International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument Wed, 15 Jul 2015 06:38:37 +0000 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 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 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 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 Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes Mon, 15 Jun 2015 06:25:17 +0000 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 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 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 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 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 Meza-Moreno and Mario Pineda-Ruelas Copyright © 2015 Rocío Meza-Moreno and Mario Pineda-Ruelas. All rights reserved. Some Results on Generalized -Derivations in -Prime Rings Tue, 28 Apr 2015 10:26:32 +0000 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 Pre-Schwarzian Norm Estimate for Analytic Concave Functions Wed, 15 Apr 2015 11:26:24 +0000 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 pre-Schwarzian 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 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. PS-Modules over Ore Extensions and Skew Generalized Power Series Rings Mon, 23 Mar 2015 13:18:24 +0000 A right -module is called a PS-module if its socle, , is projective. We investigate PS-modules 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 PS-module, then is a right PS-module. (2) If is a right PS-module, then is a right PS-module. Refaat M. Salem, Mohamed A. Farahat, and Hanan Abd-Elmalk Copyright © 2015 Refaat M. Salem et al. All rights reserved. On the -Version of the Schwab-Borchardt Mean II Mon, 16 Mar 2015 16:22:49 +0000 This paper deals with the -version of the Schwab-Borchardt 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 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 We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration 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 well-known 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/BCK-Algebras Tue, 03 Mar 2015 08:42:06 +0000 We introduce the concept of neutrosophic BCI/BCK-algebras. 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 Order-Preserving Transformations with Restricted Range Thu, 19 Feb 2015 06:54:50 +0000 Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving 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 We propose a system of partial differential equations with a single constant delay describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of . For an initial-boundary value problem associated with this system, we prove a well-posedness 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 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 Morán-Vásquez, 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 The aim of this paper is to present common fixed point results of quasi-weak 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 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 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. Complexity-Based Modeling of Scientific Capital: An Outline of Mathematical Theory Thu, 30 Oct 2014 11:17:56 +0000 The paper intends to contribute to a better understanding of the phenomenon of scientific capital. Scientific capital is a well-known 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 so-called 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 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. Erratum to “The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications” Tue, 30 Sep 2014 12:14:47 +0000 Shao-Wen Yu Copyright © 2014 Shao-Wen Yu. All rights reserved. On Maps of Period 2 on Prime and Semiprime Rings Mon, 22 Sep 2014 08:47:39 +0000 A map f of the ring R into itself is of period 2 if for all ; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings. H. E. Bell and M. N. Daif Copyright © 2014 H. E. Bell and M. N. Daif. All rights reserved. When an Extension of Nagata Rings Has Only Finitely Many Intermediate Rings, Each of Those Is a Nagata Ring Tue, 02 Sep 2014 11:24:08 +0000 Let be an extension of commutative rings, with X an indeterminate, such that the extension of Nagata rings has FIP (i.e., has only finitely many -subalgebras). Then, the number of -subalgebras of equals the number of R-subalgebras of S. In fact, the function from the set of R-subalgebras of S to the set of -subalgebras of given by is an order-isomorphism. David E. Dobbs, Gabriel Picavet, and Martine Picavet-L’Hermitte Copyright © 2014 David E. Dobbs et al. All rights reserved. Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics Thu, 14 Aug 2014 09:06:09 +0000 We show the interest of nonparametric methods taking into account the boundary correction techniques for a numerical evaluation of an approximation error between the stationary distributions of and queueing systems, when the density function of the general arrivals law in the system is unknown and defined on a bounded support. To compute this error, we use two kinds of norms: the norm and the weight norm. Numerical examples based on simulation studies are presented for the two cases of considered norms. A comparative study of the results has been provided. Aïcha Bareche and Djamil Aïssani Copyright © 2014 Aïcha Bareche and Djamil Aïssani. All rights reserved. Solving Fuzzy Multiproduct Aggregate Production Planning Problems Based on Extension Principle Sun, 03 Aug 2014 10:42:36 +0000 Aggregate production planning (APP) plays a critical role in supply chain management (SCM). This paper investigates multiproduct, multiperiod APP problems with several distinct types of fuzzy uncertainties. In contrast to the existing studies, the modelling in this work conserves the fuzziness such that the obtained APP is more effective. Based on Zadeh’s extension principle, the results obtained are fuzzy solutions described by membership functions, in contrast to results from previous studies. A pair of two-level parametric mathematical programs is formulated to calculate the lower and upper bounds of the optimum fuzzy performance measure. The membership function of the fuzzy total cost is constructed by enumerating various possibility levels. A case studied in previous research is investigated to demonstrate the validity of the proposed model and solution procedure. Because the optimal objective value and associated decision variables are expressed using fuzzy numbers rather than crisp values, the proposed approach is able to represent APP systems more accurately, and therefore, the results obtained can provide decision makers with more effective and informative APPs and more chance to achieve the optimal disaggregate plan. Shih-Pin Chen and Wen-Lung Huang Copyright © 2014 Shih-Pin Chen and Wen-Lung Huang. All rights reserved.