Abstract and Applied Analysis
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Open Access journal
ISSN (Print) 1085-3375 - ISSN (Online) 1687-0409
Published by Hindawi [333 journals]
- Itô’s Formula, the Stochastic Exponential, and Change of
Measure on General Time Scales
Abstract: 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).
PubDate: Tue, 18 Apr 2017 00:00:00 +000
- New Conditions for the Exponential Stability of Nonlinear Differential
Abstract: 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.
PubDate: Mon, 10 Apr 2017 00:00:00 +000
- On Approximations by Trigonometric Polynomials of Classes of Functions
Defined by Moduli of Smoothness
Abstract: 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.
PubDate: Tue, 21 Mar 2017 07:02:36 +000
- Some Notes about the Continuous-in-Time Financial Model
Abstract: 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.
PubDate: Tue, 21 Mar 2017 06:19:03 +000
- Modification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell
Abstract: 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.
PubDate: Sun, 05 Mar 2017 10:20:04 +000
- Boundedness Criteria and Norm of Some Multilinear Hilbert-Type Operators
Abstract: 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.
PubDate: Wed, 08 Feb 2017 09:02:13 +000
- A Variation on Uncertainty Principle and Logarithmic Uncertainty Principle
for Continuous Quaternion Wavelet Transforms
Abstract: 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.
PubDate: Mon, 30 Jan 2017 00:00:00 +000
- Qualitative Theory of Functional Differential and Integral Equations 2016
PubDate: Wed, 04 Jan 2017 06:53:31 +000
- Analysis and Models in Interdisciplinary Mathematics 2016
PubDate: Tue, 27 Dec 2016 11:40:43 +000
- Lie Group Solutions of Magnetohydrodynamics Equations and Their
Abstract: 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.
PubDate: Mon, 19 Dec 2016 09:38:55 +000
- Pricing Strategy versus Heterogeneous Shopping Behavior under Market Price
Abstract: 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.
PubDate: Mon, 19 Dec 2016 09:18:04 +000
- Generation and Identification of Ordinary Differential Equations of
Maximal Symmetry Algebra
Abstract: 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.
PubDate: Tue, 13 Dec 2016 08:10:38 +000
- The Impact of Cocreation on the Student Satisfaction: Analysis through
Structural Equation Modeling
Abstract: 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.
PubDate: Thu, 08 Dec 2016 15:14:33 +000
- An Efficient Method for Solving Spread Option Pricing Problem: Numerical
Analysis and Computing
Abstract: 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.
PubDate: Wed, 07 Dec 2016 14:12:46 +000
- Capturing the Data Uncertainty Change in the Cocaine Consumption in Spain
Using an Epidemiologically Based Model
Abstract: 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.
PubDate: Wed, 30 Nov 2016 06:34:12 +000
- A Variational Approach to Perturbed Discrete Anisotropic Equations
Abstract: 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.
PubDate: Sun, 20 Nov 2016 13:06:26 +000
- Existence and Boundedness of Solutions for Nonlinear Volterra Difference
Equations in Banach Spaces
Abstract: 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.
PubDate: Sun, 20 Nov 2016 11:29:31 +000
- Integrodifferential Inequalities Arising in the Theory of Differential
Abstract: 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.
PubDate: Mon, 14 Nov 2016 13:16:59 +000
- Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular
Abstract: 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.
PubDate: Sun, 13 Nov 2016 12:31:01 +000
- Mathematical Modeling of Hidden Intimate Partner Violence in Spain: A
Quantitative and Qualitative Approach
Abstract: 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.
PubDate: Thu, 10 Nov 2016 07:49:06 +000
- Fréchet Envelopes of Nonlocally Convex Variable Exponent
Abstract: 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.
PubDate: Wed, 09 Nov 2016 13:26:34 +000
- Completeness of Ordered Fields and a Trio of Classical Series Tests
Abstract: 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.
PubDate: Sun, 06 Nov 2016 11:45:48 +000
- The Approximate Solutions of Three-Dimensional Diffusion and Wave
Equations within Local Fractional Derivative Operator
Abstract: 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.
PubDate: Sun, 30 Oct 2016 10:59:11 +000
- Quasi-Hyperbolicity and Delay Semigroups
Abstract: 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.
PubDate: Thu, 27 Oct 2016 14:44:01 +000
- Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic
Abstract: 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.
PubDate: Mon, 24 Oct 2016 10:56:22 +000
- A Note on First Passage Functionals for Lévy Processes with Jumps of
Rational Laplace Transforms
Abstract: 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.
PubDate: Mon, 24 Oct 2016 07:18:39 +000
- Approximating the Solution Stochastic Process of the Random Cauchy
One-Dimensional Heat Model
Abstract: 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.
PubDate: Wed, 19 Oct 2016 06:43:21 +000
- Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space
Abstract: 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.
PubDate: Wed, 19 Oct 2016 06:36:08 +000
- Antinormal Weighted Composition Operators
Abstract: 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 .
PubDate: Mon, 10 Oct 2016 11:18:36 +000
- Certain Properties of Some Families of Generalized Starlike Functions with
respect to -Calculus
Abstract: 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.
PubDate: Sun, 25 Sep 2016 09:46:43 +000