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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Hyperbolic Barycentric Coordinates
Author(s):
Abraham A. Ungar
Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL: http://math.ndsu.nodak.edu/faculty/ungar/
Abstract:
A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.
Paper's Title:
A Unifying View of Some Banach Algebras
Author(s):
R. Kantrowitz
Mathematics & Statistics Department,
Hamilton College,
198 College Hill Road,
Clinton, NY 13323, USA.
E-mail: rkantrow@hamilton.edu
Abstract:
The purpose of this article is to shed light on a unifying framework for some normed algebras and, in particular, for some Banach algebras. The focus is on linear operators T between normed algebras X and Y and specified subalgebras A of Y. When the action of T on products in X satisfies a certain operative equation, the subspace T-1(A) is stable under the multiplication of X and is readily equipped with a family of canonical submultiplicative norms. It turns out that many familiar and important spaces are encompassed under this versatile perspective, and we offer a sampling of several such. In this sense, the article presents an alternative lens through which to view a host of normed algebras. Moreover, recognition that a normed linear space conforms to this general structure provides another avenue to confirming that it is at once stable under multiplication and also outfitted with an abundance of equivalent submultiplicative norms.
Paper's Title:
Viability
Theory And Differential Lanchester Type Models For Combat.
Differential Systems.
Author(s):
G. Isac and A. Gosselin
Department Of
Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston,
Ontario, Canada K7k 7b4
isac-g@rmc.ca
gosselin-a@rmc.ca
URL:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html
Abstract:
In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.
Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Nonlinear System of Mixed Ordered Variational Inclusions Involving XOR Operation
Author(s):
Iqbal Ahmad, Abdullah and Syed Shakaib Irfan
Department of Mechanical Engineering,
College of Engineering, Qassim University
Buraidah 51452, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa,
i.ahmad@qu.edu.sa
Zakir Husain Delhi College,
University of Delhi,
JLN Marg, New Delhi- 110 002,
India.
E-mail: abdullahdu@qec.edu.sa
Department of Mathematics,
Aligarh Muslim University, Aligarh,
India.
E-mail: shakaibirfan@gmail.com
Abstract:
In this work, we introduce and solve an NSMOVI frameworks system involving XOR operation with the help of a proposed iterative algorithm in real ordered positive Hilbert spaces. We discuss the existence of a solution of a considered system of inclusions involving XOR operation by applying the resolvent operator technique with XOR operation and also study the strong convergence of the sequences generated by the considered algorithm. Further, we give a numerical example in support of our considered problem which gives the grantee that all the proposed conditions of our main result are fulfilled.
Paper's Title:
Asymptotic Inequalities for the Maximum Modulus of the Derivative of a Polynomial
Author(s):
Clément Frappier
Département de Mathématiques et de Génie industriel École Polytechnique de
Montréal,
C.P.~6079, succ. Centre-ville Montréal (Québec),
H3C 3A7, CANADA
Abstract:
Let
be an algebraic polynomial of degree
≤n, and let ∥p∥= max {|p(z)|:|z| = 1}.
We study the asymptotic behavior of the best possible constant φn,k (R), for
k = 0 and k=1, in the inequality ∥p'(Rz)∥ + φn,k (R) |ak|
≤ nRn-1 ∥p∥, R → ∞.
Paper's Title:
Reconstruction of Discontinuities of Functions Given Noisy Data
Author(s):
Eric D. Mbakop
67A Beaver Park Rd,
Framingham, MA, 01702,
U. S. A.
ericsteve86@yahoo.fr
Abstract:
Suppose one is given noisy data of a discontinuous piecewise-smooth function along with a bound on its second derivative. The locations of the points of discontinuity of f and their jump sizes are not assumed known, but are instead retrieved stably from the noisy data. The novelty of this paper is a numerical method that allows one to locate some of these points of discontinuity with an accuracy that can be made arbitrarily small.
Paper's Title:
On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains
Author(s):
Janusz Brzdęk
Department of Mathematics
Pedagogical University Podchorąźych 2,
30-084 Kraków,
Poland
jbrzdek@ap.krakow.pl
Abstract:
We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable
Paper's Title:
Equivalence of the Nonsmooth Nonlinear Complementarity Problems to Unconstrained Minimization
Author(s):
M. A. Tawhid and J. L. Goffin
Department of Mathematics and Statistics,
School of Advanced Technologies and Mathematics,
Thompson Rivers University,
900 McGill Road, PO Box 3010, Kamloops, BC V2C 5N3
Canada
Alexandria University and Egypt Japan University of Science and Technology,
Alexandria-Egypt
mtawhid@tru.ca
Faculty of Management, McGill University,
1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5
Canada.
Jean-Louis.Goffin@McGill.ca
Abstract:
This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the H-differentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe H-differentials of the associated penalized Fischer-Burmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P0, semimonotone (E0), P, positive definite, and strictly semimonotone (E) -conditions on an H-differential of f, finding local/global minimum of a merit function (or a `stationary point' of a merit function) leads to a solution of the given nonlinear complementarity problem. Our results not only give new results but also unify/extend various similar results proved for C1.
Paper's Title:
An Efficient Modification of Differential Transform Method for Solving Integral and Integro-differential Equations
Author(s):
S. Al-Ahmad, Ibrahim Mohammed Sulaiman*, and M. Mamat
Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Terengganu, Besut Campus, 22200,
Malaysia.
E-mail: Alahmad.shadi@yahoo.com,
*sulaimanib@unisza.edu.my,
must@unisza.edu.my
Abstract:
In this paper, classes of integral and integro-differential equations are solved using a modified differential transform method. This proposed technique is based on differential transform method (DTM), Laplace transform (LT) procedure and Pad\'{e} approximants (PA). The proposed method which gives a good approximation for the true solution in a large region is referred to modified differential transform method (MDTM). An algorithm was developed to illustrate the flow of the proposed method. Some numerical problems are presented to check the applicability of the proposed scheme and the obtained results from the computations are compared with other existing methods to illustrates its efficiency. Numerical results have shown that the proposed MDTM method is promising compared to other existing methods for solving integral and integro-differential equations.
Paper's Title:
A general theory of decision making
Author(s):
Frank Hansen
Department of Economics,
University of Copenhagen,
Studiestraede 6, DK-1455 Copenhagen K
Denmark
Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh
Abstract:
We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of non-additive measures.
Paper's Title:
Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings
Author(s):
M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi
The Open University of Japan,
Chiba, 261-8586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp
Yamagata University,
Yonezawa 992-8510,
Japan
miura@yz.yamagata-u.ac.jp
Toho University, Yamagata University,
Chiba, 273-0866,
Japan
sin_ei1@yahoo.co.jp
Abstract:
We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.
Paper's Title:
Jordan Canonical Form of Interval Matrices and Applications
Author(s):
S. Hema Surya, T. Nirmala and K. Ganesan
Department of Mathematics, College of
Engineering and Technology,
SRM Institute of Science and Technology,
Kattankulathur,
Chennai-603203,
India.
E-mail: nirmalat@srmist.edu.in
URL:
https://www.srmist.edu.in/faculty/dr-t-nirmala/
Abstract:
A square interval matrix over R can be converted to diagonal form if certain prerequisites are satisfied. However not all square matrices can be diagonalized. As a consequence, we strive the next simplest form to which it can be reduced while retaining important properties such as eigenvalues, rank, nullity, and so on. It turns out that any real interval matrix has a Jordan Canonical Form (JCF) over E if it has n interval eigenvalues in IR. We discuss in this paper a method for computing the Jordan canonical form of an interval matrix using a new pairing technique and a new type of interval arithmetic that will make classifying and analyzing interval matrices easier and more efficient. We conclude with a numerical example that supports the theory and application of predator-prey model.
Paper's Title:
Weak Solution for Hyperbolic Equations with a Non-Local Condition
Author(s):
Lazhar Bougoffa
King Khalid
University, Faculty of Science, Department of Mathematics,
P.O.Box 9004, Abha, Saudi Arabia
abogafah@kku.edu.sa
Abstract:
In this paper, we study hyperbolic equations with a non-local condition. We prove the existence and uniqueness of weak solutions, using energy inequality and the density of the range of the operator generated by the problem.
Paper's Title:
A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral
Author(s):
Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1
1Dept. of Mathematics and Computer
Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail: domenico.candeloro@unipg.it,
anna.sambucini@unipg.it
2Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro,
gavrilut@uaic.ro
Abstract:
In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.
Paper's Title:
Attempts to Define a Baum--Connes Map Via Localization of Categories for Inverse Semigroups
Author(s):
Bernhard Burgstaller
Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040-900 Florianopolis-SC,
Brasil.
E-mail:
bernhardburgstaller@yahoo.de
URL:
http://mathematik.work/bernhardburgstaller/index.html
Abstract:
An induction functor in inverse semigroup equivariant KK-theory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any so-called E-continuous inverse semigroup its equivariant KK-theory satisfies the universal property and is a triangulated category.
Paper's Title:
Construction of a Frame Multiresolution Analysis on Locally Compact Abelian Groups
Author(s):
R. Kumar and Satyapriya
Department of Mathematics,
Kirori Mal College,
University of Delhi,
Delhi,
India.
E-mail: rajkmc@gmail.com
Department of Mathematics,
University of Delhi,
Delhi,
India.
E-mail: kmc.satyapriya@gmail.com
Abstract:
The frame multiresolution analysis (FMRA) on locally compact Abelian groups has been studied and the results concerning classical MRA have been worked upon to obtain new results. All the necessary conditions, which need to be imposed on the scaling function φ to construct a wavelet frame via FMRA, have been summed up. This process of construction of FMRA has aptly been illustrated by sufficient examples.
Paper's Title:
A Note on Schur's Lemma in Banach Function Spaces
Author(s):
R. E. Castillo, H. Rafeiro and E. M. Rojas
Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: recastillo@unal.edu.co
United Arab Emirates University,
Department of Mathematical Sciences, Al Ain,
United Arab Emirates.
E-mail: rafeiro@uaeu.ac.ae
Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: emrojass@unal.edu.co
Abstract:
In this small note, in a self contained presentation, we show the validity of Schur's type lemma in the framework of Banach function spaces.
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
E-mail: hbolledla@gmail.com
Department of Mathematics,
Kakatiya Institute of Technology and Science
E-mail: dr.mh@kitsw.ac.in
Department of Mathematics,
Kakatiya University
E-mail: ladalla@gmail.com
Department of Mathematics,
Kakatiya University
E-mail: 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=QT+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:
Using an Euler Type Transform for Accelerating Convergence of Series
Author(s):
Nimete Sh. Berisha, Faton M. Berisha*, Murat Sadiku
Faculty of Economics, University of
Prishtina,
Agim Ramadani st., 10000 Pristina,
Kosovo.
E-mail: nimete.berisha@uni-pr.edu
URL:
https://staff.uni-pr.edu/profile/nimeteberisha
Faculty of Mathematics and Sciences,
University of Prishtina,
Mother Teresa st., 10000 Pristina,
Kosovo.
E-mail: faton.berisha@uni-pr.edu
URL:
https://staff.uni-pr.edu/profile/fatonberisha
Faculty of Business Administration,
South East European University,
Tetovo,
North Macedonia.
E-mail: m.sadiku@seeu.edu.mk
Abstract:
In the paper we give a property of an operator of generalised difference, defined earlier, linear on a set of sequences, and use it to establish Euler type transforms for alternating series. These transforms accelerate the convergence of series under the same conditions as the transforms of non-alternating series. We also give analysis of an algorithm for computing a partial sum of the transformed series by using a higher order operator of generalised difference, and prove a theorem stating its order of complexity.
Paper's Title:
Results Concerning Fixed Point for Soft Weakly Contraction In Soft Metric Spaces
Author(s):
Abid Khan, Santosh Kumar Sharma, Anurag Choubey, Girraj Kumar Verma, Umashankar Sharma, Ramakant Bhardwaj
Department of Mathematics,
AUMP, Gwalior,
India.
abid69304@gmail.com
Department of Mathematics,
AUMP, Gwalior,
India.
sksharma1@gwa.amity.edu
Department of Computer Science,
Technocrats Institute of Technology,
Bhopal, MP,
India.
directoracademicstit@gmail.com
Department of Mathematics,
AUMP, Gwalior,
India.
gkverma@gwa.amity.edu
Department of Physics,
RJIT BSF Tekanpur, MP,
India.
ussharma001@gmail.com
School of Applied Science
AUK, WB,
India.
rkbhardwaj100@gmail.com
Abstract:
The basic objective of the proposed research work is to make people acquainted with the concept of soft metric space by generalizing the notions of soft (ψ,φ)-weakly contractive mappings in soft metric space, as well as to look at specific fundamental and topological parts of the underlying spaces. A compatible example is given to explain the idea of said space structure. The theory is very useful in decision making problems and secure transmission as fixed point provides exact output. The fixed-point theorems on subsets of Rm that are useful in game theoretic settings.
Paper's Title:
A New Family of Periodic Functions as Explicit Roots of a Class of Polynomial Equations
Author(s):
M. Artzrouni
Department of Mathematics, University of Pau
64013 Pau Cedex
Pau, France
marc.artzrouni@univ-pau.fr
URL: http://www.univ-pau.fr/~artzroun
Abstract:
For any positive integer n a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equations of order n. The n roots are the values of the appropriate function from that family taken at 0, 1, ... , n-1.
Paper's Title:
A New Method for Comparing Closed Intervals
Author(s):
Ibraheem Alolyan
Department of Mathematics, College of Sciences,
King Saud University, P. O. Box 2455, Riyadh 11451,
Saudi Arabia
ialolyan@ksu.edu.sa
URL:http://faculty.ksu.edu.sa/ALolyan
Abstract:
The usual ordering ``≤" on R is a total ordering, that is, for any two real numbers in R, we can determine their order without difficulty. However, for any two closed intervals in R, there is not a natural ordering among the set of all closed intervals in R. Several methods have been developed to compare two intervals. In this paper, we define the μ-ordering which is a new method for ordering closed intervals.
Paper's Title:
Expected Utility with Subjective Events
Author(s):
Jacob Gyntelberg and Frank Hansen
Bank for International Settlements,
Basel,
Switzerland
Tohoku University, Institute for International Education,
Sendai,
Japan
Abstract:
We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a ``small world'' as a context dependent or local state space embedded into a subjective set of events, the ``grand world''. For each situation the decision makers' subjective ``small world'' reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.
Paper's Title:
A Nonhomogeneous Subdiffusion Heat Equation
Author(s):
Joel-Arturo Rodriguez-Ceballos, Ana-Magnolia Marin, Ruben-Dario Ortiz
Instituto Tecnológico de Morelia,
Morelia, Michoacan,
Mexico
E-mail: joel@ifm.umich.mx
Universidad de Cartagena,
Campus San Pablo,
Cartagena de Indias, Bolivar,
Colombia
E-mail: amarinr@unicartagena.edu.co
E-mail: joel@ifm.umich.mx
Abstract:
In this paper we consider a nonhomogeneous subdiffusion heat equation of fractional order with Dirichlet boundary conditions.
Paper's Title:
Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
E-mail:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
E-mail:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>A:=<Au|v>, u,v ∈ H induces a semi-norm || .||A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities for operators on semi Hilbertian space (H,||.||A), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasi-hyponormal operators. An operator T ∈ BA (H) is said to be (A, k)-quasi-hyponormal if
Paper's Title:
New Exact Taylor's Expansions without the Remainder: Application to Finance
Author(s):
Moawia Alghalith
Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.
E-mail: malghalith@gmail.com
Abstract:
We present new exact Taylor's expansions with fixed coefficients and without the remainder. We apply the method to the portfolio model.
Corrigendum.
A corrigendum for this article has been published. To view the corrigendum,
please click
here.
Paper's Title:
On Closed Range C*-modular Operators
Author(s):
Javad Farokhi-Ostad and Ali Reza Janfada
Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: j.farokhi@birjand.ac.ir
ajanfada@birjand.ac.ir
Abstract:
In this paper, for the class of the modular operators on Hilbert C*-modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C*-modules are discussed. Moreover, the mixed reverse order law for the Moore-Penrose invertible modular operators are given.
Paper's Title:
Solving Non-Autonomous Nonlinear Systems of Ordinary Differential Equations Using Multi-Stage Differential Transform Method
Author(s):
K. A. Ahmad, Z. Zainuddin, F. A. Abdullah
School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia.
E-mail: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my
Abstract:
Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multi-stage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and Runge-Kutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the Runge-Kutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations
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.
E-mail: 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 Mayer-vetories
sequence on Dihedral homology of lie algebra and proved that
.
Paper's Title:
Semivectorial Bilevel Optimization on Affine-Finsler-Metric Manifolds
Author(s):
Faik Mayah1, Ali S Rasheed2 and Naseif J. Al- Jawari3
1Department of Physics,
College of Sciences,
University of Wasit,
Iraq.
E-mail: faik.mayah@gmail.com
2Ministry of Higher Education and Scientific Research,
Iraq.
E-mail: ali.math2018@yahoo.com
ahmedhashem@gmail.com
3Dept.
of Mathematics,
College of Science,
Mustansiriyah University, Baghdad,
Iraq.
E-mail: nsaif642014@yahoo.com
Abstract:
A Finsler manifold is a differential manifold together with a Finsler metric, in this paper we construct a new class of Finsler metric affine manifolds on bilevel semivectorial with optimization problems. The first steps for this purpose involve the study of bilevel optimization on affine manifolds. The bilevel programming problem can be viewed as a static version of the noncooperative, two-person game which was introduced in the context of unbalanced economic markets. Bilevel optimization is a special kind of optimization where one problem is embedded within another.
Paper's Title:
Locally Bicomplex Convex Module and Their Applications
Author(s):
Stanzin Kunga and Aditi Sharma
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: stanzinkunga19@gmail.com
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
E-mail: aditi.sharmaro@gmail.com
Abstract:
Let X be a locally BC convex module and L(X) be the family of all continuous bicomplex linear operators on X. In this paper, we study some concepts of D-valued seminorms on locally BC convex module. Further, we study the bicomplex version of Co and (Co,1) semigroup. The work of this paper is inspired by the work in [2] and [6].
Paper's Title:
Numerical Solution of Certain Types of Fredholm-Volterra Integro-Fractional Differential Equations via Bernstein Polynomials
Author(s):
Alias B. Khalaf1, Azhaar H. Sallo2 and Shazad S. Ahmed3
1Department
of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail: aliasbkhalaf@uod.ac
2Department
of Mathematics, College of Science,
University of Duhok,
Kurdistan Region,
Iraq.
E-mail: azhaarsallo@uod.ac
3Department
of Mathematics, College of Science,
University of Sulaimani,
Kurdistan Region,
Iraq.
E-mail: shazad.ahmed@univsul.edu
Abstract:
In this article we obtain a numerical solution for a certain fractional order integro-differential equations of Fredholm-Volterra type, where the fractional derivative is defined in Caputo sense. The properties of Bernstein polynomials are applied in order to convert the fractional order integro-differential 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:
The Automatic Continuity of N-Homomorphisms in Certain *-Banach Algebras
Author(s):
M. Aboulekhlef, Y. Tidli
Laboratory of Applied Mathematics and
Information and Communication Technology
Polydisciplinary Faculty of Khouribga
University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com
y.tidli@gmail.com
Abstract:
In this study, we prove the automatic continuity of surjective n-homomorphism between complete p-normed algebras. We show also that if Α and Β are complete *-p-normed algebras, Β is *simple and ψ: Α → Β is a surjective n-homomorphism under certain conditions, then ψ is continuous.
Paper's Title:
Automatic Continuity of Generalized Derivations in Certain *-Banach Algebras
Author(s):
M. Aboulekhlef, Y. Tidli and M. Belam
Laboratory of Applied Mathematics and
Information and Communication Technology Polydisciplinary
Faculty of Khouribga University of Sultan Moulay Slimane
Morocco.
E-mail:
aboulekhlef@gmail.com
y.tidli@gmail.com
m.belam@gmail.com
Abstract:
Consider the map φ of the Banach algebra Β in Β, if there exists a derivation δ of Β in Β so that for every x, y ∈ Β , φ(xy) =φ(x)y+xδ(y) . φ is called a generalized derivation of Β. In [9], Bresar introduced the concept of generalized derivations. We prove several results about the automatic continuity of generalized derivations on certain Banach algebras.
Paper's Title:
New Fast Extragradient-like Methods for Non-Lipschitzian Pseudo-monotone Variational Inequalities
Author(s):
Morad Ali Peyvand
Department of Mathematics
Yasouj University
Yasouj,
Iran.
E-mail: peyvand@yu.ac.ir
Abstract:
An efficient double-projection method, with a new search strategy, is designed for solving variational inequalities in real Hilbert spaces with pseudo-monotone cost operator. Our proposed method uses a computationally inexpensive simple line search procedure based on local information of the operator and very weak conditions of parameters to obtain larger step sizes. A description of the algorithm along with its weak convergence is provided without assuming Lipschitz continuity. Also, a modification to the proposed method is presented, wherein the second projection onto the closed and convex subset is replaced with the one onto a subgradient half space. Numerical experiments and comparisons with related methods demonstrate the reliability and benefits of the proposed schemes.
Paper's Title:
Some Generalizations of Steffensen's Inequality
Author(s):
W. T. Sulaiman
College of Computer Science and Mathematics
University of Mosul , Iraq
Abstract:
Some generalization of Steffensen's inequalities are given.
Paper's Title:
Essential Random Fixed Point Set of Random Operators
Author(s):
Ismat Beg
Centre for Advanced Studies in Mathematics,
Lahore University of Management Sciences (LUMS),
54792-Lahore, PAKISTAN.
ibeg@lums.edu.pk
URL: http://web.lums.edu.pk/~ibeg
Abstract:
We obtain necessary and sufficient conditions for the existence of essential random fixed point of a random operator defined on a compact metric space. The structure of the set of essential random fixed points is also studied.
Paper's Title:
Some Approximation for the linear combinations of modified Beta operators
Author(s):
Naokant Deo
Department of Applied Mathematics
Delhi College of Engineering
Bawana Road, Delhi - 110042,
India.
dr_naokant_deo@yahoo.com
Abstract:
In this paper, we propose a sequence of new positive linear operators βn to study the ordinary approximation of unbounded functions by using some properties of the Steklov means.
Paper's Title:
On the Hohov Convolution Of The Class Sp(α,β)
Author(s):
T. N. Shanmugam and S. Sivasubramanian
Department of Mathematics,
Anna University,
Chennai 600025,
Tamilnadu, India.
shan@annauniv.edu
Department of Mathematics,
Easwari Engineering College,
Chennai-600089,
Tamilnadu, India,
sivasaisastha@rediffmail.com
Abstract:
Let F(a,b;c;z) be the Gaussian hypergeometric function and Ia,b;c(f)=zF(a,b;c;z)*f(z) be the Hohlov operator defined on the class A of all normalized analytic functions. We determine conditions on the parameters a,b,c such that Ia,b;c(f) will be in the class of parabolic starlike functions Sp(α,β). Our results extend several earlier results.
Paper's Title:
Boundary Value Problems for Fractional Diffusion-Wave equation
Author(s):
Varsha Daftardar-Gejji and Hossein Jafari
Department of Mathematics, University of Pune,
Ganeshkhind, Pune - 411007,
INDIA.
vsgejji@math.unipune.ernet.in
jafari_h@math.com
Abstract:
Non homogeneous fractional diffusion-wave equation has been solved under linear/nonlinear boundary conditions. As the order of time derivative changes from
0 to 2, the process changes from slow diffusion to classical diffusion to mixed diffusion-wave behaviour.
Numerical examples presented here confirm this inference. Orthogonality of eigenfunctions in case of fractional Stürm-Liouville problem has been established
Paper's Title:
Analysis of the Flow Field in Stenosed Bifurcated Arteries Through a Mathematical Model
Author(s):
S. Chakravarty and S. Sen
Department of Mathematics, Visva-Bharati University,
Santiniketan 731235,
India
santabrata2004@yahoo.co.in
Abstract:
The present study is dealt with an appropriate mathematical model of the arotic bifurcation in the presence of constrictions using which the physiological flow field is analized. The geometry of the bifurcated arterial segment having constrictions in both the parent and its daughter arterial lumen frequently occurring in the diseased arteries causing malfunction of the cardiovascular system , is formed mathematically with the introduction of appropriate curvatures at the lateral junctions and the flow divider. The flowing blood contained in the stenosed bifurcated artery is treated to be Newtonian and the flow is considered to be two dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for Newtonian fluid. The flow field can be obtained primarily following the radial coordinate transformation and using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of the arterial wall distensibility and the presence of stenosis on the flow field, the flow rate and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.
Paper's Title:
Coincidences and Fixed Points of Hybrid Maps in Symmetric Spaces
Author(s):
S. L. Singh and Bhagwati Prasad
Vedic MRI, 21 Govind Nagar,
Rishikesh 249201
India
vedicmri@gmail.com
Department of Mathematics, Gurukula Kangri University,
Hardwar 249404,
India
Abstract:
The purpose of this paper is to obtain a new coincidence theorem for a single-valued and two multivalued operators in symmetric spaces. We derive fixed point theorems and discuss some special cases and applications.
Paper's Title:
A Method for Solving Systems of Nonlinear Equations
Author(s):
J. Shokri
Department of Mathematics, Urmia University,
P. O. Box 165, Urmia,
Iran
j.shokri@urmia.ac.ir
Abstract:
In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation systems using the combination of midpoint quadrature rule and Trapezoidal quadrature rule. We prove that this method has quadratic convergence. Several examples are given to illustrate the efficiency of the proposed method.
Paper's Title:
Purely Unrectifiable Sets with Large Projections
Author(s):
Harold R. Parks
Department of Mathematics,
Oregon State University,
Corvallis, Oregon 97331--4605,
USA
parks@math.oregonstate.edu
URL: http://www.math.oregonstate.edu/people/view/parks/
Abstract:
For n≥2,
we give a construction of a compact
subset of 
that is dispersed enough that it is
purely unrectifiable, but that nonetheless
has an orthogonal projection that hits every
point of an (n-1)-dimensional unit cube.
Moreover, this subset has the additional
surprising property that
the orthogonal projection onto
any straight line in
is a set of positive
1-dimensional Hausdorff measure.
Paper's Title:
On the product of M-measures in l-groups
Author(s):
A. Boccuto, B. Riěcan, and A. R. Sambucini
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
boccuto@dipmat.unipg.it
URL:
http://www.dipmat.unipg.it/~boccuto
Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk-97401 Banská Bystrica,
Slovakia.
riecan@fpv.umb.sk
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I-06123 Perugia,
Italy.
matears1@unipg.it
URL:
http://www.unipg.it/~matears1
Abstract:
Some extension-type theorems and compactness
properties for the
product of l-group-valued M-measures are proved.
Paper's Title:
Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory
Author(s):
R. Mythili Priyadharshini and N. Ramanujam
Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.
matram2k3@yahoo.com
URL:
http://www.bdu.ac.in/depa/science/ramanujam.htm
Abstract:
In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.
Paper's Title:
Generalizing Polyhedra to Infinite Dimension
Author(s):
Paolo d'Alessandro
Department of Mathematics, Third University of Rome,
Lgo S.L. Murialdo 1, 00146 Rome, Italy.
URL:
http://www.mat.uniroma3.it/users/dalex/dalex.html.
Abstract:
This paper generalizes polyhedra to infinite dimensional Hilbert spaces as countable intersections of closed semispaces. Highlights are the structure theory that shows that a polyhedron is the sum of compact set (in a suitable topology) plus a closed pointed cone plus a closed subspace, giving the internal representation of polyhedra. In the final part the dual range space technique is extended to the solution of infinite dimensional LP problems.
Paper's Title:
Solving Fractional Transport Equation via Walsh Function
Author(s):
A. Kadem
L. M. F. N., Mathematics Department,
University of Setif,
Algeria
abdelouahak@yahoo.fr
Abstract:
In this paper we give a complete proof of A method for the solution of fractional transport equation in three-dimensional case by using Walsh function is presented. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem.
Paper's Title:
On an Autocorrection Phenomenon of the Eckhoff Interpolation
Author(s):
A. Poghosyan
Institute of Mathematics, National Academy
of Sciences,
24b Marshal Baghramian ave., Yerevan 0019,
Republic of Armenia
arnak@instmath.sci.am
Abstract:
The paper considers the Krylov-Lanczos and the Eckhoff interpolations of a function with a discontinuity at a known point. These interpolations are based on certain corrections associated with jumps in the first derivatives. In the Eckhoff interpolation, approximation of the exact jumps is accomplished by the solution of a system of linear equations. We show that in the regions where the 2-periodic extension of the interpolated function is smooth, the Eckhoff interpolation converges faster compared with the Krylov-Lanczos interpolation. This accelerated convergence is known as the autocorrection phenomenon. The paper presents a theoretical explanation of this phenomenon. Numerical experiments confirm theoretical estimates.
Paper's Title:
Some Functional Inequalities for the Geometric Operator Mean
Author(s):
Mustapha Raissouli
Taibah University, Faculty of Sciences,
Department of Mathematics,
Al Madinah Al Munawwarah, P.O.Box 30097,
Kingdom of Saudi Arabia.
Abstract:
In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.
Paper's Title:
New Solutions to Non-Smooth PDEs
Author(s):
Moawia Alghalith
University of the West Indies,
St. Augustine,
Trinidad
Abstract:
We provide strong solutions to partial differential equations when the function is non-differentiable.
Paper's Title:
L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational 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.
E-mail:
saadisamira69@yahoo.fr
allmehri@yahoo.fr
Abstract:
In this work, we study Schwarz method for a class of elliptic quasi-variational 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:
Application of Equivalence Method to Classify Monge-Ampčre Equations of Elliptic Type
Author(s):
Moheddine Imsatfia
E-mail: imsatfia@math.jussieu.fr
Abstract:
In this paper, we apply Cartan's equivalence method to give a local classification of Monge-Ampčre equations of elliptic type. Then we find a necessary and sufficient conditions such that a Monge-Ampčre equation is either contactomorphic to the Laplace equation or to an Euler-Lagrange equation.
Paper's Title:
On the Regularization of Hammerstein's type Operator Equations
Author(s):
E. Prempeh, I. Owusu-Mensah and K. Piesie-Frimpong
Department of Mathematics,
KNUST, Kumasi-
Ghana.
Department of Science Education,
University of Education,
Winneba
Department of Mathematics,
Presbyterian University College, Abetifi,
Ghana
E-mail: isaacowusumensah@gmail.com
E-mail: eprempeh.cos@knust.edu.gh
E-mail: piesie74@yahoo.com
Abstract:
We have studied Regularization of Hammerstein's Type Operator Equations in general Banach Spaces. In this paper, the results have been employed to establish regularized solutions to Hammerstein's type operator equations in Hilbert spaces by looking at three cases of regularization.
Paper's Title:
Asymptotic Analysis of Positive Decreasing Solutions of a Class of Systems of Second Order Nonlinear Differential Equations in the Framework of Regular Variation
Author(s):
Jaroslav Jaroš, Kusano Takaŝi, Tomoyuki Tanigawa
Department of Mathematical Analysis and
Numerical Mathematics,
Faculty of Mathematics, Physics and Informatics,
Comenius Universiy, 842 48 Bratislava,
Slovakia.
E-mail: ksntksjm4@gmail.com
Professor Emeritus at: Hiroshima
University,
Department of Mathematics, Faculty of Science,
Higashi-Hiroshima 739-8526,
Japan.
E-mail: jaros@fmph.uniba.sk
Department of Mathematics, Faculty of
Education,
Kumamoto University, Kumamoto 860-8555,
Japan.
E-mail:
tanigawa@educ.kumamoto-u.ac.jp
Abstract:
The system of nonlinear differential equations
is under consideration, where αi
and βi are positive constants and
pi(t) and qi(t) are continuous regularly varying functions
on [a,∞). Two kinds of criteria are established for
the existence of strongly decreasing regularly varying solutions with negative
indices of (A) with precise asymptotic behavior at infinity. Fixed point
techniques and basic theory of regular variation are utilized for this purpose.
Paper's Title:
New Stochastic Calculus
Author(s):
Moawia Alghalith
Department of Economics,
University of the West Indies, St. Augustine,
Trinidad and Tobago.
E-mail:
malghalith@gmail.com
Abstract:
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Paper's Title:
Credibility Based Fuzzy Entropy Measure
Author(s):
G. Yari, M. Rahimi, B. Moomivand and P. Kumar
Department of Mathematics,
Iran University
of Science and Technology,
Tehran,
Iran.
E-mail:
Yari@iust.ac.ir
E-mail:
Mt_Rahimi@iust.ac.ir
URL:
http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL:
http://webpages.iust.ac.ir/mt_rahimi/en.html
Qarzol-hasaneh
Mehr Iran Bank, Tehran,
Iran.
E-mail:
B.moomivand@qmb.ir
Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
E-mail:
Pranesh.Kumar@unbc.ca
Abstract:
Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.
Paper's Title:
Bilinear Regular Operators on Quasi-Normed Functional Spaces
Author(s):
D. L. Fernandez and E. B. Silva
Universidade Estadual de Campinas -
Unicamp
Instituto de Matematica
Campinas - SP
Brazil.
E-mail: dicesar@ime.unicamp.br
Universidade Estadual de Maringa--UEM
Departamento de Matematica
Av.~Colombo 5790
Maringa - PR
Brazil.
E-mail: ebsilva@uem.br
Abstract:
Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators and their adjoints in normed functional spaces are also studied.
Paper's Title:
New Implicit Kirk-Type Schemes for General Class of Quasi-Contractive Operators in Generalized Convex Metric Spaces
Author(s):
K. Rauf, O. T. Wahab and A. Ali
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail: krauf@unilorin.edu.ng
Department of Statistics and Mathematical
Sciences,
Kwara State University, Malete,
Nigeria.
Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.
Abstract:
In this paper, we introduce some new implicit Kirk-type iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasi-contractive type operators. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.
Paper's Title:
Iterative Approximation of Zeros of Accretive Type Maps, with Applications
Author(s):
Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo
African University of Science and
Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: chinedu.ezea@gmail.com
E-mail: mrzzaka@yahoo.com
Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
E-mail: chinedu.ezea@gmail.com
Ebonyi State University,
Abakaliki,
Nigeria
E-mail: mrzzaka@yahoo.com
Abstract:
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E→ E* be the normalized duality map on E and let A:E*→ E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)-1(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u* in (AJ)-1(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, non-trivial examples of maps A for which AJ is accretive are presented..
Paper's Title:
A Note on Taylor Expansions Without the Differentiability Assumption
Author(s):
Moawia Alghalith
Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.
E-mail: malghalith@gmail.com
Abstract:
We introduce new Taylor expansions when the function is not differentiable.
Retraction
This article has been retracted under the authority of the Editor on Chief on 1 April, 2021. The PDF file is no longer available, but can be obtained from the editorial office upon request.
Paper's Title:
Formulation of Approximate Mathematical Model for Incoming Water to Some Dams on Tigris and Euphrates Rivers Using Spline Function
Author(s):
Nadia M. J. Ibrahem, Heba A. Abd Al-Razak, and Muna M. Mustafa
Mathematics Department,
College of Sciences for Women,
University of Baghdad, Baghdad,
Iraq.
E-mail:
Nadiamj_math@csw.uobaghdad.edu.iq
Abstract:
In this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and Al-Hindya.
Paper's Title:
On the Polyconvolution of Hartley Integral Transforms H1, H2, H1 and Integral Equations
Author(s):
Nguyen Minh Khoa and Dau Xuan Luong
Department of Mathematics,
Electric Power University,
Ha Noi, and Faculty of Fundamental Science,
Ha Long University, Quang Ninh,
Viet Nam.
E-mail: khoanm@epu.edu.vn,
dauxuanluong@gmail.com
Abstract:
In this paper, we construct and study a new polyconvolution * (f,g,h)(x) of functions f, g, h. We will show that the polyconvolution satisfy the following factorization equality
H1[*(f,g,h)](y)=(H2f)(y)(H1g)(y)(H1h)(y), ∀y∈ R.
We prove the existence of this polyconvolution in the space L(R). As examples, applications to solve an integral equation of polyconvolution type and two systems of integral equations of polyconvolution type are presented.
Paper's Title:
Oblique Projectors from the Simpson Discrete Fourier Transformation Matrix
Author(s):
P. Singh and V. Singh
School of Mathematics, Computer Science
and Statistics,
University of Kwazulu-Natal,
Private Bag X54001, Durban 4001,
South Africa.
E-mail: singhp@ukzn.ac.za,
singhv@ukzn.ac.za
Abstract:
In this paper we examine the projectors of the Simpson Discrete Fourier Transform matrix of dimension two modulus four and show how they decompose the complex vector space into a direct sum of oblique eigenspaces. These projection operators are used to define a Simpson Discrete Fractional Fourier Transform (SDFRFT).
Paper's Title:
Several Applications of a Local Non-convex Young-type Inequality
Author(s):
Loredana Ciurdariu, Sorin Lugojan
Department of Mathematics,
"Politehnica" University of Timisoara,
P-ta. Victoriei, No.2, 300006-Timisoara,
Romania.
E-mail: ltirtirau87@yahoo.com
Abstract:
A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.
Paper's Title:
A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces
Author(s):
F. U. Ogbuisi
School of Mathematics, Statistics and
Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng
fudochukwu@yahoo.com
Abstract:
In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.
Paper's Title:
Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3
Author(s):
F. Mofarreh, R. Abdel-Baky and N. Alluhaibi
Mathematical Science Department, Faculty
of Science,
Princess Nourah bint Abdulrahman University
Riyadh 11546,
Saudi Arabia.
E-mail: fyalmofarrah@pnu.edu.sa
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
E-mail: rbaky@live.com
Department of Mathematics Science and
Arts, College Rabigh Campus,
King Abdulaziz University
Jeddah,
Saudi Arabia.
E-mail: nallehaibi@kau.edu.sa
Abstract:
The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.
Paper's Title:
Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers
Author(s):
M. Bustos Gonzalez and A. I. Stan
The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
E-mail:
margarita-bustosgonzalez@uiowa.edu
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
E-mail: stan.7@osu.edu
Abstract:
Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the Fermat-Torricelli point of a triangle.
Paper's Title:
Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators
Author(s):
B. Deruni1, A. S. Hacinliyan1,2, E. Kandiran3, A. C. Keles2, S. Kaouache4, M.-S. Abdelouahab4, N.-E. Hamri4
1Department
of Physics,
University of Yeditepe,
Turkey.
2Department
of Information Systems and Technologies,
University of Yeditepe,
Turkey
3Department
of Software Development,
University of Yeditepe,
Turkey.
4Laboratory
of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.
E-mail:
berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz
Abstract:
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.
Paper's Title:
On Admissible Mapping via Simulation Function
Author(s):
Anantachai Padcharoen and Pakeeta Sukprasert
Department of Mathematics,
Faculty of Science and Technology,
Rambhai Barni Rajabhat University,
Chanthaburi 22000,
Thailand.
E-mail: anantachai.p@rbru.ac.th
Department of Mathematics and Computer Science
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT),
Thanyaburi, Pathumthani 12110,
Thailand.
E-mail: pakeeta_s@rmutt.ac.th
Abstract:
In this paper, we present some fixed point results in complete metric spaces by using generalized admissible mapping embedded in the simulation function. Its applications, Our results used to study the existence problem of nonlinear Hammerstein integral equations.
Paper's Title:
Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings
Author(s):
Mathew Olajiire Aibinu1, Surendra Colin Thakur2, Sibusiso Moyo3
1Institute for Systems Science
& KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
1DSI-NRF
Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: moaibinu@yahoo.com
mathewa@dut.ac.za
2 KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
E-mail: thakur@dut.ac.za
3Institute for Systems Science & Office of the DVC Research,
Innovation & Engagement Milena Court,
Durban University of Technology,
Durban 4000,
South Africa.
E-mail: dvcrie@dut.ac.za
Abstract:
The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μ-strictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.
Paper's Title:
A Review on Minimally Supported Frequency Wavelets
Author(s):
K Pallavi1, M C Lineesh1, A Noufal2
1Department of
Mathematics,
National Institute of Technology Calicut,
Kerala 673601,
India.
E-mail:
pavikrishnakumar@gmail.com
lineesh@nitc.ac.in
2Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
E-mail: noufal@cusat.ac.in
Abstract:
This paper provides a review on Minimally Supported Frequency (MSF) wavelets that includes the construction and characterization of MSF wavelets. The characterization of MSF wavelets induced from an MRA is discussed and the nature of the low-pass filter associated with it is explained. The concept of wavelet set and dimension function is introduced to study this class of wavelets. Along with MSF wavelets, s-elementary wavelets and unimodular wavelets are also considered due to the similarity in definitions. Examples and illustrations are provided for more clarity.
Paper's Title:
On General Class of Nonlinear Contractive Maps and their Performance Estimates
Author(s):
Olalekan Taofeek Wahab and Salaudeen Alaro Musa
Department of Mathematics and
Statistics
Kwara State University, Malete
P. M. B. 1530 Ilorin,
Nigeria.
E-mail: taofeek.wahab@kwasu.edu.ng
Abstract:
This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.
Paper's Title:
A Fuzzy Soft Quotient Topology and Its Properties
Author(s):
Haripamyu, Riri Alfakhriati, Monika Rianti Helmi, Jenizon
Department of Mathematics and Data Science, Andalas University, Padang, Indonesia.
E-mail: haripamyu@sci.unand.ac.id
ririalfakhriati123@gmail.com
monikariantihelmi@sci.unand.ac.id
jenizon@gmail.com
Abstract:
This research is to construct a new topology on fuzzy soft set by using the concept of quotient topology. Then we study the concept of quotient map to define the fuzzy soft quotient map and provide some relevant properties of fuzzy soft quotient map. Furthermore, we give some examples related to fuzzy soft quotient topology and fuzzy soft quotient map to apply some properties of fuzzy soft quotient map.
Paper's Title:
Introducing the Picard-S3 Iteration for Fixed Points
Author(s):
Pravin Singh, Virath Singh and Shivani Singh
University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000
South Africa.
Unisa,
Department of Decision Sciences,
PO Box 392,
Pretoria, 0003
South Africa.
E-mail: singhprook@gmail.com
singhv@ukzn.ac.za
shivstarsingh@gmail.com
Abstract:
In this paper we introduce a three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with other three step iterative methods by examining the speed of convergence. Results are presented in tables to support our conclusion.
Paper's Title:
D-Iterative Method for Solving a Delay Differential Equation and a Two-Point Second-Order Boundary Value Problems in Banach Spaces
Author(s):
Francis Akutsah1, Akindele Adebayo Mebawondu2, Oluwatosin Babasola3, Paranjothi Pillay4 and Ojen Kumar Narain5
1School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
2School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za
3Department
of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY
UK.
E-mail: ob377@bath.ac.uk
4School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: pillaypi@ukzn.ac.za
5School
of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za
Abstract:
The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [2, 3], it further extends and improve some existing results in the literature.
Paper's Title:
Approximately Dual p-Approximate Schauder Frames
Author(s):
K. Mahesh Krishna and P. Sam Johnson
Stat-Math Unit, Indian Statistical
Institute, Bangalore Centre,
Karnataka 560 059
India.
Department of Mathematical and
Computational Sciences,
National Institute of Technology Karnataka (NITK),
Surathkal, Mangaluru 575 025,
India.
E-mail: kmaheshak@gmail.com
sam@nitk.edu.in
Abstract:
Approximately dual frame in Hilbert spaces was introduced by Christensen and Laugesen to overcome difficulties in constructing dual frames for a given Hilbert space frame. It becomes even more difficult in Banach spaces to construct duals. For this purpose, we introduce approximately dual frames for a class of approximate Schauder frames for Banach spaces and develop basic theory. Approximate dual for this subclass is completely characterized and its perturbation is also studied.
Paper's Title:
On Automorphisms and Bi-derivations of Semiprime Rings
Author(s):
Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah
Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com,
ansari.abuzaid@iu.edu.sa
Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com,
fullahkhan@taibahu.edu.sa
Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: Afallatah@taibahu.edu.sa
Abstract:
In this article, our goal is to figure out a functional equation involving automorphisms and bi-derivations on certain semiprime ring. Also, we characterize the structure of automorphism, in case of prime rings.
Paper's Title:
Optimal Conditions using Multi-valued G-Presic type Mapping
Author(s):
Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com
School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in
Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com
Abstract:
In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.
Paper's Title:
A New Look at the Equations of the Calculus of Variations
Author(s):
Olivier de La Grandville
Faculty of Economics, Goethe University
Frankfurt,
Theodore Adorno Platz 4, 60323 Frankfurt,
Germany.
E-mail: odelagrandville@gmail.com
Abstract:
We first offer an entirely new way to derive the celebrated Euler equation of the calculus of variations. The advantage of this approach is two-fold. On the one hand, it entirely eschews the two hurdles encountered by Lagrange, which become challenging in the case of elaborate functionals: getting rid of the arbitrary character of the perturbation given to the optimal function, and demonstrating the fundamental lemma of the calculus of variations. On the other hand, it leads in a direct way to the remarkable discovery made by Robert Dorfman ( 1969) when he introduced a modified Hamiltonian, which we called a Dorfmanian (2018) to honor his memory. In turn, extending the Dorfmanian enables to obtain readily the fundamental equations of the calculus of variations for the optimization of high-order functionals, or multiple integrals.
Paper's Title:
On the Integral Equations via Hartley Superconvolutions
Author(s):
Nguyen Minh Khoa
Department of Mathematics, Electric Power
University,
Ha Noi,
Viet Nam.
E-mail:
khoanm@epu.edu.vn
Abstract:
The new superconvolutions for the Hartley integral transforms are formulated and their properties are studied. Furthermore, we also formulate the Young type theorem for these superconvolutions in the function space Lsαβγ(R) and get its norm estimations. We apply them to solve integral equations and system of integral equations of Toeplitz plus Hankel type.
Paper's Title:
Dyadic Riesz Wavelets on Local Fields of Positive Characteristics
Author(s):
Kartik Garg, Raj Kumar, Satyapriya
Department of Mathematics,
University of Delhi,
Delhi,
India.
kartikgarg1421@gmail.com,
rajkmc@gmail.com
kmc.satyapriya@gmail.com
Abstract:
In this research paper, we introduce a novel theory for the construction of a Riesz wavelet basis in the space L2(K), where K is a local field with positive characteristics. Our approach is two fold: firstly, we derive some essential characterizations of the scaling function associated with the structure of a Riesz MRA on a local field, and secondly, we review existing methods for constructing wavelet frames in L2(K). We also present a well elaborated example for a better comprehension of our theory. Due to mathematical convenience, we limit ourselves to the case of dyadic dilations only.
Paper's Title:
Indonesia's GDP Forecast: Evidence From Fuzzy Time Series Model Using Particle Swarm Optimization Algorithm
Author(s):
Ismail Djakaria1, Djihad Wungguli2, Regina Sugi Pakadang3, Sri Endang Saleh4, Maman Abdurachman Djauhari5
1,2,3Universitas
Negeri Gorontalo,
Department of Statistics, Gorontalo,
Indonesia.
4Universitas Negeri Gorontalo,
Department of Development Economics, Gorontalo,
Indonesia.
5Indonesian Institute of Education,
Jl. Terusan Pahlawan 32, Garut 44151,
Indonesia.
E-mail: iskar@ung.ac.id
URL:
https://orcid.org/0000-0003-1358-2356
Abstract:
Gross Domestic Product (GDP) is a principal indicator used to measure the economic condition of a country. Indonesia's GDP growth from 2017 to 2019 was approximately 6 percent; however, it experienced a decline in 2020 and 2021, with rates of only -0.02 percent and 2.41 percent, respectively. In the process of economic development planning, a forecasting system is required to determine GDP in the future. The forecasting method employed in this research is fuzzy time series optimized using Particle Swarm Optimization (PSO), to enhance the accuracy and convergence of forecasted values. The dataset used comprises secondary data, specifically 54 sets of Indonesian GDP data spanning from the first quarter of 2010 to the second quarter of 2023. The analysis results indicate that the proposed method is better than the conventional fuzzy time series approach. The former method provides a predictive value for one period in the future with a Mean Absolute Percentage Error (MAPE) value of 4.40%. In contrast, the latter yields higher predictive values with a MAPE value of 7.93%.
Paper's Title:
On Saturation of Norm Convergence of Walsh-Fourier Matrix Transform Means
Author(s):
István Blahota
Institute of Mathematics and Computer Sciences,
University of Nyíregyháza,
H-4400 Nyíregyháza,
Sóstói street 31/b,
Hungary
E-mail: blahota.istvan@nye.hu
Abstract:
In this paper we investigate the saturation of norm convergence issues for regular matrix transform means in case of Walsh-Paley system. The main result is the observation of equality ||σTn (f) - f ||p=0(a)n where an sequence of positive numbers tends to zero and there exists constant $c$, for which t1,n≤ can for every n∈P.
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