International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay Mon, 05 Oct 2015 12:25:29 +0000 We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form . Considering a convergent power series of an auxiliary equation with the relation , we obtain an analytic solution . Furthermore, we characterize a polynomial solution when is a polynomial. Jiraphorn Somsuwan and Keaitsuda Maneeruk Nakprasit Copyright © 2015 Jiraphorn Somsuwan and Keaitsuda Maneeruk Nakprasit. All rights reserved. Faber Polynomial Coefficients of Classes of Meromorphic Bistarlike Functions Sun, 04 Oct 2015 09:08:38 +0000 Applying the Faber polynomial coefficient expansions to certain classes of meromorphic bistarlike functions, we demonstrate the unpredictability of their early coefficients and also obtain general coefficient estimates for such functions subject to a given gap series condition. Our results improve some of the coefficient bounds published earlier. Jay M. Jahangiri and Samaneh G. Hamidi Copyright © 2015 Jay M. Jahangiri and Samaneh G. Hamidi. All rights reserved. Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order Sun, 04 Oct 2015 08:50:49 +0000 We generalize the lacunary statistical convergence by introducing the generalized difference operator of fractional order, where is a proper fraction and is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order. Ugur Kadak Copyright © 2015 Ugur Kadak. All rights reserved. Green’s Function for a Slice of the Korányi Ball in the Heisenberg Group Sun, 04 Oct 2015 06:18:11 +0000 We give a representation formula for solution of the inhomogeneous Dirichlet problem on the upper half Korányi ball and for the slice of the Korányi ball in the Heisenberg group by obtaining explicit expressions of Green-like kernel when the given data has certain radial symmetry. Shivani Dubey, Ajay Kumar, and Mukund Madhav Mishra Copyright © 2015 Shivani Dubey et al. All rights reserved. On the Local Minima of the Order of Appearance Function Thu, 01 Oct 2015 16:11:41 +0000 The order of appearance of the positive integer is the smallest positive integer such that divides , the th member of the Fibonacci sequence. In this paper, we improve upon some results from (Marques, 2011) concerning local minima of . Florian Luca and Thato Mosima Copyright © 2015 Florian Luca and Thato Mosima. All rights reserved. Fuzzy -Fold Filters of Pseudoresiduated Lattices Thu, 01 Oct 2015 08:28:37 +0000 Given a pseudoresiduated lattice and a lattice , we introduce and characterize the fuzzy versions of different -fold implicative (resp., obstinate, Boolean, normal, and extended involutive) filters of . Moreover, we study some relationships between these different types of fuzzy -fold filters. Albert Kadji, Celestin Lele, and Marcel Tonga Copyright © 2015 Albert Kadji et al. All rights reserved. A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations Thu, 03 Sep 2015 08:56:02 +0000 We suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale problems (500,000 variables) with lower storage requirement compared to some existing methods. Under appropriate conditions, the global convergence of our method is reported. Numerical results on some benchmark test problems show that the proposed method is practically effective. Mohammed Yusuf Waziri and Jamilu Sabi’u Copyright © 2015 Mohammed Yusuf Waziri and Jamilu Sabi’u. All rights reserved. Certain Properties of -Hypergeometric Functions Thu, 20 Aug 2015 06:37:03 +0000 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 Let be the polynomial algebra in variables , of degree one, over the field of two elements. The mod-2 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 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 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 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 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.