Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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. A Unified Software Framework for Empirical Gramians Thu, 19 Sep 2013 08:42:14 +0000 A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method. This work introduces a unified software framework supplying routines for six types of empirical Gramians. The Gramian types will be discussed and applied in a model reduction framework for multiple-input multiple-output systems. Christian Himpe and Mario Ohlberger Copyright © 2013 Christian Himpe and Mario Ohlberger. All rights reserved. On the Finite Volume Element Method for Self-Adjoint Parabolic Integrodifferential Equations Tue, 06 Aug 2013 09:48:42 +0000 Finite volume element schemes for non-self-adjoint parabolic integrodifferential equations are derived and stated. For the spatially discrete scheme, optimal-order error estimates in , , and , norms for are obtained. In this paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived. Mohamed Bahaj and Anas Rachid Copyright © 2013 Mohamed Bahaj and Anas Rachid. All rights reserved. Dynamics of a New Hyperchaotic System with Only One Equilibrium Point Sun, 28 Jul 2013 08:42:31 +0000 A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results. Xiang Li and Ranchao Wu Copyright © 2013 Xiang Li and Ranchao Wu. All rights reserved. Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings Thu, 18 Jul 2013 09:25:01 +0000 Let be a real Hilbert space. Let be -, -strictly pseudononspreading mappings; let and be two real sequences in (0,1). For given , the sequence is generated iteratively by , , where with and is strongly monotone and Lipschitzian. Under some mild conditions on parameters and , we prove that the sequence converges strongly to the set of fixed points of a pair of strictly pseudononspreading mappings and . Bin-Chao Deng and Tong Chen Copyright © 2013 Bin-Chao Deng and Tong Chen. All rights reserved. Exact Multiplicity of Solutions for a Class of Singular Generalized One-Dimensional -Laplacian Problem Wed, 17 Jul 2013 10:21:26 +0000 We describe the existence of positive solutions for a class of singular generalized one-dimensional -Laplacian problem. By applying the related fixed point theory in cone, some new and general results on the existence of positive solutions to the singular generalized -Laplacian problem are obtained. Note that the nonlinear term involves the first-order derivative explicitly. Youwei Zhang Copyright © 2013 Youwei Zhang. All rights reserved. A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems Sun, 14 Jul 2013 11:16:11 +0000 We present a topological result, named crossing lemma, dealing with the existence of a continuum which crosses a topological space between a pair of “opposite” sides. This topological lemma allows us to obtain some fixed point results. In the works of Pascoletti et al., 2008, and Pascoletti and Zanolin, 2010, we have widely exposed the crossing lemma for planar regions homeomorphic to a square, and we have also presented some possible applications to the theory of topological horseshoes and to the study of chaotic-like dynamics for planar maps. In this work, we move from the framework of the generalized rectangles to two other settings (annular regions and invariant sets), trying to obtain similar results. An application to a model of fluid mixing is given. Anna Pascoletti and Fabio Zanolin Copyright © 2013 Anna Pascoletti and Fabio Zanolin. All rights reserved. Effect of Internal Heat Generation/Absorption on Dusty Fluid Flow over an Exponentially Stretching Sheet with Viscous Dissipation Tue, 25 Jun 2013 17:03:08 +0000 A numerical analysis has been carried out to describe the boundary layer flow and heat transfer of a dusty fluid over an exponentially stretching surface in the presence of viscous dissipation and internal heat generation/absorption. The governing partial differential equations are reduced to nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by Runge-Kutta-Fehlberg 45 method. The heat transfer analysis has been carried out for both PEST and PEHF cases. The numerical results are compared with the earlier study and found to be in excellent agreement. Some important features of the flow and heat transfer in terms of velocities and temperature distributions for different values of the governing parameters like fluid-particle interaction parameter, Prandtl number, Eckert number, Number density, heat source/sink parameter, and suction parameter which are of physical and engineering interests are analyzed, discussed, and presented through tables and graphs. G. M. Pavithra and B. J. Gireesha Copyright © 2013 G. M. Pavithra and B. J. Gireesha. All rights reserved. Mathematical Analysis of a Single-Species Population Model in a Polluted Environment with Discrete Time Delays Sun, 16 Jun 2013 10:42:22 +0000 We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view. Swarnali Sharma and G. P. Samanta Copyright © 2013 Swarnali Sharma and G. P. Samanta. All rights reserved. Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions Thu, 13 Jun 2013 10:56:26 +0000 We investigate a new class of cocoercive operators named generalized -cocoercive operators in Hilbert spaces. We prove that generalized -cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with -cocoercive operators to the generalized -cocoercive operators. Some examples are given to justify the definition of generalized -cocoercive operators. Further, we consider a generalized set-valued variational-like inclusion problem involving generalized -cocoercive operator. In terms of the new resolvent operator technique, we give the approximate solution and suggest an iterative algorithm for the generalized set-valued variational-like inclusions. Furthermore, we discuss the convergence criteria of iterative algorithm under some suitable conditions. Our results can be viewed as a generalization of some known results in the literature. Shamshad Husain, Sanjeev Gupta, and Vishnu Narayan Mishra Copyright © 2013 Shamshad Husain et al. All rights reserved. The Measure-Theoretic Entropy and Topological Entropy of Actions over Wed, 12 Jun 2013 12:52:35 +0000 This paper studies the quantitative behavior of a class of one-dimensional cellular automata, named weakly permutive cellular automata, acting on the space of all doubly infinite sequences with values in a finite ring , . We calculate the measure-theoretic entropy and the topological entropy of weakly permutive cellular automata with respect to any invariant measure on the space . As an application, it is shown that the uniform Bernoulli measure is the unique maximal measure for linear cellular automata among the Markov measures. Chih-Hung Chang and Yu-Wen Chen Copyright © 2013 Chih-Hung Chang and Yu-Wen Chen. All rights reserved. On the Variational Problems without Having Desired Variational Symmetries Tue, 11 Jun 2013 11:51:45 +0000 We will have an attempt to present a method for constructing variational problems without having a desired one-parameter transformation group as a variational symmetry. For this, we use the notation of μ-symmetry which was introduced by Giuseppe Gaeta and Paola Morando in 2004. Moreover, our given method enabled us to solve those constructed variational problems using μ-symmetries. Mehdi Nadjafikhah, Saeed Dodangeh, and Parastoo Kabi-Nejad Copyright © 2013 Mehdi Nadjafikhah et al. All rights reserved. Twin TQFTs and Frobenius Algebras Mon, 10 Jun 2013 13:29:50 +0000 We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra consists of a commutative Frobenius algebra , a symmetric Frobenius algebra , and an algebra homomorphism with dual , satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category. Carmen Caprau Copyright © 2013 Carmen Caprau. All rights reserved. Finite -Group with Small Abelian Subgroups Wed, 05 Jun 2013 15:02:27 +0000 A finite -group is said to have the property , if, for any abelian subgroup of , there is . We show that if satisfies , then has the following two types: (1) is isoclinic to some stem groups of order , which form an isoclinic family. (2) is isoclinic to a special -group of exponent . Elementary structures of groups with are determined. Yuemei Mao and Qianlu Li Copyright © 2013 Yuemei Mao and Qianlu Li. All rights reserved. On Intra-Regular Left Almost Semihypergroups with Pure Left Identity Sun, 02 Jun 2013 14:10:23 +0000 We characterize intra-regular LA-semihypergroups by using the properties of their left and right hyperideals, and we investigate some useful conditions for an LA-semihypergroup to become an intra-regular LA-semihypergroup. Naveed Yaqoob, Piergiulio Corsini, and Faisal Yousafzai Copyright © 2013 Naveed Yaqoob et al. All rights reserved. Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems Thu, 30 May 2013 09:28:31 +0000 We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equation , where , are two matrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems. Zhenhua Hu and Shuqing Zhou Copyright © 2013 Zhenhua Hu and Shuqing Zhou. All rights reserved. Rate Estimation of Identical Synchronization by Designing Controllers Sun, 26 May 2013 16:06:30 +0000 This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system. Mitul Islam, Bipul Islam, and Nurul Islam Copyright © 2013 Mitul Islam et al. All rights reserved. The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates Thu, 23 May 2013 19:02:58 +0000 We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows. Yilun Shang Copyright © 2013 Yilun Shang. All rights reserved. An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate Wed, 22 May 2013 11:08:27 +0000 A mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to the analysis of free vibrations of nonhomogeneous rectangular plate clamped at all the four edges. Authors studied the bilinear effect of thickness as well as temperature variations in both and directions. Variation in Poisson's ratio is also considered linearly in -direction due to nonhomogeneity. Rayleigh-Ritz method is used to analyze the frequencies for the first two modes of vibrations for different values of thermal gradient, nonhomogeneity constant, taper constants and aspect ratio. All the numerical computations have been performed for an alloy of aluminum, that is, duralumin. All the results are presented in the form of graphs. Anupam Khanna and Ashish Singhal Copyright © 2013 Anupam Khanna and Ashish Singhal. All rights reserved.