## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (204.172 recursos)

Abstract and Applied Analysis

1. #### A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

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.

2. #### Multiresolution Analysis Applied to the Monge-Kantorovich Problem

Sánchez-Nungaray, Armando; González-Flores, Carlos; López-Martínez, Raquiel R.
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.

3. #### The Existence and Structure of Rotational Systems in the Circle

Ramanathan, Jayakumar
By a rotational system, we mean a closed subset $X$ of the circle, $\mathbb{T}=\mathbb{R}/\mathbb{Z}$ , together with a continuous transformation $f:X\to X$ with the requirements that the dynamical system $(X,f)$ be minimal and that $f$ respect the standard orientation of $\mathbb{T}$ . We show that infinite rotational systems $(X,f)$ , with the property that map $f$ 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, $F:\mathbb{T}\to \mathbb{T}$ . Because our main result makes no explicit mention of a global transformation on $\mathbb{T}$ ,...

4. #### Generalized Fractional Integral Operators Involving Mittag-Leffler Function

Amsalu, Hafte; Suthar, D. L.
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 $H$ -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and $K$ -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.

5. #### Controllability and Observability of Nonautonomous Riesz-Spectral Systems

Sutrima, Sutrima; Indrati, Christiana Rini; Aryati, Lina
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...

6. #### The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method

Alnafisah, Yousef
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.

7. #### ${C}^{\mathrm{1}}$ Hermite Interpolation with PH Curves Using the Enneper Surface

Lee, Hyun Chol; Kong, Jae Hoon; Kim, Gwangil
We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular ${C}^{\mathrm{1}}$ 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.

8. #### A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions

Cheng, Hongjun; Li, Shiwei
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...

9. #### A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

Bahri, Mawardi; Resnawati; Musdalifah, Selvy
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.

10. #### Optimal Rational Approximations by the Modified Fourier Basis

Poghosyan, Arnak V.; Bakaryan, Tigran K.
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.

11. #### On Solvability Theorems of Second-Order Ordinary Differential Equations with Delay

Yeh, Nai-Sher

17. #### Two Sufficient Conditions for Convex Ordering on Risk Aggregation

Zhu, Dan; Yin, Chuancun
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.

18. #### Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

Bevilacqua, Paolo; Bosi, Gianni; Zuanon, Magalì
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.

19. #### Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

N’Guérékata, G. M.; Kostić, Marko
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.