International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications. .::. Invited Lecture
1
SUN: 27-12-2015 Main Hall Inauguration Lecture Sec01 ( 1 )
 10:15 : 11:00

16
Orthogonal Polynomials in Two Variables

 University of Central Florida, Orlando, FL USA 32816, and King Saud University, Riyadh, Saudi Arabia.

ABSTRACT
The first examples of orthogonal polynomials in 2 variables go back to the 19th century. We briefly discuss the development of the theory of 2 variable orthogonal polynomials and the recent applications in physics and present a new class of orthogonal polynomials similar in spirit to the Askey Scheme.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications. .::. Invited Lecture
2
SUN: 27-12-2015 Main Hall Invited Speaker Sec02 ( 1 )
 11:00 : 11:30

16
MATHEMATICS IN EGYPT

 Dept of Maths ,Faculty of Science Al-Azhar University Nasr City

ABSTRACT
AN OVERLOOK OVER THE MATHEMATICS AND MATHEMATICIANS IN EGYPT FROM ANCIENT TIME DURING THE PHARAOHS ERA THROUGH GREEK ERA AND THE OLD LIBRARY OF ALEXANDRIA THEN THE ISLAMIC TIMES AND THE RULE PLAYED BY AL-AZHAR AND FINALLY THE MODERN TIME

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications. .::. Invited Lecture
3
SUN: 27-12-2015 Main Hall Invited Speaker Sec06 ( 1 )
 02:45 : 03:15

16
On weakly H-embedded subgroups of finite groups

 Department of Mathematics, Faculty of Science, Cairo University Department of Mathematics, Faculty of Science, Cairo University

ABSTRACT
Let G be a finite group and H a subgroup of G. We say that H is an H-subgroup in G if NG(H)Hg  H for all gG; H is called weakly H-subgroup in G if G has a normal subgroup K such that G=HK and HK is an H-subgroup in G. We say that H is weakly H-embedded in G if G has a normal subgroup K such that HG = HK and HK is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that some subgroups of prime power order are weakly H-embedded in G. Our results improve and generalize several recent results in the literature.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications. .::. Invited Lecture
4
MON: 28-12-2015 Main Hall Invited Speaker Sec10 ( 1 )
 12:45 : 01:15

ALG - 16 EG Prof. M. A. Saleem hasan@hotmail.com

16
Algebra
M. A. Saleem

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

ABSTRACT
-

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
5
MON: 28-12-2015 Hall[C] Oral - Sec06 ( 1 )
 09:00 : 09:15

ALG - 9 EG Ms. hala Abd-Elmageed halla_mohamed2010@yahoo.com

16
Cauchy Integral Formula for Matrix Functions
Z. Kishka , M. Abdalla , H. Abd-Elmageed

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

ABSTRACT
In this paper, we shall introduce Cauchy integral formula for functions of single complex matrix. Also, we shall extend the formula to the case of several complex matrices. Moreover, generalized Cauchy integral formula in the case of complex matrices will be established.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
6
MON: 28-12-2015 Hall[C] Oral - Sec06 ( 2 )
 09:15 : 09:30

ALG - 10 EG Dr. samia abdelwahab samia.mohamed.abdelwahab@gmail.com

16
The Family of Right N-semilocal Rings
Mohamed H. Fahmy , Abdelrahman Mohamed Hassanein , Samia Mohamed Abdelwahab

 Mathematics Department, Faculty of Science,Al-AzharUniversity Mathematics Department, Faculty of Science, Al-Azhar University Mathematics Department, Faculty of Science, Helwan University

ABSTRACT
In this paper we extend the notion of semilocal rings, giving the properties of the family of right and left N-semilocal rings. We give examples to show that these classes are proper classes of the family of local rings and right Noetherian rings.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
7
MON: 28-12-2015 Hall[C] Oral - Sec06 ( 3 )
 09:30 : 09:45

ALG - 11 EG Ms. Sarah Kamal El-Din sarakamal81@yahoo.com

16
(sigma,tau)-GENERALIZED POWER SERIES OVER ZIP AND WEAK ZIP RINGS
Mohamed H. Fahmy , Abdel-Rahman M. Hassanein , M. A. Farahat , Sarah Kamal El-Din

 Al-Azhar University Al-Azhar University Al-Azhar University Al-Azhar University (Girls)

ABSTRACT
In this paper we give a new class of extension rings called the (sigma;tau)-generalized power series ring with coefficients in a ring R and exponents in a strictly ordered monoid S which extends Ribenboim's and Ziembowski's constructions of generalized and skew generalized power series rings, respectively. The weak annihilator property of this class is investigated in this paper. We also show, under certain conditions, that the (sigma;tau)-generalized power series ring is a right zip (weak zip) ring if and only if R is a right zip (weak zip) ring.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
8
MON: 28-12-2015 Hall[C] Oral - Sec06 ( 4 )
 09:45 : 10:00

ALG - 12 EG Mr. Muhammad El Gebali m.elgebali@aucegypt.edu

16
A Combinatorial Interpretation of the LDU Decomposition of Totally Positive Matrices
Muhammad El Gebali , Nermine El-Sissi

 The American University in Cairo The American University in Cairo

ABSTRACT
We study the combinatorial description of the LDU decomposition of totally positive matrices. We give a description of the lower triangular L, the diagonal D, and the upper triangular U matrices of the LDU decomposition of totally positive matrices in terms of the combinatorial structure of essential planar networks described by Zelvinsky and Fomin. Similarly, we find a combinatorial description of the inverses of these matrices. In addition, we provide recursive formulae for computing the L, D, and U matrices of a totally positive matrix.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
9
MON: 28-12-2015 Poster - Sec 01 ( 5 )
 11:30 : 12:15

ALG - 13 LY Mr. Faraj Abdunabi farajarkeas1@gmail.com

16
Fixed Points On NG-Groups
Faraj.A.Abdunabi

 CCNU

ABSTRACT
We consider the NG-group which consisting of transformations on a non-empty set A and the group has no bijection as its element. Recall a permutation group on A is a group consisting of bijections from A to A with respect to compositions of mappings. It is well known that any permutation group on a set A with cardinality n has order not greater than n!. There are some authors, [10], [9], Problem 1.4 in [1], considering groups which consists of non-bijective transformations on A where the binary operation is the composition of mappings. Our result is on the orders of such groups are mapping on a non-empty set A with respect to function compositions which are not subsets of symmetric groups by using the fixed points.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
10
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 1 )
 03:15 : 03:30

ALG - 1 NG Mr. Ejegwa Augustine ocholohi@gmail.com

16
On anti-fuzzy subgroups
P. A. Ejegwa

 Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi Nigeria

ABSTRACT
In this paper, we studied the notion of anti-fuzzy subgroups and deduced some theorems, propositions and corollaries with proofs. The concepts of anti-fuzzy cosets, abelian anti-fuzzy subgroups and semi anti-fuzzy subgroups are introduced and some relevant theorems deduced and proved.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
11
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 2 )
 03:30 : 03:45

16
Homomorphisms and subalgebras of decomposable MS-algebras
Abd El-Mohsen Mohamed Badawy , Ragaa Abd El-mawgoud El-Fawal

 Mathematics Departement, Faculty of Science, Tanta University, Egypt. Mathematics Departement, Faculty of Science (girls branch), El-Azhar University, Egypt.

ABSTRACT
Decomposable MS-algebras have been introduced and characterized by A. Badawy, D. Guffova and M. Haviar in terms of the decomposable MS-triple $(M,D,\varphi)$, where $M$ is a De Morgan algebra, $D$ is a distributive lattice with unit and $\varphi$ is a bounded lattice homomorphism of $M$ into the lattice of filters of $D$. In this paper we study homomorphisms, subalgebras and solve the "Fill-in" problem for such decomposable MS-algebras.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
12
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 3 )
 03:45 : 04:00

ALG - 3 EG Mr. amr elrway amrmath1985@yahoo.com

16
On new methods of the inverse of Certain Matrices
Prof.Dr. Z. M. G. Kishka , Dr. M. A. Saleem , Dr. M. A. Abul-Dahab , A. M. Elrawy

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

ABSTRACT
In this paper, we introduce algebraic system each of whose elements is a matrix of matrices. Moreover we discuss some of the algebraic properties for this system. Also we shall give some methods for computing the inverse of a non-singular matrix of matrices. Besids we shall give some applications.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
13
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 4 )
 04:00 : 04:15

ALG - 4 EG Assoc.Prof. Mohamed Fahmy msfahmy@msa.eun.eg

16
On Maximal clones in 4-Valued Logic
M.S. Fahmy , E.H. Hamouda

 Faculty of Engineering, October University for Modern Sciences and Arts (MSA univ.) Department of Basic Science, Faculty of Industrial Education Beni-Suef University, Egypt

ABSTRACT
If E_k={0,1,…,k-1},k≥2, we denote P_k^n={f:E_k^n→E_k ,n=1,2,…}, the set of all k- valued logic functions of n variables defined on E_k. Let P_k=⋃_(n≥1)▒P_k^n . A set M⊂P_k is called a clone if it contains all projections and is closed under composition. The problem of functional completeness is an important problem in P_k that has been discussed and solved in P_2 by Post, in P_3 by Yablonski and finally in P_k by Rosenberg who described all maximal clones in P_k as the set of all functions preserving six families of relations on E_k. Rosenberg used a pure complicated combinatorial formula to determine the total number π(k) of the maximal clones and pointed out that, some of computed numerical values were incorrect for some values of k. In our paper, we compute the number of maximal clones in P_4 using a simple trend and fix some of incorrect values for π(k), as he predicted in his paper.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
14
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 5 )
 04:15 : 04:30

ALG - 5 LY Dr. Shaban Traina shabantraina@yahoo.com

16
Variety of Commutative Quasi-Groups
Shaban Traina , Almabrok Elsnosi

 University of Benghazi Sabha University

ABSTRACT
A variety is a class of algebras closed under subalgebras, homomorphic images and direct products. We show that each class of generalized coherent Lallement sum ( gcL-sum ) of commutative quasi-groups over a left-zero band is a variety.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
15
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 6 )
 04:30 : 04:45

ALG - 7 EG Mr. usama wadie pasotier@gmail.com

16
A New Method for Solving Linear Systems of Algebraic Equations

 pursuing the M.S. degree in computer and systems engineering at the faculty of engineering -Ain Shams University- Egypt.

ABSTRACT
This document gives a new method for solving the linear systems. My method contains equations and rules.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Algebra and applications.
16
MON: 28-12-2015 Hall[B] Oral - Sec08 ( 7 )
 04:45 : 05:00

ALG - 8 EG Prof. Abdelrahman Heliel Heliel9@yahoo.com

16
On weakly Z-permutable subgroups of finite groups
A. A. Heliel , M. M. Al-Shomrani , T. M. Al-Gafri

 Department of Mathematics, Faculty of Science, Beni-Suef University, 62511, Beni-Suef, Egypt. King Abdulaziz University, Jeddah 21589, Saudi Arabia King Abdulaziz University, Jeddah 21589, Saudi Arabia

ABSTRACT
Let Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, Z contains exactly one and only one Sylow p-subgroup of G. A subgroup H of G is said to be Z-permutable of G if H permutes with every member of Z. A subgroup H of G is said to be a weakly Z-permutable subgroup of G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ HZ, where HZ is the subgroup of H generated by all those subgroups of H which are Z-permutable subgroups of G. In this paper, we prove that if p is the smallest prime dividing the order of G and the maximal subgroups of Gp ∈ Z are weakly Z-permutable subgroups of G, then G is p-nilpotent. Moreover, we prove that if F is a saturated formation containing the class of all supersolvable groups, then G ∈ F iff there is a solvable normal subgroup H in G such that G/H ∈ F and the maximal subgroups of the Sylow subgroups of the Fitting subgroup F(H) are weakly Z-permutable subgroups of G. These two results generalize and unify several results in the literature.