Solvability of the resonant 1-dimensional periodic p-Laplacian equations

In this paper we study the existence of 2π-periodic solutions of

     

Multivariate polynomial perturbations of algebraic equations

In this note we study multivariate perturbations of algebraic equations. In general, it is not possible to represent the perturbed solution as a Puiseux-type power series in a connected neighborhood. For the case of two perturbation parameters we provide a sufficient condition that guarantees such a representation. Then, we extend this result to the case of more than two perturbation parameters. We motivate our study by the perturbation analysis of a weighted random walk on the Web Graph. In an instance of the latter the stationary distribution of the weighted random walk, the so-called Weighted PageRank, may depend on two (or more) perturbation parameters in a manner that illustrates our theoretical development.     

An analytical approximation for solving nonlinear Blasius equation by NHPM

In this article, an analytic approximation to the solution of Blasius equation is obtained by using a new modification of homotopy perturbation method. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The comparison with Howart's numerical solution shows that the new homotopy perturbation method is an effective mathematical method with high accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Upper semicontinuity of the global attractor for the Gierer-Meinhardt model

We are concerned with the following Gierer-Meinhardt model on a bounded domain with smooth boundary ∂Ω which is a biological pattern formation model proposed by A. Gierer and H. Meinhardt

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Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation

In this paper, by using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by Mathematical software.     

A single-machine scheduling problem with maintenance activities to minimize makespan

We study a single-machine scheduling problem with periodic maintenance activity under two maintenance stratagems. Although the scheduling problem with single or periodic maintenance and nonresumable jobs has been well studied, most of past studies considered only one maintenance stratagem. This research deals with a single-machine scheduling problem where the machine should be stopped for maintenance after a fixed periodic interval (T) or after a fixed number of jobs (K) have been processed. The objective is to minimize the makespan for the addressed problem. A two-stage binary integer programming (BIP) model is provided for driving the optimal solution up to 350-job instances. For the large-sized problems, two efficient heuristics are provided for the different combinations of T and K. Computational results show that the proposed algorithm Best-Fit-Butterfly (BBF) performs well because the total average percentage error is below 1%. Once the constraint of the maximum number of jobs (K) processed in the machine’s available time interval (T) is equal or larger than half of jobs, the heuristic Best-Fit-Decreasing (DBF) is strongly recommended.     

一类具有动力边界条件的进化方程解的衰减性

本文研究了一类具有动力边界条件的方程解的衰减性.利用能量扰动法,得到了解的衰减性与外力f(x,t)之间的关系,即它们具有相同的指数衰减性和代数衰减性.     

Existence of periodic solutions in predator-prey with Watt-type functional response and impulsive effects

In this paper, the existence of a periodic solution and the permanence of a periodic Watt-type predator-prey system where the prey disperses in patchy environment with two patches are investigated. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. We assume the Watt-type functional response within-patch dynamics and provide a sufficient condition to guarantee the predator and prey species to be permanent. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful to ecosystem control.