Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Note on Lax Pairs of the Sawada-Kotera Equation Sun, 24 Aug 2014 12:04:31 +0000 We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to each other if and only if the spectral parameter is nonzero, while for zero spectral parameter a nongauge transformation is required. Sergei Sakovich Copyright © 2014 Sergei Sakovich. All rights reserved. On Some Grüss-Type Fractional Inequalities Using Saigo Fractional Integral Operator Sun, 24 Aug 2014 09:44:14 +0000 The main aim of this paper is to establish some new fractional integral inequalities of Grüss-type via the Saigo fractional integral operator. Vaijanath L. Chinchane and Deepak B. Pachpatte Copyright © 2014 Vaijanath L. Chinchane and Deepak B. Pachpatte. All rights reserved. On Iterated Entire Functions with ()th Order Sun, 17 Aug 2014 00:00:00 +0000 We prove some results relating to the comparative growth properties of iterated entire functions using (p, q)th order ((p, q)th lower order). Sanjib Kumar Datta, Tanmay Biswas, and Chinmay Biswas Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved. Associate, Hyperdomainlike, and Presimplifiable Hyperrings Thu, 14 Aug 2014 13:27:03 +0000 Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented. Agboola Adesina Abdul Akeem and Davvaz Bijan Copyright © 2014 Agboola Adesina Abdul Akeem and Davvaz Bijan. All rights reserved. A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications Wed, 13 Aug 2014 13:04:03 +0000 We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals. Hui Bao and Xingdi Chen Copyright © 2014 Hui Bao and Xingdi Chen. All rights reserved. Solving Systems of Volterra Integral and Integrodifferential Equations with Proportional Delays by Differential Transformation Method Tue, 12 Aug 2014 09:17:18 +0000 In this paper, the differential transformation method is applied to the system of Volterra integral and integrodifferential equations with proportional delays. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series forms. If the solutions of the problem can be expanded to Taylor series, then the method gives opportunity to determine the coefficients of Taylor series. Hence, the exact solution can be obtained in Taylor series form. In illustrative examples, the method is applied to a few types of systems. Şuayip Yüzbaşı and Nurbol Ismailov Copyright © 2014 Şuayip Yüzbaşı and Nurbol Ismailov. All rights reserved. Complete Invariance Property with respect to Homeomorphism over Frame Multiwavelet and Super-Wavelet Spaces Mon, 04 Aug 2014 08:27:23 +0000 We discuss the complete invariance property with respect to homeomorphism (CIPH) over various sets of wavelets containing all orthonormal multiwavelets, all tight frame multiwavelets, all super-wavelets of length n, and all normalized tight super frame wavelets of length n. Saurabh Chandra Maury Copyright © 2014 Saurabh Chandra Maury. All rights reserved. Harmonic Subtangent Structures Thu, 24 Jul 2014 00:00:00 +0000 The concept of harmonic subtangent structures on almost subtangent metric manifolds is introduced and a Bochner-type formula is proved for this case. Conditions for a subtangent harmonic structure to be preserved by harmonic maps are also given. Adara M. Blaga Copyright © 2014 Adara M. Blaga. All rights reserved. Remarks on Homogeneous Al-Salam and Carlitz Polynomials Thu, 17 Jul 2014 08:15:02 +0000 Several multilinear generating functions of the homogeneous Al-Salam and Carlitz polynomials are derived from -operator. In addition, two interesting relationships of product of this kind of polynomials are obtained. Jian-Ping Fang Copyright © 2014 Jian-Ping Fang. All rights reserved. On Generalized Derivations of BCI-Algebras and Their Properties Wed, 16 Jul 2014 12:03:00 +0000 We introduce the concept of -derivations of BCI-algebras and we investigate some fundamental properties and establish some results on -derivations. Also, we treat to generalization of right derivation and left derivation of BCI-algebras and consider some related properties. L. Kamali Ardekani and B. Davvaz Copyright © 2014 L. Kamali Ardekani and B. Davvaz. All rights reserved. Novel Properties of Fuzzy Labeling Graphs Wed, 09 Jul 2014 00:00:00 +0000 The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle. Some properties related to fuzzy bridge and fuzzy cut node have also been discussed. A. Nagoor Gani, Muhammad Akram, and D. Rajalaxmi (a) Subahashini Copyright © 2014 A. Nagoor Gani et al. All rights reserved. Asymptotic Law of the th Records in the Bivariate Exponential Case Tue, 08 Jul 2014 07:17:56 +0000 We consider a sequence of independent and identically distributed random variables with joint cumulative distribution , which has exponential marginals and with parameter . We also assume that , , and . We denote and by the sequences of the th records in the sequences , , respectively. The main result of of the paper is to prove the asymptotic independence of and using the property of stopping time of the th record times and that of the exponential distribution. Grine Azedine Copyright © 2014 Grine Azedine. All rights reserved. Startpoints and -Contractions in Quasi-Pseudometric Spaces Wed, 02 Jul 2014 09:34:29 +0000 We introduce the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued maps. Yaé Ulrich Gaba Copyright © 2014 Yaé Ulrich Gaba. All rights reserved. Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales Tue, 01 Jul 2014 09:19:19 +0000 Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equation . In order to improve the error estimate available by Vasin and George (2013), in the present paper we extend the iterative method considered by Vasin and George (2013), in the setting of Hilbert scales. The error estimates obtained under a general source condition on ( is the initial guess and is the actual solution), using the adaptive scheme proposed by Pereverzev and Schock (2005), are of optimal order. The algorithm is applied to numerical solution of an integral equation in Numerical Example section. Monnanda Erappa Shobha and Santhosh George Copyright © 2014 Monnanda Erappa Shobha and Santhosh George. All rights reserved. Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions Thu, 19 Jun 2014 08:32:34 +0000 A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given. İmdat İşcan Copyright © 2014 İmdat İşcan. All rights reserved. Euler Type Integrals and Integrals in Terms of Extended Beta Function Thu, 12 Jun 2014 00:00:00 +0000 We derive the evaluations of certain integrals of Euler type involving generalized hypergeometric series. Further, we establish a theorem on extended beta function, which provides evaluation of certain integrals in terms of extended beta function and certain special polynomials. The possibility of extending some of the derived results to multivariable case is also investigated. Subuhi Khan and Mustafa Walid Al-Saad Copyright © 2014 Subuhi Khan and Mustafa Walid Al-Saad. All rights reserved. Inclusion Properties of Certain Subclasses of -Valent Functions Associated with the Integral Operator Thu, 29 May 2014 06:03:29 +0000 The purpose of the present paper is to introduce two subclasses of -valent functions by using the integral operator and to investigate various properties for these subclasses. Tamer M. Seoudy Copyright © 2014 Tamer M. Seoudy. All rights reserved. Shape Preserving Properties for -Bernstein-Stancu Operators Mon, 05 May 2014 06:43:22 +0000 We investigate shape preserving for -Bernstein-Stancu polynomials introduced by Nowak in 2009. When , reduces to the well-known -Bernstein polynomials introduced by Phillips in 1997; when , reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; when , , we obtain classical Bernstein polynomials. We prove that basic basis is a normalized totally positive basis on and -Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on . Yali Wang and Yinying Zhou Copyright © 2014 Yali Wang and Yinying Zhou. All rights reserved. Some Relations between Certain Complex Equations and Nonnormalized Meromorphic Functions Tue, 08 Apr 2014 07:20:37 +0000 The purpose of this investigation is first to reveal some relations between certain complex (differential) equations and nonnormalized meromorphic functions and then to point some of their useful consequences out. Hüseyin Irmak Copyright © 2014 Hüseyin Irmak. All rights reserved. Odd Jacobi Manifolds and Loday-Poisson Brackets Mon, 07 Apr 2014 11:48:45 +0000 We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi structure and the Loday-Poisson structure. Furthermore, we show that the Loday-Poisson bracket satisfies the Leibniz rule over the noncommutative product derived from the homological vector field. Andrew James Bruce Copyright © 2014 Andrew James Bruce. All rights reserved. Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters Sun, 06 Apr 2014 06:06:36 +0000 By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of  -dimension periodic impulsive functional differential equations with multiple delays and two parameters: ), a.e., , , , , , and ), a.e., , , , , , As an application, we study some special cases of the previous systems, which have been studied extensively in the literature. Zhenguo Luo Copyright © 2014 Zhenguo Luo. All rights reserved. A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization Thu, 03 Apr 2014 13:33:31 +0000 A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved. Zhijun Luo and Lirong Wang Copyright © 2014 Zhijun Luo and Lirong Wang. All rights reserved. Essential Self-Adjointness of Anticommutative Operators Thu, 27 Mar 2014 12:47:23 +0000 The self-adjoint extensions of symmetric operators satisfying anticommutation relations are considered. It is proven that an anticommutative type of the Glimm-Jaffe-Nelson commutator theorem follows. Its application to an abstract Dirac operator is also considered. Toshimitsu Takaesu Copyright © 2014 Toshimitsu Takaesu. All rights reserved. Dynamics of a Beddington-DeAngelis Type Predator-Prey Model with Impulsive Effect Tue, 24 Dec 2013 18:23:39 +0000 In view of the logical consistence, the model of a two-prey one-predator system with Beddington-DeAngelis functional response and impulsive control strategies is formulated and studied systematically. By using the Floquet theory of impulsive equation, small amplitude perturbation method, and comparison technique, we obtain the conditions which guarantee the global asymptotic stability of the two-prey eradication periodic solution. We also proved that the system is permanent under some conditions. Numerical simulations find that the system appears the phenomenon of competition exclusion. Sun Shulin and Guo Cuihua Copyright © 2013 Sun Shulin and Guo Cuihua. All rights reserved. On the Existence of Strongly Consistent Indirect Estimators When the Binding Function Is Compact Valued Sun, 10 Nov 2013 13:20:39 +0000 We provide sufficient conditions for the definition and the existence of strongly consistent indirect estimators when the binding function is a compact valued correspondence. We use conditions that concern the asymptotic behavior of the epigraphs of the criteria involved, a relevant notion of continuity for the binding correspondence as well as an indirect identification condition that restricts the behavior of the aforementioned correspondence. These are generalizations of the analogous results in the relevant literature and hence permit a broader scope of statistical models. We examine simple examples involving Levy and ergodic conditionally heteroskedastic processes. Stelios Arvanitis Copyright © 2013 Stelios Arvanitis. All rights reserved. Common Fixed Point Theorems of Multivalued Maps in Fuzzy Ultrametric Spaces Sat, 02 Nov 2013 13:29:19 +0000 In the setting of fuzzy ultrametric spaces, we study common fixed point theorems of multivalued maps. Our results unify, extend, and generalize some related common fixed point theorems of the literature for both ultrametric spaces (Wang and Song (2013), Gajić (2002) and (2001)) and fuzzy metric spaces (Vijayaraju and Sajath (2011)). A. F. Sayed Copyright © 2013 A. F. Sayed. All rights reserved. Metric Divergence Measures and Information Value in Credit Scoring Tue, 29 Oct 2013 13:25:34 +0000 Recently, a series of divergence measures have emerged from information theory and statistics and numerous inequalities have been established among them. However, none of them are a metric in topology. In this paper, we propose a class of metric divergence measures, namely, , and study their mathematical properties. We then study an important divergence measure widely used in credit scoring, called information value. In particular, we explore the mathematical reasoning of weight of evidence and suggest a better alternative to weight of evidence. Finally, we propose using as alternatives to information value to overcome its disadvantages. Guoping Zeng Copyright © 2013 Guoping Zeng. All rights reserved. Two Parameters Deformations of Ninth Peregrine Breather Solution of the NLS Equation and Multi-Rogue Waves Thu, 24 Oct 2013 08:36:43 +0000 This paper is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and their deformations. Here we construct Peregrine breathers of order and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given. Pierre Gaillard Copyright © 2013 Pierre Gaillard. All rights reserved. The Concentration Function Problem for Locally Compact Groups Revisited: Nondissipating Space-Time Random Walks, -Decomposable Laws, and Their Continuous Time Analogues Wed, 23 Oct 2013 08:24:36 +0000 The concentration function problem for locally compact groups is concerned with the structure of groups admitting adapted nondissipating random walks. It is closely related to discrete relatively compact M- or skew convolution semigroups and corresponding space-time random walks, and to -decomposable laws, respectively, where denotes an automorphism. Analogous results are obtained in the case of continuous time: nondissipating Lévy processes are related to relatively compact distributions of generalized Ornstein-Uhlenbeck processes and corresponding space-time processes and to -decomposable laws, respectively with denoting a continuous group of automorphisms acting as contracting mod. a compact subgroup. Wilfried Hazod Copyright © 2013 Wilfried Hazod. All rights reserved. Pattern Formation of a Keller-Segel Model with the Source Term Mon, 07 Oct 2013 15:30:53 +0000 Nonlinear dynamics near an unstable constant equilibrium in a Keller-Segel model with the source term is considered. It is proved that nonlinear dynamics of a general perturbation is determined by the finite number of linear growing modes over a time scale of , where is a strength of the initial perturbation. Shengmao Fu and Fenli Cao Copyright © 2013 Shengmao Fu and Fenli Cao. All rights reserved.