Abstract and Applied Analysis
http://www.hindawi.com
The latest articles from Hindawi Publishing Corporation
© 2016 , Hindawi Publishing Corporation . All rights reserved.

Density by Moduli and Statistical Boundedness
Wed, 10 Feb 2016 09:01:33 +0000
http://www.hindawi.com/journals/aaa/2016/2143018/
We have generalized the notion of statistical boundedness by introducing the concept of statistical boundedness for scalar sequences where is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are statistically bounded for every unbounded modulus . A decomposition theorem for statistical convergence for vector valued sequences and a structure theorem for statistical boundedness have also been established.
Vinod K. Bhardwaj, Shweta Dhawan, and Sandeep Gupta
Copyright © 2016 Vinod K. Bhardwaj et al. All rights reserved.

Unbounded Solutions for Functional Problems on the HalfLine
Sun, 07 Feb 2016 14:01:32 +0000
http://www.hindawi.com/journals/aaa/2016/8987374/
This paper presents an existence and localization result of unbounded solutions for a secondorder differential equation on the halfline with functional boundary conditions. By applying unbounded upper and lower solutions, Green’s functions, and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an EmdenFowler equation are shown to illustrate our results.
Hugo Carrasco and Feliz Minhós
Copyright © 2016 Hugo Carrasco and Feliz Minhós. All rights reserved.

Second Hankel Determinants for the Class of Typically Real Functions
Wed, 03 Feb 2016 09:18:26 +0000
http://www.hindawi.com/journals/aaa/2016/3792367/
We discuss the Hankel determinants for typically real functions, that is, analytic functions which satisfy the condition in the unit disk Δ. Main results are concerned with and . The sharp upper and lower bounds are given. In general case, for , the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.
Paweł Zaprawa
Copyright © 2016 Paweł Zaprawa. All rights reserved.

Timelike Tangent Developable Surfaces and Bonnet Surfaces
Mon, 01 Feb 2016 06:56:19 +0000
http://www.hindawi.com/journals/aaa/2016/6837543/
A criterion was given for a timelike surface to be a Bonnet surface in 3dimensional Minkowski space by Chen and Li, 1999. In this study, we obtain a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface by the aid of this criterion. This is examined under the condition of the curvature and torsion of the base curve of the timelike developable surface being nonconstant. Moreover, we investigate the nontrivial isometry preserving the mean curvature for a timelike flat helicoidal surface by considering the curvature and torsion of the base curve of the timelike developable surface as being constant.
Soley Ersoy and Kemal Eren
Copyright © 2016 Soley Ersoy and Kemal Eren. All rights reserved.

Behavior of the Solutions for PredatorPrey Dynamic Systems with BeddingtonDeAngelis Type Functional Response on Periodic Time Scales in Shifts
Wed, 27 Jan 2016 07:57:32 +0000
http://www.hindawi.com/journals/aaa/2016/1463043/
We consider twodimensional predatorprey system with BeddingtonDeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has periodic solution.
Neslihan Nesliye Pelen, Ayşe Feza Güvenilir, and Billur Kaymakçalan
Copyright © 2016 Neslihan Nesliye Pelen et al. All rights reserved.

Best Proximity Point Theorem in QuasiPseudometric Spaces
Sun, 24 Jan 2016 07:22:04 +0000
http://www.hindawi.com/journals/aaa/2016/9784592/
In quasipseudometric spaces (not necessarily sequentially complete), we continue the research on the quasigeneralized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasipseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error , and hence the existence of a consummate approximate solution to the equation .
Robert Plebaniak
Copyright © 2016 Robert Plebaniak. All rights reserved.

Exact Solutions of Travelling Wave Model via Dynamical System Method
Wed, 20 Jan 2016 07:05:38 +0000
http://www.hindawi.com/journals/aaa/2016/9290734/
By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear SchrödingerBoussinesq equations are studied. Based on this method, the bounded exact travelling wave solutions are obtained which contain solitary wave solutions and periodic travelling wave solutions. The solitary wave solutions and periodic travelling wave solutions are expressed by the hyperbolic functions and the Jacobian elliptic functions, respectively. The results show that the presented findings improve the related previous conclusions. Furthermore, the numerical simulations of the solitary wave solutions and the periodic travelling wave solutions are given to show the correctness of our results.
Heng Wang, Longwei Chen, and Hongjiang Liu
Copyright © 2016 Heng Wang et al. All rights reserved.

Local Hypoellipticity by Lyapunov Function
Sun, 17 Jan 2016 13:57:47 +0000
http://www.hindawi.com/journals/aaa/2016/7210540/
We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: , , where is a selfadjoint linear operator, positive with , in a Hilbert space , and is a series of nonnegative powers of with coefficients in , being an open set of , for any , different from what happens in the work of Hounie (1979) who studies the problem only in the case . We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problem ′, , being the first coefficient of . Besides, to get over the problem out of the elliptic region, that is, in the points ∗ such that ∗ = 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operator .
E. R. AragãoCosta
Copyright © 2016 E. R. AragãoCosta. All rights reserved.

A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform
Wed, 06 Jan 2016 11:20:21 +0000
http://www.hindawi.com/journals/aaa/2016/5874930/
We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.
Mawardi Bahri and Ryuichi Ashino
Copyright © 2016 Mawardi Bahri and Ryuichi Ashino. All rights reserved.

On a Degenerate Evolution System Associated with the Bean CriticalState for Type II Superconductors
Thu, 31 Dec 2015 06:34:38 +0000
http://www.hindawi.com/journals/aaa/2015/875190/
We study a degenerate evolution system containing the curl system in a bounded domain with initial and boundary conditions for the magnetic field under the influence of a system force . This is concerned with an approximation of Bean’s criticalstate model for type II superconductors. We will show the existence, uniqueness, and regularity of solutions. Moreover we will get the properties of the limit solution as .
Junichi Aramaki
Copyright © 2015 Junichi Aramaki. All rights reserved.

On Bleimann, Butzer, and HahnType Operators
Tue, 29 Dec 2015 13:19:59 +0000
http://www.hindawi.com/journals/aaa/2015/480925/
Sequence of Bleimann, Butzer, and Hahn operators which is based on a continuously differentiable function on , with , , has been considered. Uniform approximation by such a sequence has been studied and degree of approximation by the operators has been obtained. Moreover, shape preserving properties of the sequence of operators have been investigated.
Dilek Söylemez
Copyright © 2015 Dilek Söylemez. All rights reserved.

Existence and Uniqueness Results for Fractional Differential Equations with RiemannLiouville Fractional Integral Boundary Conditions
Tue, 29 Dec 2015 13:00:48 +0000
http://www.hindawi.com/journals/aaa/2015/290674/
We prove the existence and uniqueness of solution for fractional differential equations with RiemannLiouville fractional integral boundary conditions. The first existence and uniqueness result is based on Banach’s contraction principle. Moreover, other existence results are also obtained by using the Krasnoselskii fixed point theorem. An example is given to illustrate the main results.
Mohamed I. Abbas
Copyright © 2015 Mohamed I. Abbas. All rights reserved.

Generalized Variability Orderings among Nonnegative Fuzzy Random Variables
Tue, 29 Dec 2015 08:45:25 +0000
http://www.hindawi.com/journals/aaa/2015/757943/
The variability ordering for more and less variables of fuzzy random variables in terms of its distribution function is defined. A property of new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) is derived as an application to the variability ordering of fuzzy random variables. The concept of generalized variability orderings of nonnegative fuzzy random variables representing lifetime of components is introduced. The domination is a generalized variability ordering. We proposed an integral inequality to the case of fuzzy random variables using ordering. The results included equivalent conditions which justify the generalized variability orderings.
S. Ramasubramanian and P. Mahendran
Copyright © 2015 S. Ramasubramanian and P. Mahendran. All rights reserved.

A Semilinear Wave Equation with a Boundary Condition of ManyPoint Type: Global Existence and Stability of Weak Solutions
Sun, 27 Dec 2015 07:29:03 +0000
http://www.hindawi.com/journals/aaa/2015/531872/
This paper is devoted to the study of a wave equation with a boundary condition of manypoint type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.
Giai Giang Vo
Copyright © 2015 Giai Giang Vo. All rights reserved.

Positive Solutions for Nonlinear Fractional Difference Eigenvalue Problem with Nonlocal Conditions
Mon, 21 Dec 2015 06:25:15 +0000
http://www.hindawi.com/journals/aaa/2015/759378/
The problem of positive solutions for nonlinear fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem.
Wafa Shammakh and Maryam AlYami
Copyright © 2015 Wafa Shammakh and Maryam AlYami. All rights reserved.

Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem
Tue, 15 Dec 2015 12:40:13 +0000
http://www.hindawi.com/journals/aaa/2015/659072/
The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven.
Wichai Witayakiattilerd
Copyright © 2015 Wichai Witayakiattilerd. All rights reserved.

Comment on “Soft Open Sets and Soft Continuous Functions”
Tue, 15 Dec 2015 08:40:43 +0000
http://www.hindawi.com/journals/aaa/2015/913034/
Ahmed Mostafa Khalil
Copyright © 2015 Ahmed Mostafa Khalil. All rights reserved.

The Dirichlet Problem for SecondOrder Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz
Tue, 15 Dec 2015 06:27:24 +0000
http://www.hindawi.com/journals/aaa/2015/276810/
We investigate the Dirichlet problem related to linear elliptic secondorder partial differential operators with smooth coefficients in divergence form in bounded connected domains of () with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.
Alberto Cialdea, Vita Leonessa, and Angelica Malaspina
Copyright © 2015 Alberto Cialdea et al. All rights reserved.

Infinite Matrix Products and the Representation of the Matrix Gamma Function
Thu, 10 Dec 2015 11:21:48 +0000
http://www.hindawi.com/journals/aaa/2015/564287/
We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.
J.C. Cortés, L. Jódar, Francisco J. Solís, and Roberto KuCarrillo
Copyright © 2015 J.C. Cortés et al. All rights reserved.

Classes of Harmonic Functions Defined by Subordination
Thu, 26 Nov 2015 12:13:14 +0000
http://www.hindawi.com/journals/aaa/2015/756928/
New classes of univalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. By using extreme points theory we also obtain coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. Radii of convexity and starlikeness of the classes are also considered.
Jacek Dziok
Copyright © 2015 Jacek Dziok. All rights reserved.

On Sharp Hölder Estimates of the CauchyRiemann Equation on Pseudoconvex Domains in with One Degenerate Eigenvalue
Thu, 26 Nov 2015 11:22:02 +0000
http://www.hindawi.com/journals/aaa/2015/731068/
Let be a smoothly bounded pseudoconvex domain in with one degenerate eigenvalue and assume that there is a smooth holomorphic curve whose order of contact with at is larger than or equal to . We show that the maximal gain in Hölder regularity for solutions of the equation is at most .
Sanghyun Cho and Young Hwan You
Copyright © 2015 Sanghyun Cho and Young Hwan You. All rights reserved.

Linear Sobolev Type Equations with Relatively Sectorial Operators in Space of “Noises”
Mon, 23 Nov 2015 05:54:09 +0000
http://www.hindawi.com/journals/aaa/2015/697410/
The concept of “white noise,” initially established in finitedimensional spaces, is transferred to infinitedimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the NelsonGliklikh derivative is introduced and the spaces of “noises” are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable “noises.” The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened ShowalterSidorov initial condition is considered as an application.
A. Favini, G. A. Sviridyuk, and N. A. Manakova
Copyright © 2015 A. Favini et al. All rights reserved.

Corrigendum to “Soft Open Sets and Soft Continuous Functions”
Wed, 18 Nov 2015 13:25:11 +0000
http://www.hindawi.com/journals/aaa/2015/329509/
Metin Akdag, Alkan Ozkan, A. Ghareeb, and A. K. Mousa
Copyright © 2015 Metin Akdag et al. All rights reserved.

A Computational Study of HSV2 with Poor Treatment Adherence
Wed, 18 Nov 2015 09:48:37 +0000
http://www.hindawi.com/journals/aaa/2015/850670/
Herpes simplex virus type 2 (HSV2) is the most prevalent sexually transmitted disease worldwide, despite the availability of highly effective antiviral treatments. In this paper, a basic mathematical model for the spread of HSV2 incorporating all the relevant biological details and poor treatment adherence is proposed and analysed. Equilibrium states of the model are determined and their stability has been investigated. The basic model is then extended to incorporate a time dependent intervention strategy. The aim of the control is tied to reducing the rate at which HSV2 patients in treatment quit therapy before completion. Practically, this control can be implemented through monitoring and counselling all HSV2 patients in treatment. The Pontryagin’s maximum principle is used to characterize the optimal level of the control, and the resulting optimality system is solved numerically. Overall, the study demonstrates that though time dependent control will be effective on controlling new HSV2 cases it may not be sustainable for certain time intervals.
A. Mhlanga, C. P. Bhunu, and S. Mushayabasa
Copyright © 2015 A. Mhlanga et al. All rights reserved.

Exponential Robust Consensus of Multiagent Systems with Markov Jump Parameters
Sun, 15 Nov 2015 06:44:22 +0000
http://www.hindawi.com/journals/aaa/2015/363251/
Exponential robust consensus of stochastic multiagent systems is studied. Coupling structures of multiagent systems are Markov jump switching; that is,
multiagent systems contain Markov jump parameters.
Sufficient conditions of almost surely exponential robust consensus are derived by utilizing the
stochastic method and the approach of the matrix inequality.
Finally, two simulations are shown to demonstrate the validity of the achieved theoretical results.
He Zhang, Huihui Ji, Zhiyong Ye, and Tan Senping
Copyright © 2015 He Zhang et al. All rights reserved.

On Tricomi Problem of Chaplygin’s Hodograph Equation
Wed, 04 Nov 2015 09:33:03 +0000
http://www.hindawi.com/journals/aaa/2015/754781/
The existence and uniqueness results for the Tricomi problem of Chaplygin’s hodograph equation are shown, in the case that the domain considered is close to the parabolic degenerate line, by adopting the energy integral methods and choosing judiciously suitable multipliers.
Meng Xu, Li Liu, and Hairong Yuan
Copyright © 2015 Meng Xu et al. All rights reserved.

An Efficient Numerical Algorithm for Solving Fractional HigherOrder Nonlinear Integrodifferential Equations
Mon, 02 Nov 2015 12:36:45 +0000
http://www.hindawi.com/journals/aaa/2015/616438/
This paper is devoted to both theoretical and numerical study of boundary value problems for higherorder nonlinear fractional integrodifferential equations. Existence and uniqueness results for the considered problem are provided and proved. The numerical method of solution for the problem is based on a conjugate collocation and spline approach combined with shooting method. Some numerical examples are discussed to demonstrate the efficiency and the accuracy of the proposed algorithm.
Muhammed I. Syam, Qasem M. AlMdallal, and M. Naim Anwar
Copyright © 2015 Muhammed I. Syam et al. All rights reserved.

Analysis and Models in Interdisciplinary Mathematics 2015
Mon, 02 Nov 2015 08:54:12 +0000
http://www.hindawi.com/journals/aaa/2015/592063/
L. Jódar and E. De la Poza
Copyright © 2015 L. Jódar and E. De la Poza. All rights reserved.

Effects of Heat Transfer and an Endoscope on Peristaltic Flow of a Fractional Maxwell Fluid in a Vertical Tube
Thu, 22 Oct 2015 07:16:14 +0000
http://www.hindawi.com/journals/aaa/2015/360918/
We investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Maxwell model
through two coaxial vertical tubes. This analysis has been carried under low Reynolds number and long wavelength approximations.
Analytical solution of the problem is obtained by using a fractional calculus approach. The effects of Grashof number, heat
parameter, relaxation time, fractional time derivative parameter, amplitude ratio, and the radius ratio on the pressure gradient,
pressure rise, and the friction forces on the inner and outer tubes are graphically presented and discussed.
H. Rachid
Copyright © 2015 H. Rachid. All rights reserved.

Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis
Sun, 18 Oct 2015 13:10:11 +0000
http://www.hindawi.com/journals/aaa/2015/302185/
We consider boundary value problems for scalar differential equation , , , where is a seventhdegree polynomial and is a parameter. We use the phase plane method combined with evaluations of timemap functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes.
A. Kirichuka and F. Sadyrbaev
Copyright © 2015 A. Kirichuka and F. Sadyrbaev. All rights reserved.