International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Existence Results for Some Equilibrium Problems Involving -Monotone Bifunction Wed, 03 Feb 2016 13:20:03 +0000 This paper deals with some existence results of equilibrium problems on convex and closed sets (either bounded or unbounded) in Banach spaces. Moreover, an application to the existence of solution for a differential inclusion is given. Ayed E. Hashoosh, Mohsen Alimohammady, and M. K. Kalleji Copyright © 2016 Ayed E. Hashoosh et al. All rights reserved. On Graphs of the Cone Decompositions for the Min-Cut and Max-Cut Problems Mon, 01 Feb 2016 14:02:35 +0000 We consider maximum and minimum cut problems with nonnegative weights of edges. We define the graphs of the cone decompositions and find a linear clique number for the min-cut problem and a superpolynomial clique number for the max-cut problem. These values characterize the time complexity in a broad class of algorithms based on linear comparisons. Vladimir Bondarenko and Andrei Nikolaev Copyright © 2016 Vladimir Bondarenko and Andrei Nikolaev. All rights reserved. Characterizations of Regular Ordered Semirings by Ordered Quasi-Ideals Mon, 18 Jan 2016 06:44:38 +0000 We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals. Pakorn Palakawong na Ayutthaya and Bundit Pibaljommee Copyright © 2016 Pakorn Palakawong na Ayutthaya and Bundit Pibaljommee. All rights reserved. Homotopic Chain Maps Have Equal -Homology and -Homology Tue, 05 Jan 2016 13:18:53 +0000 The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and -homologies of homotopic chain maps is established. As a special case, if and are the same homotopy type, then their th -homology -modules are isomorphic, and if is a contractible space, then its th -homology -modules for are trivial. M. Z. Kazemi-Baneh Copyright © 2016 M. Z. Kazemi-Baneh. All rights reserved. -Digit Benford Converges to Benford Tue, 29 Dec 2015 12:46:24 +0000 Using the sum invariance property of Benford random variables, we prove that an -digit Benford variable converges to a Benford variable as approaches infinity. Azar Khosravani and Constantin Rasinariu Copyright © 2015 Azar Khosravani and Constantin Rasinariu. All rights reserved. Metrics on the Sets of Nonsupersingular Elliptic Curves in Simplified Weierstrass Form over Finite Fields of Characteristic Two Mon, 28 Dec 2015 12:43:18 +0000 Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization. Mishra and Gupta (2008) have found an interesting property of the sets of elliptic curves in simplified Weierstrass form (or short Weierstrass form) over prime fields. The property is that one can induce metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. Later, Vetro (2011) has found some other metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. However, to our knowledge, no analogous result is known in the characteristic two case. In this paper, we will prove that one can induce metrics on the sets of nonsupersingular elliptic curves in simplified Weierstrass form over finite fields of characteristic two. Keisuke Hakuta Copyright © 2015 Keisuke Hakuta. All rights reserved. On Generalized Semiderivations of Prime Near Rings Sun, 08 Nov 2015 06:43:00 +0000 Let be a near ring. An additive mapping is said to be a generalized semiderivation on if there exists a semiderivation associated with a function such that and for all . In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring . Abdelkarim Boua, A. Raji, Asma Ali, and Farhat Ali Copyright © 2015 Abdelkarim Boua et al. All rights reserved. Certain Bound for -Starlike and -Convex Functions with respect to Symmetric Points Thu, 29 Oct 2015 07:54:58 +0000 The aim of this paper is to establish the coefficient estimates for the subclasses of -starlike and -convex functions with respect to symmetric points involving -difference operator. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given. C. Ramachandran, D. Kavitha, and T. Soupramanien Copyright © 2015 C. Ramachandran et al. All rights reserved. The Hankel Transform of -Noncentral Bell Numbers Wed, 28 Oct 2015 07:28:59 +0000 We define two forms of -analogue of noncentral Stirling numbers of the second kind and obtain some properties parallel to those of noncentral Stirling numbers. Certain combinatorial interpretation is given for the second form of the -analogue in the context of 0-1 tableaux which, consequently, yields certain additive identity and some convolution-type formulas. Finally, a -analogue of noncentral Bell numbers is defined and its Hankel transform is established. Cristina B. Corcino, Roberto B. Corcino, Jay M. Ontolan, Charrymae M. Perez-Fernandez, and Ednelyn R. Cantallopez Copyright © 2015 Cristina B. Corcino et al. All rights reserved. Recent Trends in Special Numbers and Special Functions and Polynomials Tue, 20 Oct 2015 06:27:02 +0000 Serkan Araci, Mehmet Acikgoz, Cenap Özel, H. M. Srivastava, and Toka Diagana Copyright © 2015 Serkan Araci et al. All rights reserved. The Peak of Noncentral Stirling Numbers of the First Kind Mon, 12 Oct 2015 08:26:59 +0000 We locate the peak of the distribution of noncentral Stirling numbers of the first kind by determining the value of the index corresponding to the maximum value of the distribution. Roberto B. Corcino, Cristina B. Corcino, and Peter John B. Aranas Copyright © 2015 Roberto B. Corcino et al. All rights reserved. A Domain-Specific Architecture for Elementary Function Evaluation Sun, 11 Oct 2015 11:36:15 +0000 We propose a Domain-Specific Architecture for elementary function computation to improve throughput while reducing power consumption as a model for more general applications: support fine-grained parallelism by eliminating branches, and eliminate the duplication required by coprocessors by decomposing computation into instructions which fit existing pipelined execution models and standard register files. Our example instruction architecture (ISA) extension supports scalar and vector/SIMD implementations of table-based methods of calculating all common special functions, with the aim of improving throughput by (1) eliminating the need for tables in memory, (2) eliminating all branches for special cases, and (3) reducing the total number of instructions. Two new instructions are required, a table lookup instruction and an extended-precision floating-point multiply-add instruction with special treatment for exceptional inputs. To estimate the performance impact of these instructions, we implemented them in a modified Cell/B.E. SPU simulator and observed an average throughput improvement of 2.5 times for optimized loops mapping single functions over long vectors. Anuroop Sharma and Christopher Kumar Anand Copyright © 2015 Anuroop Sharma and Christopher Kumar Anand. All rights reserved. Explicit Formulas for Meixner Polynomials Sun, 11 Oct 2015 09:51:32 +0000 Using notions of composita and composition of generating functions, we show an easy way to obtain explicit formulas for some current polynomials. Particularly, we consider the Meixner polynomials of the first and second kinds. Dmitry V. Kruchinin and Yuriy V. Shablya Copyright © 2015 Dmitry V. Kruchinin and Yuriy V. Shablya. 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.