Abstract and Applied Analysis https://www.hindawi.com The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales Tue, 18 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/9140138/ We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (-time scale). Wenqing Hu Copyright © 2017 Wenqing Hu. All rights reserved. New Conditions for the Exponential Stability of Nonlinear Differential Equations Mon, 10 Apr 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/4640835/ We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration. Rigoberto Medina Copyright © 2017 Rigoberto Medina. All rights reserved. On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness Tue, 21 Mar 2017 07:02:36 +0000 http://www.hindawi.com/journals/aaa/2017/9323181/ In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities. Nimete Sh. Berisha, Faton M. Berisha, Mikhail K. Potapov, and Marjan Dema Copyright © 2017 Nimete Sh. Berisha et al. All rights reserved. Some Notes about the Continuous-in-Time Financial Model Tue, 21 Mar 2017 06:19:03 +0000 http://www.hindawi.com/journals/aaa/2017/6985820/ In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem. Tarik Chakkour Copyright © 2017 Tarik Chakkour. All rights reserved. Modification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Search Sun, 05 Mar 2017 10:20:04 +0000 http://www.hindawi.com/journals/aaa/2017/7238134/ Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods. Ahmad Alhawarat and Zabidin Salleh Copyright © 2017 Ahmad Alhawarat and Zabidin Salleh. All rights reserved. Boundedness Criteria and Norm of Some Multilinear Hilbert-Type Operators Wed, 08 Feb 2017 09:02:13 +0000 http://www.hindawi.com/journals/aaa/2017/6829093/ We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators. Justice S. Bansah and Benoît F. Sehba Copyright © 2017 Justice S. Bansah and Benoît F. Sehba. All rights reserved. A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle for Continuous Quaternion Wavelet Transforms Mon, 30 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2017/3795120/ The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform. Mawardi Bahri and Ryuichi Ashino Copyright © 2017 Mawardi Bahri and Ryuichi Ashino. All rights reserved. Qualitative Theory of Functional Differential and Integral Equations 2016 Wed, 04 Jan 2017 06:53:31 +0000 http://www.hindawi.com/journals/aaa/2017/3454192/ Cemil Tunç, Bingwen Liu, Luís R. Sanchez, Mohsen Alimohammady, Octavian G. Mustafa, and Samir H. Saker Copyright © 2017 Cemil Tunç et al. All rights reserved. Analysis and Models in Interdisciplinary Mathematics 2016 Tue, 27 Dec 2016 11:40:43 +0000 http://www.hindawi.com/journals/aaa/2016/1971628/ J. C. Cortés, B. Chen-Charpentier, R. Company, Francisco J. Solis, J. R. Torregrosa, and R. J. Villanueva Copyright © 2016 J. C. Cortés et al. All rights reserved. Lie Group Solutions of Magnetohydrodynamics Equations and Their Well-Posedness Mon, 19 Dec 2016 09:38:55 +0000 http://www.hindawi.com/journals/aaa/2016/8183079/ Based on classical Lie Group method, we construct a class of explicit solutions of two-dimensional ideal incompressible magnetohydrodynamics (MHD) equation by its infinitesimal generator. Via these explicit solutions we study the uniqueness and stability of initial-boundary problem on MHD. Fu-zhi Li, Jia-li Yu, Yang-rong Li, and Gan-shan Yang Copyright © 2016 Fu-zhi Li et al. All rights reserved. Pricing Strategy versus Heterogeneous Shopping Behavior under Market Price Dispersion Mon, 19 Dec 2016 09:18:04 +0000 http://www.hindawi.com/journals/aaa/2016/3254240/ We consider the ubiquitous problem of a seller competing in a market of a product with dispersed prices and having limited information about both his competitors’ prices and the shopping behavior of his potential customers. Given the distribution of market prices, the distribution of consumers’ shopping behavior, and the seller’s cost as inputs, we find the computational solution for the pricing strategy that maximizes his expected profits. We analyze the seller’s solution with respect to different exogenous perturbations of parametric and functional inputs. For that purpose, we produce synthetic price data using the family of Generalized Error Distributions that includes normal and quasiuniform distributions as particular cases, and we also generate consumers’ shopping data from different behavioral assumptions. Our analysis shows that, beyond price mean and dispersion, the shape of the price distribution plays a significant role in the seller’s pricing solution. We focus on the seller’s response to an increasing diversity in consumers’ shopping behavior. We show that increasing heterogeneity in the shopping distribution typically lowers seller’s prices and expected profits. Francisco Álvarez, José-Manuel Rey, and Raúl G. Sanchis Copyright © 2016 Francisco Álvarez et al. All rights reserved. Generation and Identification of Ordinary Differential Equations of Maximal Symmetry Algebra Tue, 13 Dec 2016 08:10:38 +0000 http://www.hindawi.com/journals/aaa/2016/1796316/ An effective method for generating linear ordinary differential equations of maximal symmetry in their most general form is found, and an explicit expression for the point transformation reducing the equation to its canonical form is obtained. New expressions for the general solution are also found, as well as several identification and other results and a direct proof of the fact that a linear ordinary differential equation is iterative if and only if it is reducible to the canonical form by a point transformation. New classes of solvable equations parameterized by an arbitrary function are also found, together with simple algebraic expressions for the corresponding general solution. J. C. Ndogmo Copyright © 2016 J. C. Ndogmo. All rights reserved. The Impact of Cocreation on the Student Satisfaction: Analysis through Structural Equation Modeling Thu, 08 Dec 2016 15:14:33 +0000 http://www.hindawi.com/journals/aaa/2016/3729791/ The objective of this study is to apply the cocreation initiative as a marketing tool in the context of university undergraduate programs. Considering that cocreation is a practice that involves stakeholders in different phases of product production or service, this research analyzes the interactions between some of the factors during the cocreation process as students collaborate with the university. These factors are participation, communication, cocreation, and satisfaction, and this study focuses on how they fuse together at the moment of cocreation. After a literature review, which supplied the basis for creating a model, we used exploratory and confirmatory factor analysis and structural equation modeling to validate the hypothesized relations between the variables; finally, the proposed cocreation model was verified. The results could empower academic institutions to develop managerial strategies in order to increase students’ collaboration and satisfaction. Odette Pantoja Díaz, Gabriela Ribes-Giner, and María Rosario Perello-Marin Copyright © 2016 Odette Pantoja Díaz et al. All rights reserved. An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing Wed, 07 Dec 2016 14:12:46 +0000 http://www.hindawi.com/journals/aaa/2016/1549492/ This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach. R. Company, V. N. Egorova, and L. Jódar Copyright © 2016 R. Company et al. All rights reserved. Capturing the Data Uncertainty Change in the Cocaine Consumption in Spain Using an Epidemiologically Based Model Wed, 30 Nov 2016 06:34:12 +0000 http://www.hindawi.com/journals/aaa/2016/1758459/ A probabilistic model is proposed to study the transmission dynamics of the cocaine consumption in Spain during the period of 1995–2011. Using the so-called probabilistic fitting technique, we study if the model is able to capture the data uncertainty coming from surveys. The proposed model is formulated through a nonlinear system of difference equations whose coefficients are treated as stochastic processes. A discussion regarding the usefulness and limitations of probabilistic fitting technique in order to capture the data uncertainty of the proposed model is presented. Christopher Anaya, Clara Burgos, Juan-Carlos Cortés, and Rafael-J. Villanueva Copyright © 2016 Christopher Anaya et al. All rights reserved. A Variational Approach to Perturbed Discrete Anisotropic Equations Sun, 20 Nov 2016 13:06:26 +0000 http://www.hindawi.com/journals/aaa/2016/5676138/ We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory. Amjad Salari, Giuseppe Caristi, David Barilla, and Alfio Puglisi Copyright © 2016 Amjad Salari et al. All rights reserved. Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces Sun, 20 Nov 2016 11:29:31 +0000 http://www.hindawi.com/journals/aaa/2016/1319049/ We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated. Rigoberto Medina Copyright © 2016 Rigoberto Medina. All rights reserved. Integrodifferential Inequalities Arising in the Theory of Differential Equations Mon, 14 Nov 2016 13:16:59 +0000 http://www.hindawi.com/journals/aaa/2016/3520236/ The goal of this paper is to achieve some new results related to integrodifferential inequalities of one independent variable which can be applied as a study of qualitative and quantitative properties of solutions of some nonlinear integral equations. Zareen A. Khan Copyright © 2016 Zareen A. Khan. All rights reserved. Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential Sun, 13 Nov 2016 12:31:01 +0000 http://www.hindawi.com/journals/aaa/2016/2964817/ A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained. Aleksandr Mikhailovich Kholkin Copyright © 2016 Aleksandr Mikhailovich Kholkin. All rights reserved. Mathematical Modeling of Hidden Intimate Partner Violence in Spain: A Quantitative and Qualitative Approach Thu, 10 Nov 2016 07:49:06 +0000 http://www.hindawi.com/journals/aaa/2016/8372493/ The fact that women are abused by their male partner is something that happens worldwide in the 21st century. In numerous cases, abuse only becomes publicly known when a fatal event occurs and is beyond any possible remedy, that is, when men murder their female partner. Since 2003, 793 (September 4, 2015) women have been assassinated by their significant other or excouple in Spain. Only 7.2% of murdered women had reported their fear and previous intimate partner violence (IPV) to the police. Even when the number of female victims is comparable to the number of victims by terrorism, the Government has not assigned an equal amount of resources to diminish the magnitude of this hidden social problem. In this paper, a mathematical epidemiological model to forecast intimate partner violence in Spain is constructed. Both psychological and physical aggressor subpopulations are predicted and simulated. The model’s robustness versus uncertain parameters is studied by a sensitivity analysis. E. De la Poza, L. Jódar, and S. Barreda Copyright © 2016 E. De la Poza et al. All rights reserved. Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces Wed, 09 Nov 2016 13:26:34 +0000 http://www.hindawi.com/journals/aaa/2016/1393496/ We show that the dual of the variable exponent Hörmander space is isomorphic to the Hörmander space (when the exponent satisfies the conditions , the Hardy-Littlewood maximal operator is bounded on for some and is an open set in ) and that the Fréchet envelope of is the space . Our proofs rely heavily on the properties of the Banach envelopes of the -Banach local spaces of and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for , , are also given (e.g., all quasi-Banach subspace of is isomorphic to a subspace of , or is not isomorphic to a complemented subspace of the Shapiro space ). Finally, some questions are proposed. Joaquín Motos, María Jesús Planells, and César F. Talavera Copyright © 2016 Joaquín Motos et al. All rights reserved. Completeness of Ordered Fields and a Trio of Classical Series Tests Sun, 06 Nov 2016 11:45:48 +0000 http://www.hindawi.com/journals/aaa/2016/6023273/ This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field. It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, none of the three is valid in any proper subfield of . The argument hinges on a contractive-type property for sequences in Archimedean ordered fields that are bounded and strictly increasing. For an arbitrary ordered field, it turns out that each of the tests of Dirichlet and Dedekind is equivalent to the sequential completeness of the field. Robert Kantrowitz and Michael M. Neumann Copyright © 2016 Robert Kantrowitz and Michael M. Neumann. All rights reserved. The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator Sun, 30 Oct 2016 10:59:11 +0000 http://www.hindawi.com/journals/aaa/2016/2913539/ We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method. Hassan Kamil Jassim Copyright © 2016 Hassan Kamil Jassim. All rights reserved. Quasi-Hyperbolicity and Delay Semigroups Thu, 27 Oct 2016 14:44:01 +0000 http://www.hindawi.com/journals/aaa/2016/1984874/ We study quasi-hyperbolicity of the delay semigroup associated with the equation , where is the history function and is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup. Shard Rastogi and Sachi Srivastava Copyright © 2016 Shard Rastogi and Sachi Srivastava. All rights reserved. Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions Mon, 24 Oct 2016 10:56:22 +0000 http://www.hindawi.com/journals/aaa/2016/9238948/ The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms. Idriss Ellahiani, EL-Hassan Essoufi, and Mouhcine Tilioua Copyright © 2016 Idriss Ellahiani et al. All rights reserved. A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms Mon, 24 Oct 2016 07:18:39 +0000 http://www.hindawi.com/journals/aaa/2016/5914657/ This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time. Djilali Ait-Aoudia Copyright © 2016 Djilali Ait-Aoudia. All rights reserved. Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model Wed, 19 Oct 2016 06:43:21 +0000 http://www.hindawi.com/journals/aaa/2016/5391368/ This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given. A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló, and M. A. Sohaly Copyright © 2016 A. Navarro-Quiles et al. All rights reserved. Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample Wed, 19 Oct 2016 06:36:08 +0000 http://www.hindawi.com/journals/aaa/2016/9623090/ Suppose is a cone contained in real vector space . When does contain a hyperplane that intersects each of the 0-rays in exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient, closed Banach space cone for which there does not exist a hyperplane that intersects each 0-ray in exactly once. Chris McCarthy Copyright © 2016 Chris McCarthy. All rights reserved. Antinormal Weighted Composition Operators Mon, 10 Oct 2016 11:18:36 +0000 http://www.hindawi.com/journals/aaa/2016/5767426/ Let , where is set of all positive integers and is the counting measure whose -algebra is the power set of . In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space . We also determine a class of antinormal weighted composition operators on Hardy space . Dilip Kumar and Harish Chandra Copyright © 2016 Dilip Kumar and Harish Chandra. All rights reserved. Certain Properties of Some Families of Generalized Starlike Functions with respect to -Calculus Sun, 25 Sep 2016 09:46:43 +0000 http://www.hindawi.com/journals/aaa/2016/6180140/ By making use of the concept of -calculus, various types of generalized starlike functions of order were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of -starlike functions of order . We also introduce and study a new subclass of -starlike functions of order . Moreover, we give some properties of those -starlike functions with negative coefficient including the radius of univalency and starlikeness. Some illustrative examples are provided to verify the theoretical results in case of negative coefficient functions class. Ben Wongsaijai and Nattakorn Sukantamala Copyright © 2016 Ben Wongsaijai and Nattakorn Sukantamala. All rights reserved.