International Journal of Mathematics and Mathematical Sciences
http://www.hindawi.com
The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

Certain Properties of Hypergeometric Functions
Thu, 20 Aug 2015 06:37:03 +0000
http://www.hindawi.com/journals/ijmms/2015/489218/
The quotients of certain hypergeometric functions are presented as fractions which converge uniformly in the unit disc. These results lead to the existence of certain hypergeometric functions in the class of either convex functions, , or starlike functions .
Uzoamaka A. Ezeafulukwe and Maslina Darus
Copyright © 2015 Uzoamaka A. Ezeafulukwe and Maslina Darus. All rights reserved.

Some Relations between Admissible Monomials for the Polynomial Algebra
Thu, 13 Aug 2015 16:00:06 +0000
http://www.hindawi.com/journals/ijmms/2015/235806/
Let be the polynomial algebra in variables , of degree one, over the field of two elements. The mod2 Steenrod algebra acts on according to well known rules. A major problem in algebraic topology is of determining , the image of the action of the positively graded part of . We are interested in the related problem of determining a basis for the quotient vector space . has been explicitly calculated for but problems remain for . Both and are graded, where denotes the set of homogeneous polynomials of degree . In this paper, we show that if is an admissible monomial (i.e., meets a criterion to be in a certain basis for ), then, for any pair of integers (), , and , the monomial is admissible. As an application we consider a few cases when .
Mbakiso Fix Mothebe and Lafras Uys
Copyright © 2015 Mbakiso Fix Mothebe and Lafras Uys. All rights reserved.

Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients
Sun, 09 Aug 2015 14:28:17 +0000
http://www.hindawi.com/journals/ijmms/2015/261370/
We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the form , where is a sequence of standard Gaussian random variables, is . It is shown that the asymptotic value of expected number of times the polynomial crosses the level is also as long as does not exceed , where . The number of oscillations of about will be less than asymptotically only if , where or . In the former case the number of oscillations continues to be a fraction of and decreases with the increase in value of . In the latter case, the number of oscillations reduces to and almost no trace of the curve is expected to be present above the level if log .
Mina Ketan Mahanti, Amandeep Singh, and Lokanath Sahoo
Copyright © 2015 Mina Ketan Mahanti et al. All rights reserved.

Some Applications of New Modified Integral Type Operators
Mon, 03 Aug 2015 13:20:30 +0000
http://www.hindawi.com/journals/ijmms/2015/874178/
We introduce a new sequence of integral operators. We show that it is a weighted
approximation process in the polynomial space of continuous functions defined on unit interval. Weighted
statistical approximation theorem, Korovkin type theorems for fuzzy continuous functions, and an estimate for
the rate of convergence for these operators.
R. P. Pathak and Shiv Kumar Sahoo
Copyright © 2015 R. P. Pathak and Shiv Kumar Sahoo. All rights reserved.

Vehicle Routing Problem for Multiple Product Types, Compartments, and Trips with Soft Time Windows
Wed, 29 Jul 2015 15:59:06 +0000
http://www.hindawi.com/journals/ijmms/2015/126754/
This paper presents a mathematical model to solve the vehicle routing problem with soft time windows (VRPSTW) and distribution of products with multiple categories. In addition, we include multiple compartments and trips. Each compartment is dedicated to a single type of product. Each vehicle is allowed to have more than one trip, as long as it corresponds to the maximum distance allowed in a workday. Numerical results show the effectiveness of our model.
P. Kabcome and T. Mouktonglang
Copyright © 2015 P. Kabcome and T. Mouktonglang. All rights reserved.

Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument
Wed, 15 Jul 2015 06:38:37 +0000
http://www.hindawi.com/journals/ijmms/2015/828952/
Existence criteria are derived for the eventually periodic solutions of a class of differential equations with piecewise constant argument whose solutions at consecutive integers satisfy nonlinear recurrence relations. The proof characterizes the initial values of periodic solutions in terms of the coefficients of the resulting difference equations. Sufficient conditions for the unboundedness, boundedness, and symmetry of general solutions also follow from the corresponding properties of the difference
equations.
James Guyker
Copyright © 2015 James Guyker. All rights reserved.

A Direct Proof of a Theorem concerning Treed Overrings
Wed, 08 Jul 2015 09:42:10 +0000
http://www.hindawi.com/journals/ijmms/2015/938648/
We improve and provide a direct proof of a theorem that answered a question by Dobbs about treed overrings. More precisely, we show that if is an integrally closed local domain and each of its proper overrings is treed, then is a valuation domain or is a PVD with associated valuation overring such that .
Ahmed Ayache
Copyright © 2015 Ahmed Ayache. All rights reserved.

On the Level Set of a Function with Degenerate Minimum Point
Wed, 08 Jul 2015 06:04:22 +0000
http://www.hindawi.com/journals/ijmms/2015/493217/
For , let be an dimensional smooth closed manifold and a smooth function. We set and assume that is attained by unique point such that is a nondegenerate critical point. Then the Morse lemma tells us that if is slightly bigger than , is diffeomorphic to . In this paper, we relax the condition on from being nondegenerate to being an isolated critical point and obtain the same consequence. Some application to the topology of polygon spaces is also included.
Yasuhiko Kamiyama
Copyright © 2015 Yasuhiko Kamiyama. All rights reserved.

On Partial Sum of Tribonacci Numbers
Mon, 15 Jun 2015 13:19:17 +0000
http://www.hindawi.com/journals/ijmms/2015/301814/
We study the sum of step apart Tribonacci numbers for any . We prove that satisfies certain Tribonacci rule with integers , and .
Eunmi Choi and Jiin Jo
Copyright © 2015 Eunmi Choi and Jiin Jo. All rights reserved.

Comparative Study of Generalized QuantitativeQualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes
Mon, 15 Jun 2015 06:25:17 +0000
http://www.hindawi.com/journals/ijmms/2015/258675/
In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of order and type for 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.
H. D. Arora and Anjali Dhiman
Copyright © 2015 H. D. Arora and Anjali Dhiman. All rights reserved.

Lower Bounds on Solutions of Quadratic Polynomials Defined over Finite Rings
Wed, 10 Jun 2015 13:31:00 +0000
http://www.hindawi.com/journals/ijmms/2015/305730/
Let be a positive integer and let denote the ring , and let denote the Cartesian product of copies of . Let be a quadratic polynomial in . In this paper, we are interested in giving lower bounds on the number of solutions of the quadratic polynomial over the ring .
Ali H. Hakami
Copyright © 2015 Ali H. Hakami. All rights reserved.

Smooth Points in Some Banach Spaces
Tue, 26 May 2015 12:22:17 +0000
http://www.hindawi.com/journals/ijmms/2015/394282/
We characterize the smooth points in some Banach spaces. We will deal with injective tensor product, the Bochner space of (equivalence classes of) essentially bounded measurable valued functions, and direct sums of Banach spaces.
A. Saleh Hamarsheh
Copyright © 2015 A. Saleh Hamarsheh. All rights reserved.

On Choosability of Vertex Graphs
Tue, 12 May 2015 12:04:21 +0000
http://www.hindawi.com/journals/ijmms/2015/690517/
A list assignment of a graph is a mapping which assigns a set of size to each vertex of and . A graph is choosable if has a proper coloring such that for each list assignment . In 2011, Charoenpanitseri et al. gave a characterization of choosability of vertex graphs when and left open problems when . Recently, Ruksasakchai and Nakprasit obtain the results when . In this paper, we extend the results to case .
Wongsakorn Charoenpanitseri
Copyright © 2015 Wongsakorn Charoenpanitseri. All rights reserved.

Counting Quadratic Nonresidues in Shifted Subsets of the Set of Quadratic Nonresidues for Primes
Thu, 30 Apr 2015 19:43:14 +0000
http://www.hindawi.com/journals/ijmms/2015/163092/
Let be a prime number and the finite field with elements. For , will denote the set of quadratic nonresidues less than or equal to . In this work we calculate the number of quadratic nonresidues in the shifted set .
Rocío MezaMoreno and Mario PinedaRuelas
Copyright © 2015 Rocío MezaMoreno and Mario PinedaRuelas. All rights reserved.

Some Results on Generalized Derivations in
Prime Rings
Tue, 28 Apr 2015 10:26:32 +0000
http://www.hindawi.com/journals/ijmms/2015/583050/
We extend some well known commutativity results
concerning a nonzero square closed Lie ideal and generalized derivations of prime rings.
Muhammad Anwar Chaudhry, Öznur Gölbaşi, and Emine Koç
Copyright © 2015 Muhammad Anwar Chaudhry et al. All rights reserved.

The PreSchwarzian Norm Estimate for Analytic Concave Functions
Wed, 15 Apr 2015 11:26:24 +0000
http://www.hindawi.com/journals/ijmms/2015/814805/
Let denote the open unit disk and let denote the class of normalized univalent functions which are analytic in . Let be the class of concave functions , which have the condition that the opening angle of at infinity is less than or equal to , . In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the class . And we define a class , , which is a subclass of and we find the set of variabilities for the functional for . This gives sharp upper and lower estimates for the preSchwarzian norm of functions in . We also give a characterization for functions in in terms of Hadamard product.
Young Jae Sim and Oh Sang Kwon
Copyright © 2015 Young Jae Sim and Oh Sang Kwon. All rights reserved.

Possibility Intuitionistic Fuzzy Soft Expert Set Theory and Its Application in Decision Making
Tue, 07 Apr 2015 16:31:22 +0000
http://www.hindawi.com/journals/ijmms/2015/314285/
We propose the theory of possibility intuitionistic fuzzy soft expert theory and define some related concepts pertaining to this notion as well as the basic operations on this concept, namely, the complement, union, intersection, AND, and OR. The basic properties and relevant laws pertaining to this concept such as De Morgan’s laws are proved. Lastly, a generalized algorithm is introduced and applied to the concept of possibility intuitionistic fuzzy soft expert sets in hypothetical decision making problem.
Ganeshsree Selvachandran and Abdul Razak Salleh
Copyright © 2015 Ganeshsree Selvachandran and Abdul Razak Salleh. All rights reserved.

PSModules over Ore Extensions and Skew Generalized Power Series Rings
Mon, 23 Mar 2015 13:18:24 +0000
http://www.hindawi.com/journals/ijmms/2015/879129/
A right module is called a PSmodule if its socle, , is projective. We investigate PSmodules over Ore extension and skew generalized power series extension. Let be an associative ring with identity, a unitary right module, Ore extension, a right module, a strictly ordered additive monoid, a monoid homomorphism, the skew generalized power series ring, and the skew generalized power series module. Then, under some certain conditions, we prove the following: (1) If is a right PSmodule, then is a right PSmodule. (2) If is a right PSmodule, then is a right PSmodule.
Refaat M. Salem, Mohamed A. Farahat, and Hanan AbdElmalk
Copyright © 2015 Refaat M. Salem et al. All rights reserved.

On the Version of the SchwabBorchardt Mean II
Mon, 16 Mar 2015 16:22:49 +0000
http://www.hindawi.com/journals/ijmms/2015/351742/
This paper deals with the version of the SchwabBorchardt mean. Lower and upper bounds for this mean, expressed in terms of the weighted geometric and arithmetic means of its variables, are obtained. Applications to four bivariate means, introduced earlier by the author of this paper, are included.
Edward Neuman
Copyright © 2015 Edward Neuman. All rights reserved.

Quantum Product of Symmetric Functions
Wed, 11 Mar 2015 14:30:10 +0000
http://www.hindawi.com/journals/ijmms/2015/476926/
We provide an explicit description of the quantum product of multisymmetric functions using the elementary multisymmetric functions introduced by Vaccarino.
Rafael Díaz and Eddy Pariguan
Copyright © 2015 Rafael Díaz and Eddy Pariguan. All rights reserved.

Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces
Thu, 05 Mar 2015 11:50:38 +0000
http://www.hindawi.com/journals/ijmms/2015/368204/
We prove strong and Δconvergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using Siteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several wellknown results in Banach spaces as well as CAT(0) spaces.
Jong Kyu Kim, Ramesh Prasad Pathak, Samir Dashputre, Shailesh Dhar Diwan, and Rajlaxmi Gupta
Copyright © 2015 Jong Kyu Kim et al. All rights reserved.

Introduction to Neutrosophic BCI/BCKAlgebras
Tue, 03 Mar 2015 08:42:06 +0000
http://www.hindawi.com/journals/ijmms/2015/370267/
We introduce the concept of neutrosophic BCI/BCKalgebras. Elementary properties of neutrosophic BCI/BCK algebras are presented.
A. A. A. Agboola and B. Davvaz
Copyright © 2015 A. A. A. Agboola and B. Davvaz. All rights reserved.

A Note on Isomorphism Theorems for Semigroups of OrderPreserving Transformations with Restricted Range
Thu, 19 Feb 2015 06:54:50 +0000
http://www.hindawi.com/journals/ijmms/2015/187026/
Finding necessary and sufficient conditions for isomorphism between two semigroups of orderpreserving transformations over an infinite domain with restricted range was an open problem. In this paper, we show a proof strategy to answer that question.
Phichet Jitjankarn and Thitarie Rungratgasame
Copyright © 2015 Phichet Jitjankarn and Thitarie Rungratgasame. All rights reserved.

Solving the Linear 1D Thermoelasticity Equations with Pure Delay
Wed, 04 Feb 2015 08:24:20 +0000
http://www.hindawi.com/journals/ijmms/2015/479267/
We propose a system of partial differential equations with a single constant delay describing the behavior of a onedimensional thermoelastic solid occupying a bounded interval of . For an initialboundary value problem associated with this system, we prove a wellposedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as . Finally, we deduce an explicit solution representation for the delay problem.
Denys Ya. Khusainov and Michael Pokojovy
Copyright © 2015 Denys Ya. Khusainov and Michael Pokojovy. All rights reserved.

Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions
Tue, 20 Jan 2015 06:51:55 +0000
http://www.hindawi.com/journals/ijmms/2015/190723/
Hypergeometric functions of matrix arguments occur frequently in multivariate statistical analysis. In this paper, we define and study extended forms of Gauss and confluent hypergeometric functions of matrix arguments and show that they occur naturally in statistical distribution theory.
Daya K. Nagar, Raúl Alejandro MoránVásquez, and Arjun K. Gupta
Copyright © 2015 Daya K. Nagar et al. All rights reserved.

Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application
Mon, 12 Jan 2015 12:03:30 +0000
http://www.hindawi.com/journals/ijmms/2015/218683/
The aim of this paper is to present common fixed point results
of quasiweak commutative mappings on a closed ball in the framework of
multiplicative metric spaces. Example is presented to support the result proved
herein. We also study sufficient conditions for the existence of a common
solution of multiplicative boundary value problem. Our results extend and
improve various recent results in the existing literature.
Mujahid Abbas, Bashir Ali, and Yusuf I. Suleiman
Copyright © 2015 Mujahid Abbas et al. All rights reserved.

Retracted: Some Properties of Fuzzy Quasimetric Spaces
Thu, 08 Jan 2015 11:14:40 +0000
http://www.hindawi.com/journals/ijmms/2015/382903/
International Journal of Mathematics and Mathematical Sciences
Copyright © 2015 International Journal of Mathematics and Mathematical Sciences. All rights reserved.

On the Projective Description of Weighted (LF)Spaces of Continuous Functions
Wed, 19 Nov 2014 00:00:00 +0000
http://www.hindawi.com/journals/ijmms/2014/809584/
We solve the problem of the topological or algebraic description of countable inductive limits of weighted Fréchet spaces of continuous functions on a cone. This problem is investigated for two families of weights defined by positively homogeneous functions. Weights of this form play the important role in Fourier analysis.
Catherine V. Komarchuk and Sergej N. Melikhov
Copyright © 2014 Catherine V. Komarchuk and Sergej N. Melikhov. All rights reserved.

ComplexityBased Modeling of Scientific Capital: An Outline of Mathematical Theory
Thu, 30 Oct 2014 11:17:56 +0000
http://www.hindawi.com/journals/ijmms/2014/785058/
The paper intends to contribute to a better understanding of the phenomenon of scientific capital. Scientific capital is a wellknown concept for
measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which the scientific capital is addressed. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested microvariational principle is based upon postulate, which affirms that (under suitable conditions) the observed state of the agent in scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According to the considered macrovariational principle, the actual state of scientific field makes socalled energy functional (which is associated with the distribution of scientific capital) minimal.
Yurij L. Katchanov and Natalia A. Shmatko
Copyright © 2014 Yurij L. Katchanov and Natalia A. Shmatko. All rights reserved.

Some Condition for Scalar and Vector Measure Games to Be Lipschitz
Wed, 01 Oct 2014 07:53:11 +0000
http://www.hindawi.com/journals/ijmms/2014/849685/
We provide a characterization for vector measure games in , with vector of nonatomic probability measures, analogous to the one of Tauman for games in , and also provide a necessary and sufficient condition for a particular class of vector measure games to belong to .
F. Centrone and A. Martellotti
Copyright © 2014 F. Centrone and A. Martellotti. All rights reserved.