One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to fi...

For stochastic C0-semigroups on L1-spaces there is a wealth of results that show strong convergence to an equilibrium as t ? ?, given the semigroup contains partial integral operator. This has plenty applications transport equations and in mathematical biology. However, up now operators do not play prominent role theorems which yield uniform rather than only convergence. In this article we prov...

An adaptive perceptron with multilinear couplings is introduced. While an adap-tive perceptron exhibits severe shortcomings if it is applied to complex tasks, this is not so for the adaptive multilinear perceptron.

Suppose the observations ðXi; YiÞ taking values in Rd R; i 1⁄4 1; . . . ; n are u-mixing. Compared with the i.i.d. case, some known strong uniform convergence results for the estimators of the regression function rðxÞ 1⁄4 EðYijXi 1⁄4 xÞ need strong moment conditions under u-mixing setting. We consider the following improved kernel estimators of rðxÞ suggested by Cheng (1983): brð1Þ n ðxÞ 1⁄4 Xn...

In this paper, we will study the existence problem of minmax minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of minmax minimal torus in Theorem 5.1. Firstly we prove a strong uniformization result(Proposition 3.1) using method of [1]. Then we use this proposition to choose good parametrization for our minmax sequences. We...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...