


Paper's Title:
On the Equiform Geometry of the Involuteevolute Curve Couple in Hyperbolic and de Sitter Spaces
Author(s):
M. Khalifa Saad, H. S. AbdelAziz and A. A. AbdelSalam
Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
KSA.
Email: mohammed.khalifa@iu.edu.sa
Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email: habdelaziz2005@yahoo.com
Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email: asem2e@yahoo.com
Abstract:
In this paper, we aim to investigate the equiform differential geometric properties of the involuteevolute curve couple with constant equiform curvatures in threedimensional hyperbolic and de Sitter spaces. Also, we obtain some relations between the curvature functions of these curves and investigate some special curves with respect to their equiform curvatures. Finally, we defray two computational examples to support our main findings.
Paper's Title:
On Ruled Surfaces According to QuasiFrame in Euclidean 3Space
Author(s):
M. Khalifa Saad and R. A. AbdelBaky
Department of Mathematics, Faculty of
Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email:
mohamed_khalifa77@science.sohag.edu.eg,
mohammed.khalifa@iu.edu.sa
Department of Mathematics, Faculty of
Science,
Assiut University, Assiut,
EGYPT.
Email: rbaky@live.com
Abstract:
This paper aims to study the skew ruled surfaces by using the quasiframe of Smarandache curves in the Euclidean 3space. Also, we reveal the relationship between SerretFrenet and quasiframes and give a parametric representation of a directional ruled surface using the quasiframe. Besides, some comparative examples are given and plotted which support our method and main results.
Paper's Title:
L∞ Error Estimate of Schwarz Algorithm for Elliptic QuasiVariational Inequalities Related to Impulse Control Problem
Author(s):
Saadi Samira and Mehri Allaoua
Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.
Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.
Email:
saadisamira69@yahoo.fr
allmehri@yahoo.fr
Abstract:
In this work, we study Schwarz method for a class of elliptic quasivariational inequalities. The principal result of this investigation is to prove the error estimate in ∞norm for two domains with overlapping nonmatching grids, using the geometrical convergence, and the uniform convergence of Cortey Dumont.
Paper's Title:
Schwarz Method for Variational Inequalities Related to Ergodic Control Problems
Author(s):
S. Saadi, H. Mécheri
Department of Mathematics, Badji Mokhtar
University, Annaba 23000,
P.O.Box. 12, Annaba 23000, Algeria
Abstract:
In this paper, we study variational inequalities related to ergodic control problems studied by M. Boulbrachčne and H. Sissaoui [11], where the "discount factor" (i.e., the zero order term) is set to 0, we use an overlapping Schwarz method on nomatching grid which consists in decomposing the domain in two subdomains. For α ∈ ]0.1[ we provide the discretization on each subdomain converges in L^{∞} norm.
Paper's Title:
Generalized Triangular and Symmetric Splitting Method for Steady State Probability Vector of Stochastic Matrices
Author(s):
B. Harika, D. Rajaiah, L. P. RajKumar, Malla Reddy Perati
Department of Mathematics,
Kakatiya University
Email: hbolledla@gmail.com
Department of Mathematics,
Kakatiya Institute of Technology and Science
Email: dr.mh@kitsw.ac.in
Department of Mathematics,
Kakatiya University
Email: ladalla@gmail.com
Department of Mathematics,
Kakatiya University
Email: mperati@yahoo.com
Abstract:
To find the steady state probability vector of homogenous linear system π Q=0 of stochastic rate matrix Q, generalized triangular and symmetric (GTS) splitting method is presented. Convergence analysis and choice of parameters are given when the regularized matrix A=Q^{T}+ε I of the regularized linear system Ax=b is positive definite. Analysis shows that the iterative solution of GTS method converges unconditionally to the unique solution of the regularized linear system. From the numerical results, it is clear that the solution of proposed method converges rapidly when compared to the existing methods.
Paper's Title:
Finite and Infinite Order Solutions of a Class of Higher Order Linear Differential Equations
Author(s):
Saada Hamouda
Department of Mathematics,
Laboratory of Pure and Applied Mathematics,
University of Mostaganem, B. P 227 Mostaganem,
ALGERIA
hamouda_saada@yahoo.fr
Abstract:
In this paper, we investigate the growth of solutions of higher order linear differential equations where most of the coefficients have the same order and type with each other.
Paper's Title:
Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities Simple Proof
Author(s):
M. Haiour and E. Hadidi.
Department of mathematics, LANOS Laboratory,
Faculty of the Sciences, University Badji Mokhtar,
P.O 23000 Annaba,
Algeria.
haiourm@yahoo.fr,
ehadidi71@yahoo.fr
Abstract:
In this paper we study noncoercive variational inequalities, using the Schwarz method. The main idea of this method consists in decomposing the domain in two subdomains. We give a simple proof for the main result concerning L^{∞} error estimates, using the Zhou geometrical convergence and the L^{∞} approximation given for finite element methods by CourtyDumont.
Paper's Title:
Timelike Surfaces with a Common Line of Curvature in Minkowski 3Space
Author(s):
M.K. Saad, A.Z. Ansari, M. Akram and F. Alharbi
Department of Mathematics ,
Faculty of Science,
Islamic University of Madinah,
KSA
Abstract:
In this paper, we analyze the problem of constructing a timelike surface family from a given nonnull curve line of curvature. Using the Frenet frame of the nonnull curve in Minkowski space E_{1}^{3} we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the line of curvature and the isoparametric requirements. In addition, a necessary and sufficient condition for the given nonnull curve to satisfy the line of curvature and the geodesic requirements is investigated. The extension to timelike surfaces of revolution is also outlined. Meanwhile, some representative nonnull curves are chosen to construct the corresponding timelike surfaces which possessing these curves as lines of curvature. Results presented in this paper have applications in geometric modeling and the manufacturing of products. In addition, some computational examples are given and plotted.
Paper's Title:
Approximation of an AQCQFunctional Equation and its Applications
Author(s):
Choonkil Park and Jung Rye Lee
Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133791,
Korea;
Department of Mathematics,
Daejin University,
Kyeonggi 487711,
Korea
baak@hanyang.ac.kr
jrlee@daejin.ac.kr
Abstract:
This paper is a survey on the generalized HyersUlam stability of an AQCQfunctional equation in several spaces. Its content is divided into the following sections:
1. Introduction and preliminaries.
2. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: direct method.
3. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: fixed point method.
4. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: direct method.
5. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: fixed point method.
6. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: direct method.
7. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: fixed point method.
Paper's Title:
On the HyersUlam Stability of Homomorphisms and Lie Derivations
Author(s):
Javad Izadi and Bahmann Yousefi
Department of Mathematics, Payame Noor
University,
P.O. Box: 193953697, Tehran,
Iran.
Email: javadie2003@yahoo.com,
b_yousefi@pnu.ac.ir
Abstract:
Let A be a Lie Banach^{*}algebra. For each elements (a, b) and (c, d) in A^{2}:= A * A, by definitions
(a, b) (c, d)= (ac, bd),
(a, b)= a+ b,
(a, b)^{*}= (a^{*}, b^{*}),
A^{2} can be considered as a Banach^{*}algebra. This Banach^{*}algebra is called a Lie Banach^{*}algebra whenever it is equipped with the following definitions of Lie product:
for all a, b, c, d in A. Also, if A is a Lie Banach^{*}algebra, then D: A^{2}→A^{2} satisfying
D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]
for all $a, b, c, d∈A, is a Lie derivation on A^{2}. Furthermore, if A is a Lie Banach^{*}algebra, then D is called a Lie^{*} derivation on A^{2} whenever D is a Lie derivation with D (a, b)^{*}= D (a^{*}, b^{*}) for all a, b∈A. In this paper, we investigate the HyersUlam stability of Lie Banach^{*}algebra homomorphisms and Lie^{* }derivations on the Banach^{*}algebra A^{2}.
Paper's Title:
Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method
Author(s):
Asem AL Nemrat and Zarita Zainuddin
School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
Email: alnemrata@yahoo.com
zarita@usm.my
Abstract:
This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the roundoff errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).
Paper's Title:
Some fixed point results in partial Smetric spaces
Author(s):
M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: Rezaee.mohammad.m@gmail.com
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: sedghi.gh@qaemiau.ac.ir
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: mukheimer@psu.edu.sa
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: kamal@psu.edu.sa
Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
Email: zoran.mitrovic@tdtu.edu.vn
Abstract:
We introduce in this article a new class of generalized metric spaces, called partial Smetric spaces. In addition, we also give some interesting results on fixed points in the partial Smetric spaces and some applications.
Paper's Title:
The Higher Coefficients for Bazilevic Functions B_{1}(α)
Author(s):
Marjono, Sa'adatul Fitri, and Krisna Adilia Daniswara
Department of Mathematics,
Faculty of Mathematics and Natural Sciences,,
Brawijaya University, Malang Jawa Timur 65145
Indonesia.
Email: marjono@ub.ac.id
saadatulfitri@ub.ac.id
krisnaadiliadaniswara@gmail.com
Abstract:
Let f be analytic in D{z: z< 1} with , and normalized by the conditions f(0)=f'(0)1=0. We give sharp estimates for the seventh and eighth coefficients for the class of Bazilevic functions with logarithmic growth, B_{1}α, defined by for α≥0.
Paper's Title:
Some Properties of (co)homology of Lie Algebra
Author(s):
Alaa Hassan Noreldeen Mohamed, Hegagi Mohamed Ali, Samar Aboquota
Department of Mathematics,
Faculty of
Science,
Aswan University, Aswan,
Egypt.
Email: ala2222000@yahoo.com
hegagi_math@aswu.edu.eg
scientist_samar@yahoo.com
Abstract:
Lie algebra is one of the important types of algebras. Here, we studied lie algebra and discussed its properties. Moreover, we define the Dihedral homology of lie algebra and prove some relations among Hochschild, Cyclic and Dihedral homology of lie algebra. Finally, we prove the Mayervetories sequence on Dihedral homology of lie algebra and proved that .
Paper's Title:
Numerical Solution of Certain Types of FredholmVolterra IntegroFractional Differential Equations via Bernstein Polynomials
Author(s):
Alias B. Khalaf^{1}, Azhaar H. Sallo^{2} and Shazad S. Ahmed^{3}
^{1}Department
of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
Email: aliasbkhalaf@uod.ac
^{2}Department
of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
Email: azhaarsallo@uod.ac
^{3}Department
of Mathematics, College of Science,
University of Sulaimani,
Kurdistan Region,
Iraq.
Email: shazad.ahmed@univsul.edu
Abstract:
In this article we obtain a numerical solution for a certain fractional order integrodifferential equations of FredholmVolterra type, where the fractional derivative is defined in Caputo sense. The properties of Bernstein polynomials are applied in order to convert the fractional order integrodifferential equations to the solution of algebraic equations. Some numerical examples are investigated to illustrate the method. Moreover, the results obtained by this method are compared with the exact solution and with the results of some existing methods as well.
Paper's Title:
Fekete Szegö problem on the Class of Bazilevič functions B_{1}(α) related to the Lemniscate Bernoulli
Author(s):
N. M. Asih, Marjono, Sa'adatul Fitri, Ratno Bagus Edy Wibowo
Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Department of Mathematics,
University of Udayana,
Bali,
Indonesia.
Email: madeasih@unud.ac.id
Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Email: marjono@ub.ac.id
Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Email: saadatulfitri@ub.ac.id
Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Email: rbagus@ub.ac.id
Abstract:
We provide a sharp boundaries inequalities for Fekete Szegö problem a_{3}μ a_{2}^{2}, the coefficients of logarithmic function log~ f(z)/z, and the coefficients of the inverse function f(f'(w)) on the Bazilevič functions B_{1}(α) related to the Lemniscate Bernoulli on the unit disk D={z: z < 1}. We obtained the result by using some properties of function with positive real part relates to coefficients problems.
Paper's Title:
Walrasian Equilibrium for Setvalued Mapping
Author(s):
M. Muslikh, R.B.E Wibowo, S. Fitri
Department of Mathematics,
University of Brawijaya,
Malang,
Indonesia.
Email: mslk@ub.ac.id
rbagus@ub.ac.id
saadatul@ub.ac.id
Abstract:
In this article, we obtain the existence of Walras equilibrium for setvalued demand mappings in a pure exchange economy. In this case, the setvalued mappings are defined by the loss function. Therefore, we shall summarize the features describing the exchange economy system which contain the loss function.
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