Abstract: We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem. PubDate: Sun, 03 Jun 2018 00:00:00 +000
Abstract: An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions. PubDate: Sun, 03 Jun 2018 00:00:00 +000
Abstract: The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and -transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters. PubDate: Sun, 03 Jun 2018 00:00:00 +000
Abstract: By a rotational system, we mean a closed subset of the circle, , together with a continuous transformation with the requirements that the dynamical system be minimal and that respect the standard orientation of . We show that infinite rotational systems , with the property that map has finite preimages, are extensions of irrational rotations of the circle. Such systems have been studied when they arise as invariant subsets of certain specific mappings, . Because our main result makes no explicit mention of a global transformation on , we show that such a structure theorem holds for rotational systems that arise as invariant sets of any continuous transformation with finite preimages. In particular, there are no explicit conditions on the degree of . We then give a development of known results in the case where for an integer . The paper concludes with a construction of infinite rotational sets for mappings of the unit circle of degree larger than one whose lift to the universal cover is monotonic. PubDate: Sun, 03 Jun 2018 00:00:00 +000
Abstract: There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a -quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively. PubDate: Tue, 15 May 2018 00:00:00 +000
Abstract: Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE. PubDate: Thu, 10 May 2018 00:00:00 +000
Abstract: The Riemann solutions of a deposition model are shown. A singular flux-function limit of the obtained Riemann solutions is considered. As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient. Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of the limit system. Some numerical results exhibiting the formation processes of delta-shocks and vacuum states are presented. PubDate: Tue, 08 May 2018 09:06:18 +000
Abstract: We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping. PubDate: Tue, 08 May 2018 00:00:00 +000
Abstract: In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain. PubDate: Mon, 07 May 2018 06:13:57 +000
Abstract: We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis. PubDate: Sun, 01 Apr 2018 00:00:00 +000
Abstract: For each and , we obtain some existence theorems of periodic solutions to the two-point boundary value problem in with when is a Caratheodory function which grows linearly in as , and may satisfy a generalized Landesman-Lazer condition for all . Here denotes the subspace of spanned by and ,, , and . PubDate: Sun, 01 Apr 2018 00:00:00 +000
Abstract: Air pollutant levels in Bangkok are generally high in street tunnels. They are particularly elevated in almost closed street tunnels such as an area under the Bangkok sky train platform with high traffic volume where dispersion is limited. There are no air quality measurement stations in the vicinity, while the human population is high. In this research, the numerical simulation is used to measure the air pollutant levels. The three-dimensional air pollution measurement model in a heavy traffic area under the Bangkok sky train platform is proposed. The finite difference techniques are employed to approximate the modelled solutions. The vehicle air pollutant emission due to the high traffic volume is mathematically assumed by the pollutant sources term. The simulation is also considered in averaged and moving pollutant sources due to manner vehicle emission. The proposed approximated air pollutant concentration indicators can be replaced by user required gaseous pollutants indices such as NOx, SO2, CO, and PM2.5. PubDate: Mon, 05 Mar 2018 00:00:00 +000
Abstract: In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter . The aforementioned results are regained for the case when the time scale . Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction. PubDate: Mon, 05 Mar 2018 00:00:00 +000
Abstract: This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived. PubDate: Thu, 01 Mar 2018 00:00:00 +000
Abstract: We obtain in this article a solution of sequential differential equation involving the Hadamard fractional derivative and focusing the orders in the intervals and . Firstly, we obtain the solution of the linear equations using variation of parameter technique, and next we investigate the existence theorems of the corresponding nonlinear types using some fixed-point theorems. Finally, some examples are given to explain the theorems. PubDate: Mon, 26 Feb 2018 00:00:00 +000
Abstract: We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed. PubDate: Thu, 01 Feb 2018 00:00:00 +000
Abstract: The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical solution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several real-world applications. PubDate: Thu, 01 Feb 2018 00:00:00 +000
Abstract: We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized. PubDate: Sun, 28 Jan 2018 00:00:00 +000
Abstract: The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications. PubDate: Mon, 22 Jan 2018 00:00:00 +000
Abstract: Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of -derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions. PubDate: Mon, 01 Jan 2018 00:00:00 +000
Abstract: In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons. PubDate: Mon, 01 Jan 2018 00:00:00 +000
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