions defined in the unit disc.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Functional Analysis
101
SAT: 30-12-2017 Hall[B] Oral - Sec16 ( 4 )
 04:45 : 05:00

FUA - 12 EG Dr. S. Al-Tamemy al.tamemy505@yahoo.com

115
Second Order Optimality Conditions For Semilinear Elliptic Optimal Control Problem Infinite Order With Pointwise Mixed Control –State Constraints
Somiah Elzahaby , S. Al-Tamemy

 Al-Azhar University[Girls Branch], Faculty of Science, Mathematics Dept. Al-Azhar University[Girls Branch], Faculty of Science, Mathematics Dept.

ABSTRACT
In this paper a semiliner elliptic optimal control problem of infinite order with mixed control – state constraints are studied. The existence of regular Lagrange multipliers, first – order necessary and Second order sufficient conditions are obtained.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
102
SAT: 30-12-2017 Hall[C] Oral - Sec14 ( 1 )
 08:45 : 09:00

DEA - 2 NG Mr. Abdurrahman Abdulhamid farkeminjibir@gmail.com

115
Backward Bifurcation in Lassa Fever Model

 Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria. Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

ABSTRACT
A Mathematical Model for Lassa which incorporates quarantine and re-infection was developed for the control of Lassa fever epidemic. The basic reproduction number is calculated and it is shown that the model exhibits the phenomenon of backward bifurcation where a stable endemic equilibrium coexists with a stable disease-free equilibrium when the associated reproduction number is less than unity. This phenomenon has epidemiological implication which shows the classical requirement of the associated reproduction number to be less than unity does not guarantee control of the disease. Sensitivity and uncertainty analysis were carried out to access the importance of each parameter of the model.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
103
SAT: 30-12-2017 Hall[C] Oral - Sec14 ( 2 )
 09:00 : 09:15

DEA - 4 US Prof. Gamal Elnagar gelnagar@uscupstate.edu

115
Integro-Differential Functional Operator Control Systems:A Spectral Approach
Gamal N. Elnagar

 University of South Carolina

ABSTRACT
The spectral methods of G. N. Elnagar, which yield spectral convergence rate for the approximate solutions of Fredholm and Volterra-Hammerstein integral equations, is generalized in order to solve the larger class of integro-differential functional operator control systems with spectral accuracy. The proposed method is based on the idea of relating spectrally constructed grid points to the structure of projection operators which will be used to approximate the control vector and the associated state vector. These projection operators are spectrally constructed using Lagrange polynomials as trial functions. Due to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard integro-differential functional equation control systems. An illustrated example is included to confirm the efficiency and applicability of the proposed method.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
104
SAT: 30-12-2017 Hall[C] Oral - Sec14 ( 3 )
 09:15 : 09:30

DEA - 5 NG Mr. Abdurrahman Abdulhamid farkeminjibir@gmail.com

115
AN ANALYTIC SOLUTION OF SIMPLIFIED MATHEMATICAL MODEL OF EQUATION OF CONTINUITY (CONSERVATION OF FLOW EQUATION).

 Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria. Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria. Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

ABSTRACT
Abstract An analytic method of solving a partial differential equation (PDE) obtained from a modeled equation of continuity (conservation of flow equation) using integral transform method was proposed. The analysis of the equation was carried out with regards to the distance along road (x), time (t) and traffic flow (k). Whereas density of traffic (k0) and velocity (u) values were varied to asses how the vehicular flux changes in the study, one after the other keeping the rest fixed in order. The solution of the problem was discussed after analyzing the effect of the parameters on the traffic flow and graphs were presented to illustrate the exactness of the analytical solution where the behaviour of the traffic flux changes with distance for different initial densities and changes with distance for different initial velocities.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
105
SAT: 30-12-2017 Hall[C] Oral - Sec14 ( 4 )
 09:30 : 09:45

DEA - 6 EG Assoc.Prof. Wael Mohammed wael.mohammed@mans.edu.eg

115
Effect of the same degenerate additive noise on a coupled system of reaction-diffusion equations
Wael W. Mohammed

 Department of Mathematics, Faculty of Science, Hail University, Saudi Arabia

ABSTRACT
In this paper we present a class of stochastic system of reaction-diffusion equations. Our aim of this paper is to approximate the solutions for the system via amplitude equation with Neumann boundary conditions. We are interested on a systems that have nonlinear polynomial and give applications as Lotka-Volterra system and from chemistry the Brusselator model for the Belousov-Zhabotinsky chemical reaction to illustrate our results.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
106
SAT: 30-12-2017 Hall[C] Oral - Sec14 ( 5 )
 09:45 : 10:00

DEA - 7 EG Dr. Ahmed El-Deeb ahmedeldeeb@azhar.edu.eg

115
Diamond-Alpha Steffensen's Inequality on Time Scales
A. A. El-Deeb

 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.

ABSTRACT
In this paper, we prove some new Steffensen-type inequalities on time scales via the diamond-alpha dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales and also unify some continuous inequalities and their corresponding discrete analogues.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
107
SAT: 30-12-2017 Hall Sec Poster (03) ( 1 )
 01:15 : 02:45

DEA - 1 EG Dr. maha hamed maha_hamed8@yahoo.com

115
A Comparison Study Between the Two Wiener-Ito Expansions In Solving Stochastic Differential Equations
Maha Hamed , Ibrahim Al-Kalla , Mohamed El-Beltagy , Beih El-desouky

 Department of Mathematics, Faculty of Science, Mansoura University,Mansoura. Egypt Engineering Mathematics and Physics Dept, Faculty of Engineering, Mansoura University, Mansoura, Egypt. Engineering Mathematics and Physics Dept, Faculty of Engineering, Cairo University,Giza, Egypt. Department of Mathematics, Faculty of Science, Mansoura University,Mansoura. Egypt

ABSTRACT
In this paper, the two known Wiener-Ito expansions are compared. The methodology, performance and convergence of the two expansions are shown. The two expansions are used in solving linear and nonlinear stochastic differential equations (SDEs). The first expansion, known also as Wiener-Hermite Expansion (WHE), is truncated only in one parameter, order, but it is more difficult to handle. The second expansion, known also as Wiener-Chaos Expansion (WCE), is truncated in two parameters, order and dimension, but it is more easier. The two expansions are shown to be powerful tools when the Gaussian and/or non-Gaussian solutions are intended.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
108
SAT: 30-12-2017 Hall Sec Poster (03) ( 2 )
 01:15 : 02:45

DEA - 3 EG Dr. Sheren Abd El salam shrnahmed@yahoo.com

115
On two general nonlocal problems of an arbitrary (fractional) orders differential equations
Sheren Ahmed , Fatma Gaafar

 Lecturer Assistant Professor

ABSTRACT
In this paper, we prove some local and global existence theorems for a fractional orders differential equations with nonlocal conditions, also the uniqueness of the solution will be studied.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
109
SAT: 30-12-2017 Hall Sec Poster (03) ( 3 )
 01:15 : 02:45

115
Approximate Controllability for the Parabolic Equations

 OUM EL BOUAGHI UNIVERSITY. ALGERIA OUM EL BOUAGHI UNIVERSITY. ALGERIA

ABSTRACT
In this intervention, we study an approximate controllability problem. This problem appears naturally of approximate sentinel. The main tool is a theorem of uniqueness of the solution of ill-posed Cauchy problem for the parabolic equations.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
110
SAT: 30-12-2017 Hall Sec Poster (03) ( 4 )
 01:15 : 02:45

DEA - 11 EG Assoc.Prof. Usama Abdelsalam maths_us@hotmail.com

115
Exact solutions for coupled nonlinear partial differential equations using G'/G method
U.M. Abdelsalam

 Department of Mathematics, Faculty of Science, Fayoum University, Egypt.

ABSTRACT
(G'/G)-expansion method is examined to solve the Boiti–Leon–Pempinelli (BLP) system and the (2 + 1)-dimensional breaking soliton system. The results show that this method is a powerful tool for solving systems of nonlinear PDEs., it presents exact travelling wave solutions. The obtained solutions include rational, periodical, singular, shock wave and solitary wave solutions.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
111
SAT: 30-12-2017 Hall Sec Poster (03) ( 5 )
 01:15 : 02:45

115
Analytical solutions of fractional Huxley equation by residual power series method
Dr. Anas Arafa , Ghada Elmahdy

 Department of Mathematics and Computer Science, Faculty of Science, Port Said University Department of Mathematics and Computer Science, Faculty of Science, Port Said University

ABSTRACT
This paper investigates the approximate solution of nonlinear Huxley equation using new analytic technique. The solution was calculated in the form of a convergent power series with easily computable components. The proposed method obtains Taylor expansion of the solution and reproduces the exact solution when the solution is polynomial.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
112
SAT: 30-12-2017 Hall[C] Oral - Sec17 ( 1 )
 04:00 : 04:15

DEA - 9 AE Prof. Fathalla Rihan frihan@uaeu.ac.ae

115
An Inverse Problem for Delay Differential Equations in Biological Systems with Memory
Fathalla A. Rihan

 Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE

ABSTRACT
In this talk, we present the theoretical framework to solve inverse problems for Delay Differential Equations (DDEs). Given a parameterized DDE and experimental data, we estimate the parameters appearing in the model, using least squares approach. Some issues associated with the inverse problem, such as nonlinearity and discontinuities which make the problem more ill-posed, are studied. Sensitivity and robustness of the models to small perturbations in the parameters, using variational approach, are also investigated. The sensitivity functions may provide guidance for the modelers to determine the most informative data for a specific parameter, and select the best fit model. The consistency of delay differential equations with bacterial cell growth is shown by fitting the models to real observations.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
113
SAT: 30-12-2017 Hall[C] Oral - Sec17 ( 2 )
 04:15 : 04:30

DEA - 10 EG Dr. shaimaa salem shaimaasalem_math@yahoo.com

115
Oscillation Theorems for Nonlinear Differential Equations of Third-Order
M. M. A. El-Sheikh , R. Sallam , S. Salem

 Menoufia University Menoufia University Menoufia University

ABSTRACT
The aim of this paper is to study the oscillatory behavior of solutions of the third order neutral differential equation (a(t)[z′′(t)]^{γ})′+∑_{i=1}^{m}f_{i}(t,x(σ_{i}(t)))=0, t≥t₀, where z(t)=x(t)+∑_{j=1}ⁿp_{j}(t)x(τ_{j}(t)), m,n are positive integers, γ≥1 is a ratio of two odd positive integers and τ_{i}(t)≤t for i=1,2,..,m. A new criteria guarantees that every solution is either oscillatory or tends to zero are established. The obtained results improve some known results in the literature. Some examples are given to illustrate our results.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
114
SAT: 30-12-2017 Hall[C] Oral - Sec17 ( 3 )
 04:30 : 04:45

DEA - 12 EG Dr. Samah El-kholy samah.elkhouli1@eng.kfs.edu.eg

115
Discrete spline Numerov method for solving Swift-Hohenberg equation
W. K. Zahra , S. M. Elkoly

 Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt and Department of Mathematics, Basic and Applied Sciences School, Egypt-Japan University of Science and Technology, New Borg El-Arab City, Alexandria, 21934, Egypt Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh Univ., Egypt

ABSTRACT
Discrete spline function based method is developed to solve the time fractional Swift-Hohenberg equation in the sense of Riemann Liouville derivative. Via Fourier method, the developed method is convergent and unconditionally stable. Numerical results are demonstrated to confirm the applicability and the theoretical results.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

International Conference on Mathematics, Trends and Development ICMTD17 ,
Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,
Web Site: http://www.etms-eg.org

Differential Equation and Applications.
115
SAT: 30-12-2017 Hall[C] Oral - Sec17 ( 4 )
 04:45 : 05:00

DEA - 14 EG Dr. Samir Saker shsaker@mans.edu.eg

115
Gehring Dynamic Inequalities and Higher Integrability Theorems
Sami H. Saker

 Prof. Math. Department of Mathematics, Faculty of Science, Mnsoura University, Egypt

ABSTRACT
In this talk I will present new dynamic inequalities based on the application of the time scale version of Hardy's type inequality on a finite interval [a,b]_{T} where T is a time scale. Next, we will speak about Gehring's type inequalities on time scales by employing the obtained inequality. As an application of Gehring inequalities, we will prove some interpolation. Next, we will prove a dynamic inequality of Shum's type on a time scale T. The proof is new and different from the proof due to Shum. [Canad. Math. Bull. 14 (1971), 225-230]. Next, we prove some new integrability theorems which as a special case, when T=R, contain the results due to Muckenhoupt [Tran. Amer. Math. Soc. 165 (1972), 207-226] and the results due to Bojarski, Sbordone and Wik. [Studia Mat. VII, 10 (1992), 155-163]. By employing theorems, we will prove a higher integrability result which proves that the space L_{Δ}^{q}(0,T]_{T} of nonincreasing functions will be in the space L_{Δ}^{p}(0,T]_{T} for p>q. The results contain, as a special case, the integrability results due to Alzer [J. Math. Anal. Appl. 190 (1995), 774-779]. When T=N our results are essentially new and can be applied on different types of time scales. 2010 Mathematics Subject Classification: 26D15, 34A40, 34N05, 39A12.
 Code MPH STA NAM DSA CSC ALG TGA FUA DEA page 01 25 43 55 61 67 79 90 102

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