Abstract: In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation under the conditions . New oscillation criteria have been obtained which greatly reduce the number of conditions required for the studied equation. Some examples are presented to show the strength and applicability of the main results. PubDate: Sat, 21 Mar 2020 07:05:02 +000

Abstract: In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method. PubDate: Fri, 20 Mar 2020 15:35:01 +000

Abstract: In this article, we investigate spectrum estimation of law order moving average (MA) process. The main tool is the lag window which is one of the important components of the consistent form to estimate spectral density function (SDF). We show, based on a computer simulation, that the Blackman window is the best lag window to estimate the SDF of and at the most values of parameters and series sizes , except for a special case when and in . In addition, the Hanning–Poisson window appears as the best to estimate the SDF of when and . PubDate: Tue, 17 Mar 2020 06:35:04 +000

Abstract: In this paper, a class of linear second-order singularly perturbed differential-difference turning point problems with mixed shifts exhibiting two exponential boundary layers is considered. For the numerical treatment of these problems, first we employ a second-order Taylor’s series approximation on the terms containing shift parameters and obtain a modified singularly perturbed problem which approximates the original problem. Then a hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the modified problem. Further, we proved that the method is almost second-order ɛ-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results. In addition, the effect of the shift parameters on the layer behavior of the solution is also examined. PubDate: Mon, 16 Mar 2020 04:50:05 +000

Abstract: In this paper, we introduce the concept of a set-valued or multivalued quasi-contraction mapping in V-fuzzy metric spaces. Using this new concept, a fixed-point theorem is established. We also provide an example verifying and illustrating the fixed-point theorem in action. PubDate: Wed, 12 Feb 2020 11:05:04 +000

Abstract: In this work, the Sumudu decomposition method (SDM) is utilized to obtain the approximate solution of two-dimensional nonlinear system of Burger’s differential equations. This method is considered to be an effective tool in solving many problems. Our results have shown that the SDM offers a much better approximation for solving several numbers of systems of two-dimensional nonlinear Burger’s differential equations. To clarify the facility and accuracy of the strategy, two examples are provided. PubDate: Tue, 11 Feb 2020 11:35:01 +000

Abstract: Cholera is an infectious intestinal disease which occurs as a result of poor sanitation and lack of basic education in its transmission. It is characterized by profuse vomiting and severe diarrhea when an individual eats food or drinks water contaminated with the Vibrio cholerae. A dynamic mathematical model that explicitly simulates the transmission mechanism of cholera by taking into account the role of control measures and the environment in the transmission of the disease is developed. The model comprises two populations: the human population and bacteria population. The next-generation method is used to compute the basic reproduction number, . Both the disease-free and endemic equilibria are shown to be locally and globally stable for values less than unity and unstable otherwise. Necessary conditions of the optimal control problem were analyzed using Pontryagin’s maximum principle with control measures such as educational campaign and treatment of water bodies used to optimize the objective function. Numerical values of model parameters were estimated using the nonlinear least square method. The model simulations confirm the significant role played by control measures (education and treatment of water bodies) and the bacteria in the environment in the transmission dynamics as well as reducing the spread of cholera. PubDate: Mon, 03 Feb 2020 04:20:00 +000

Abstract: In this paper, we study generic properties of the optimal, in a certain sense, highly active antiretroviral therapy (or HAART). To address this problem, we consider a control model based on the -dimensional Nowak–May within-host HIV dynamics model. Taking into consideration that precise forms of functional responses are usually unknown, we introduce into this model a nonlinear incidence rate of a rather general form given by an unspecified function of the susceptible cells and free virus particles. We also add a term responsible to the loss of free virions due to infection of the target cells. To mirror the idea of highly active anti-HIV therapy, in this model we assume six controls that can act simultaneously. These six controls affecting different stage of virus life cycle comprise all controls possible for this model and account for all feasible actions of the existing anti-HIV drugs. With this control model, we consider an optimal control problem of minimizing the infection level at the end of a given time interval. Using an analytical mathematical technique, we prove that the optimal controls are bang-bang, find accurate estimates for the maximal possible number of switchings of these controls and establish qualitative types of the optimal controls as well as mutual relationships between them. Having the estimate for the number of switchings found, we can reduce the two-point boundary value problem for Pontryagin Maximum Principle to a considerably simpler problem of the finite-dimensional optimization, which can be solved numerically. Despite this possibility, the obtained theoretical results are illustrated by numerical calculations using BOCOP–2.0.5 software package, and the corresponding conclusions are made. PubDate: Sat, 01 Feb 2020 13:35:03 +000

Abstract: The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector that distributed as a multivariate normally with zero vector mean and variance-covariance matrix at each location , which is sized for samples at the -location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures. PubDate: Sat, 01 Feb 2020 00:05:02 +000

Abstract: The main purpose of this article is to make use of the Horadam polynomials and the generating function , in order to introduce three new subclasses of the bi-univalent function class For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations. PubDate: Thu, 30 Jan 2020 16:05:02 +000

Abstract: The aim of this paper is to give fixed point theorems for -monotone -nonexpansive mappings over -compact or -a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work. PubDate: Thu, 23 Jan 2020 09:50:04 +000

Abstract: In this paper, we investigate the existence of solution for differential systems involving a Laplacian operator which incorporates as a special case the well-known Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive. PubDate: Tue, 21 Jan 2020 04:20:05 +000

Abstract: In this paper, variable exponent function spaces ,, and are introduced in the framework of sublinear expectation, and some basic and important properties of these spaces are given. A version of Kolmogorov’s criterion on variable exponent function spaces is proved for continuous modification of stochastic processes. PubDate: Mon, 13 Jan 2020 13:50:14 +000

Abstract: A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. Lastra and the author. A finite set of sectorial holomorphic solutions is constructed by means of an enhanced version of a classical multisummability procedure due to W. Balser. These functions share a common asymptotic expansion in the perturbation parameter, which is shown to carry a double scale structure, which pairs q-Gevrey and Gevrey bounds. PubDate: Fri, 10 Jan 2020 07:35:01 +000

Abstract: We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points. These are characteristic points for the level sets of the solutions and are usually difficult to deal with. A similar property is known in the Euclidian space, and in Carnot groups, it is based on appropriate properties of a suitable homogeneous norm. We also use this idea to extend to Carnot groups the definition of generalised flow, and it works similarly to the Euclidian setting. These results simplify the handling of the singularities of the equation, for instance, to study the asymptotic behaviour of singular limits of reaction diffusion equations. We provide examples of using the simplified definition, showing, for instance, that boundaries of strictly convex subsets in the Carnot group structure become extinct in finite time when subject to the horizontal mean curvature flow even if characteristic points are present. PubDate: Wed, 08 Jan 2020 08:05:02 +000

Abstract: We define and study -solutions of the Aronsson equation (AE), a second order quasi linear equation. We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics. We give a short, general proof that -solutions are absolutely minimizing functions. We discuss how -supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold. A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold. We provide two examples for Hörmander and Grushin families of vector fields where we construct -solutions (even classical) explicitly. PubDate: Wed, 25 Dec 2019 08:20:02 +000

Abstract: We constitute some necessary and sufficient conditions for the system ,,,,, to have a solution over the quaternion skew field in this paper. A novel expression of general solution to this system is also established when it has a solution. The least norm of the solution to this system is also researched in this article. Some former consequences can be regarded as particular cases of this article. Finally, we give determinantal representations (analogs of Cramer’s rule) of the least norm solution to the system using row-column noncommutative determinants. An algorithm and numerical examples are given to elaborate our results. PubDate: Mon, 19 Aug 2019 00:05:24 +000

Abstract: This paper deals with solving numerically partial integrodifferential equations appearing in biological dynamics models when nonlocal interaction phenomenon is considered. An explicit finite difference scheme is proposed to get a numerical solution preserving qualitative properties of the solution. Gauss quadrature rules are used for the computation of the integral part of the equation taking advantage of its accuracy and low computational cost. Numerical analysis including consistency, stability, and positivity is included as well as numerical examples illustrating the efficiency of the proposed method. PubDate: Mon, 01 Jul 2019 07:05:39 +000

Abstract: In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: ,, and , where ,,,, and . Our existence result is based on Banach fixed point theorem and the approximate solution of our problem is obtained by applying the Haar wavelet operational matrix. PubDate: Mon, 17 Jun 2019 13:05:13 +000

Abstract: The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of determinant and determinant, and the dynamical behaviors of the single-soliton solution are displayed graphically. PubDate: Thu, 13 Jun 2019 07:05:05 +000

Abstract: We establish fractional integral and derivative formulas by using Marichev-Saigo-Maeda operators involving the S-function. The results are expressed in terms of the generalized Gauss hypergeometric functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals and derivatives are presented. Also we develop their composition formula by applying the Beta and Laplace transforms. Further, we point out also their relevance. PubDate: Sun, 09 Jun 2019 10:05:09 +000

Abstract: We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them. PubDate: Tue, 04 Jun 2019 08:05:17 +000

Abstract: In this paper, we study the existence of infinitely many weak solutions for nonlocal elliptic equations with critical exponent driven by the fractional -Laplacian of order . We show the above result when is small enough. We achieve our goal by making use of variational methods, more specifically, the Nehari Manifold and Lusternik-Schnirelmann theory. PubDate: Tue, 28 May 2019 12:05:17 +000

Abstract: We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain we derive the convolution theorem associated with the QLCT and obtain a few consequences. PubDate: Tue, 28 May 2019 11:06:03 +000

Abstract: In this paper, by the use of the weight functions, and the idea of introducing parameters, a discrete Mulholland-type inequality with the general homogeneous kernel and the equivalent form are given. The equivalent statements of the best possible constant factor related to a few parameters are provided. As applications, the operator expressions and a few particular examples are considered. PubDate: Mon, 20 May 2019 10:05:07 +000

Abstract: We investigate the optimal vaccination and screening strategies to minimize human papillomavirus (HPV) associated morbidity and the interventions cost. We propose a two-sex compartmental model of HPV-infection with time-dependent controls (vaccination of adolescents, adults, and screening) which can act simultaneously. We formulate optimal control problems complementing our model with two different objective functionals. The first functional corresponds to the protection of the vulnerable group and the control problem consists of minimizing the cumulative level of infected females over a fixed time interval. The second functional aims to eliminate the infection, and, thus, the control problem consists of minimizing the total prevalence at the end of the time interval. We prove the existence of solutions for the control problems, characterize the optimal controls, and carry out numerical simulations using various initial conditions. The results and properties and drawbacks of the model are discussed. PubDate: Thu, 09 May 2019 12:05:12 +000

Abstract: In this work, we want to detect the shape and the location of an inclusion via some boundary measurement on . In practice, the body is immersed in a fluid flowing in a greater domain and governed by the Stokes equations. We study the inverse problem of reconstructing using shape optimization methods by defining the Kohn-Vogelius cost functional. We aim to study the inverse problem with Neumann and mixed boundary conditions. PubDate: Mon, 15 Apr 2019 16:05:02 +000

Abstract: In the present investigation, we introduce certain new subclasses of the class of biunivalent functions in the open unit disc defined by quasi-subordination. We obtained estimates on the initial coefficients and for the functions in these subclasses. The results present in this paper would generalize and improve those in related works of several earlier authors. PubDate: Mon, 01 Apr 2019 09:05:35 +000

Abstract: In this paper, we present some common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces under the generalized fuzzy cone contraction conditions. We extend and improve some recent results given in the literature. PubDate: Mon, 01 Apr 2019 09:05:34 +000

Abstract: A general Ostrowski’s type inequality for double integrals is given. We utilize function whose partial derivative of order four exists and is bounded. PubDate: Sun, 03 Mar 2019 13:30:03 +000