Journal of Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Improving Genetic Algorithm with Fine-Tuned Crossover and Scaled Architecture Tue, 05 Apr 2016 13:37:24 +0000 http://www.hindawi.com/journals/jmath/2016/4015845/ Genetic Algorithm (GA) is a metaheuristic used in solving combinatorial optimization problems. Inspired by evolutionary biology, GA uses selection, crossover, and mutation operators to efficiently traverse the solution search space. This paper proposes nature inspired fine-tuning to the crossover operator using the untapped idea of Mitochondrial DNA (mtDNA). mtDNA is a small subset of the overall DNA. It differentiates itself by inheriting entirely from the female, while the rest of the DNA is inherited equally from both parents. This unique characteristic of mtDNA can be an effective mechanism to identify members with similar genes and restrict crossover between them. It can reduce the rate of dilution of diversity and result in delayed convergence. In addition, we scale the well-known Island Model, where instances of GA are run independently and population members exchanged periodically, to a Continental Model. In this model, multiple web services are executed with each web service running an island model. We applied the concept of mtDNA in solving Traveling Salesman Problem and to train Neural Network for function approximation. Our implementation tests show that leveraging these new concepts of mtDNA and Continental Model results in relative improvement of the optimization quality of GA. Ajay Shrestha and Ausif Mahmood Copyright © 2016 Ajay Shrestha and Ausif Mahmood. All rights reserved. Generalized Fractional Integral Operators and -Series Wed, 30 Mar 2016 09:24:38 +0000 http://www.hindawi.com/journals/jmath/2016/2872185/ Two fractional integral operators associated with Fox -function due to Saxena and Kumbhat are applied to -series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function . The Mellin and Whittaker transforms are obtained for these compositional operators with -series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms of -function, which are in compact form suitable for numerical computation. Special cases of the results are also pointed out in the form of lemmas and corollaries. A. M. Khan, R. K. Kumbhat, Amit Chouhan, and Anita Alaria Copyright © 2016 A. M. Khan et al. All rights reserved. Applications of Cesàro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to Class in -Norm Sun, 06 Mar 2016 14:00:39 +0000 http://www.hindawi.com/journals/jmath/2016/9048671/ We prove two Theorems on approximation of functions belonging to Lipschitz class in -norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results. M. L. Mittal and Mradul Veer Singh Copyright © 2016 M. L. Mittal and Mradul Veer Singh. All rights reserved. Product of the Generalized -Subgroups Thu, 03 Mar 2016 06:11:18 +0000 http://www.hindawi.com/journals/jmath/2016/4918948/ We introduce the notion of -product of -subsets. We give a necessary and sufficient condition for --subgroup of a product of groups to be -product of --subgroups. Dilek Bayrak and Sultan Yamak Copyright © 2016 Dilek Bayrak and Sultan Yamak. All rights reserved. Inner Product over Fuzzy Matrices Sun, 21 Feb 2016 14:20:38 +0000 http://www.hindawi.com/journals/jmath/2016/6521893/ The purpose of this study was to introduce the inner product over fuzzy matrices. By virtue of this definition, -norm is defined and the parallelogram law is proved. Again the relative fuzzy norm with respect to the inner product over fuzzy matrices is defined. Moreover Cauchy Schwarz inequality, Pythagoras, and Fundamental Minimum Principle are established. Some equivalent conditions are also proved. A. Nagoor Gani, K. Kannan, and A. R. Manikandan Copyright © 2016 A. Nagoor Gani et al. All rights reserved. Hermite-Hadamard-Fejér Type Inequalities for Quasi-Geometrically Convex Functions via Fractional Integrals Thu, 18 Feb 2016 11:30:04 +0000 http://www.hindawi.com/journals/jmath/2016/6523041/ Some Hermite-Hadamard-Fejér type integral inequalities for quasi-geometrically convex functions in fractional integral forms have been obtained. İmdat İşcan and Mehmet Kunt Copyright © 2016 İmdat İşcan and Mehmet Kunt. All rights reserved. Herd Behavior and Financial Crashes: An Interacting Particle System Approach Thu, 11 Feb 2016 12:08:48 +0000 http://www.hindawi.com/journals/jmath/2016/7510567/ We provide an approach based on a modification of the Ising model to describe the dynamics of stock markets. Our model incorporates three different factors: imitation, the impact of external news, and private information; moreover, it is characterized by coupling coefficients, static in time, but not identical for each agent. By analogy with physical models, we consider the temperature parameter of the system, assuming that it evolves with memory of the past, hence considering how former news influences realized market returns. We show that a standard Ising potential assumption is not sufficient to reproduce the stylized facts characterizing financial markets; this is because it assigns low probabilities to rare events. Hence, we study a variation of the previous setting providing, also by concrete computations, new insights and improvements. Vincenzo Crescimanna and Luca Di Persio Copyright © 2016 Vincenzo Crescimanna and Luca Di Persio. All rights reserved. Automorphisms and Inner Automorphisms Sun, 07 Feb 2016 13:09:45 +0000 http://www.hindawi.com/journals/jmath/2016/3983895/ Let be a field of characteristic not and let be central simple superalgebra over , and let be superinvolution on . Our main purpose is to classify the group of automorphisms and inner automorphisms of (i.e., commuting with ) by using the classical theorem of Skolem-Noether. Also we study two examples of groups of automorphisms and inner automorphisms on even central simple superalgebras with superinvolutions. Ameer Jaber and Moh’D Yasein Copyright © 2016 Ameer Jaber and Moh’D Yasein. All rights reserved. A Fixed Point Theorem for Monotone Maps and Its Applications to Nonlinear Matrix Equations Thu, 24 Dec 2015 16:01:30 +0000 http://www.hindawi.com/journals/jmath/2015/167049/ By using the fixed point theorem for monotone maps in a normal cone, we prove a uniqueness theorem for the positive definite solution of the matrix equation , where is a monotone map on the set of positive definite matrices. Then we apply the uniqueness theorem to a special equation and prove that the equation has a unique positive definite solution when and and . For this equation the basic fixed point iteration is discussed. Numerical examples show that the iterative method is feasible and effective. Dongjie Gao Copyright © 2015 Dongjie Gao. All rights reserved. New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators Tue, 22 Dec 2015 11:22:25 +0000 http://www.hindawi.com/journals/jmath/2015/684598/ We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results. Hassan Kamil Jassim Copyright © 2015 Hassan Kamil Jassim. All rights reserved. An Extension of Wright Function and Its Properties Tue, 08 Dec 2015 05:50:05 +0000 http://www.hindawi.com/journals/jmath/2015/950728/ The paper is devoted to the study of the function , which is an extension of the classical Wright function and Kummer confluent hypergeometric function. The properties of including its auxiliary functions and the integral representations are proven. Moustafa El-Shahed and Ahmed Salem Copyright © 2015 Moustafa El-Shahed and Ahmed Salem. All rights reserved. Coefficient Bounds for Certain Subclasses of -Fold Symmetric Biunivalent Functions Wed, 25 Nov 2015 14:06:04 +0000 http://www.hindawi.com/journals/jmath/2015/241683/ We consider two new subclasses and of consisting of analytic and -fold symmetric biunivalent functions in the open unit disk . Furthermore, we establish bounds for the coefficients for these subclasses and several related classes are also considered and connections to earlier known results are made. Şahsene Altınkaya and Sibel Yalçın Copyright © 2015 Şahsene Altınkaya and Sibel Yalçın. All rights reserved. Ordering Properties of the First Eigenvector of Certain Similarity Matrices Thu, 12 Nov 2015 11:52:01 +0000 http://www.hindawi.com/journals/jmath/2015/582731/ It is shown for coefficient matrices of Russell-Rao coefficients and two asymmetric Dice coefficients that ordinal information on a latent variable model can be obtained from the eigenvector corresponding to the largest eigenvalue. Matthijs J. Warrens and Alexandra de Raadt Copyright © 2015 Matthijs J. Warrens and Alexandra de Raadt. All rights reserved. Symplectic Toric Geometry and the Regular Dodecahedron Wed, 11 Nov 2015 11:55:06 +0000 http://www.hindawi.com/journals/jmath/2015/967417/ The regular dodecahedron is the only simple polytope among the platonic solids which is not rational. Therefore, it corresponds neither to a symplectic toric manifold nor to a symplectic toric orbifold. In this paper, we associate to the regular dodecahedron a highly singular space called symplectic toric quasifold. Elisa Prato Copyright © 2015 Elisa Prato. All rights reserved. Irreducible Modular Representations of the Reflection Group Mon, 09 Nov 2015 08:54:56 +0000 http://www.hindawi.com/journals/jmath/2015/808520/ In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of type . In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of types and . In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of type . José O. Araujo, Tim Bratten, and Cesar L. Maiarú Copyright © 2015 José O. Araujo et al. All rights reserved. Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series Wed, 04 Nov 2015 09:39:10 +0000 http://www.hindawi.com/journals/jmath/2015/134842/ New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders are directly connected with the derivatives . In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation. Vasily E. Tarasov Copyright © 2015 Vasily E. Tarasov. All rights reserved. On -Symmetric -Paracontact Metric Manifolds Thu, 29 Oct 2015 11:01:24 +0000 http://www.hindawi.com/journals/jmath/2015/728298/ The notions of -symmetric, 3-dimensional locally -symmetric, -Ricci symmetric, and 3-dimensional locally -Ricci symmetric -paracontact metric manifolds have been introduced and properties of these structures have been discussed. D. G. Prakasha and K. K. Mirji Copyright © 2015 D. G. Prakasha and K. K. Mirji. All rights reserved. Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method Tue, 27 Oct 2015 10:47:03 +0000 http://www.hindawi.com/journals/jmath/2015/456392/ We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem by using Infeasible Newton’s method applied to the KKT system of equations which can be started from any point. We implement the method using backtracking line search technique and also study the effect of large weights on the method. We use numerical experiments to compare Infeasible Newton’s method with Standard Newton’s method. The results show that Infeasible Newton’s method moves in the interior of the feasible regions often very quickly, starting from any point. We recommend it as a method for finding an interior point by setting each weight to be 1. It appears to work better than Standard Newton’s method in finding the weighted analytic center when none of weights is very large relative to the other weights. However, we find that Infeasible Newton’s method is more sensitive than Standard Newton’s method to large variation in the weights. Shafiu Jibrin Copyright © 2015 Shafiu Jibrin. All rights reserved. Killing Vector Fields in Generalized Conformal -Change of Finsler Spaces Mon, 26 Oct 2015 08:29:36 +0000 http://www.hindawi.com/journals/jmath/2015/456291/ We consider a Finsler space equipped with a Generalized Conformal β-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformal β-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformal β-change of metric. Mallikarjun Yallappa Kumbar, Narasimhamurthy Senajji Kampalappa, Thippeswamy Komalobiah Rajanna, and Kavyashree Ambale Rajegowda Copyright © 2015 Mallikarjun Yallappa Kumbar et al. All rights reserved. Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach Wed, 21 Oct 2015 13:34:36 +0000 http://www.hindawi.com/journals/jmath/2015/487513/ The theory of generalized thermoelasticity with fractional order strain is employed to study the problem of one-dimensional disturbances in a viscoelastic solid in the presence of a moving internal heat source and subjected to a mechanical load. The problem is in the context of Green-Naghdi theory of thermoelasticity with energy dissipation. Laplace transform and state space techniques are used to obtain the general solution for a set of boundary conditions. To tackle the expression of heat source, Fourier transform is also employed. The expressions for different field parameters such as displacement, stress, thermodynamical temperature, and conductive temperature in the physical domain are derived by the application of numerical inversion technique. The effects of fractional order strain, two-temperature parameter, viscosity, and velocity of internal heat source on the field variables are depicted graphically for copper material. Some special cases of interest have also been presented. Renu Yadav, Kapil Kumar Kalkal, and Sunita Deswal Copyright © 2015 Renu Yadav et al. All rights reserved. Some Theorems about -Contraction in Fuzzy Metric Spaces Sun, 18 Oct 2015 13:04:34 +0000 http://www.hindawi.com/journals/jmath/2015/873807/ We previously proved a number of fixed point theorems for some kinds of contractions like -contraction and contraction in fuzzy metric spaces. In this paper, we discuss the problem of existence of fixed point for -contraction in fuzzy metric spaces in sense of George and Veeramani. Parvin Azhdari Copyright © 2015 Parvin Azhdari. All rights reserved. The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order Mon, 12 Oct 2015 14:23:52 +0000 http://www.hindawi.com/journals/jmath/2015/460191/ Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski. Mengkun Zhu and Xinzhong Huang Copyright © 2015 Mengkun Zhu and Xinzhong Huang. All rights reserved. The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras Mon, 12 Oct 2015 11:17:41 +0000 http://www.hindawi.com/journals/jmath/2015/876251/ We study the restriction of simple modules of Birman-Murakami-Wenzl algebras with   being not a root of 1. Precisely, we study the module structure for the restriction of to and describe the socle and head of the restriction of each simple module completely. Xu Xu Copyright © 2015 Xu Xu. All rights reserved. Norm Estimates for Solutions of Polynomial Operator Equations Sun, 04 Oct 2015 16:08:26 +0000 http://www.hindawi.com/journals/jmath/2015/524829/ We consider the equations and , where   , , are given linear bounded operators in a Banach space and is to be found. Representations of solutions are derived. In the cases of Euclidean and Hilbert spaces, norm estimates for the solutions are suggested. Michael Gil’ Copyright © 2015 Michael Gil’. All rights reserved. Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions Thu, 01 Oct 2015 12:02:20 +0000 http://www.hindawi.com/journals/jmath/2015/302012/ We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable. Binayak S. Choudhury and Chaitali Bandyopadhyay Copyright © 2015 Binayak S. Choudhury and Chaitali Bandyopadhyay. All rights reserved. On a Theorem of Ziv Ran concerning Abelian Varieties Which Are Product of Jacobians Thu, 01 Oct 2015 09:45:36 +0000 http://www.hindawi.com/journals/jmath/2015/431098/ We give a new proof for a theorem of Ziv Ran which generalizes some results of Matsusaka and Hoyt. These results provide criteria for an Abelian variety to be a Jacobian or a product of Jacobians. The advantage of our method is that it works in arbitrary characteristic. Cristian Anghel and Nicolae Buruiana Copyright © 2015 Cristian Anghel and Nicolae Buruiana. All rights reserved. The Partition Function of the Dirichlet Operator on a -Dimensional Rectangle Cavity Tue, 15 Sep 2015 06:16:23 +0000 http://www.hindawi.com/journals/jmath/2015/785720/ We study the asymptotic behavior of the free partition function in the limit for a diffusion process which consists of -independent, one-dimensional, symmetric, -stable processes in a hyperrectangular cavity with an absorbing boundary. Each term of the partition function for this polyhedron in -dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis. Agapitos N. Hatzinikitas Copyright © 2015 Agapitos N. Hatzinikitas. All rights reserved. Maps Preserving Idempotence on Matrix Spaces Wed, 09 Sep 2015 07:13:00 +0000 http://www.hindawi.com/journals/jmath/2015/428203/ Suppose is an arbitrary field. Let be the number of the elements of . Let be the space of all matrices over , let be the subset of consisting of all symmetric matrices, and let be the subset of consisting of all upper-triangular matrices. Let ; a map is said to preserve idempotence if is idempotent if and only if is idempotent for any and . In this paper, the maps preserving idempotence on , , and were characterized in case . Yuqiu Sheng and Hanyu Zhang Copyright © 2015 Yuqiu Sheng and Hanyu Zhang. All rights reserved. Some Applications of Ordinary Differential Operator to Certain Multivalent Functions Tue, 18 Aug 2015 16:28:56 +0000 http://www.hindawi.com/journals/jmath/2015/825903/ The aim of this paper is to apply the well-known ordinary differential operator to certain multivalent functions which are analytic in the certain domains of the complex plane and then to determine some criteria concerning analytic and geometric properties of the related complex functions. Müfit Şan, Hüseyin Irmak, and Ayhan Şerbetçi Copyright © 2015 Müfit Şan et al. All rights reserved. Locally Defined Operators in the Space of Functions of Bounded Riesz-Variation Mon, 06 Jul 2015 11:18:12 +0000 http://www.hindawi.com/journals/jmath/2015/925091/ We study the locally defined operator on the spaces of bounded Riesz -variation functions and we prove that those operators are the Nemytskii operator. W. Aziz, J. A. Guerrero, K. Maldonado, and N. Merentes Copyright © 2015 W. Aziz et al. All rights reserved.