Homotopy Analysis Approach to Periodic Solutions of a Nonlinear Jerk Equation

The homotopy analysis method is applied to seek periodic solutions of a nonlinear jerk equation involving the third-order time-derivative. The periodic solutions can be approximated via an analytical series. An auxiliary parameter is introduced to control the convergence region of the solution series. Two numerical examples are presented to demonstrate the effectiveness of the homotopy analysis approach. The examples indicate that, by choosing a proper value of the auxiliary parameter, the first few terms in the solution series yield excellent results.     

一对姐妹题的隐形误解及探究

2009年高考数学江西文理第15题都是以无理不等式为背景的求参数值的姐妹题． 文科题 若不等式√4-x^2≤k（x＋1）的解集为区间[a,b],且b-a=1,则k=__．     

从一道求奇函数参数值问题的错解谈起

剖析一道求奇函数参数值问题的错解,给出该题的正确解法并进行变式训练,加深学生对函数定义、奇偶性等相关概念的理解.     

Response of a Superconducting Quantum Interference Device to Alternating Magnetic Field

We study the response of a superconducting quantum interference device （SQUID） to an alternating magnetic field. It is found that, for some suitably selected parameters＇ values, we can obtain stochastic resonance for the amplitude of the steady average voltage of the SQUID versus the dichotomous noise strength, and frequency （stochastic） resonance for the amplitude of the stationary average voltage of the SQUID as a function of the frequency of the alternating magnetic field. Our results can be useful for electrical power generation using the alternating magnetic field energy of a SQUID.     

Generation of a novel spherical chaotic attractor from a new three-dimensional system

A new three-dimensional （3D） system is constructed and a novel spherical chaotic attractor is generated from the system. Basic dynamical behaviors of the chaotic system are investigated respectively. Novel spherical chaotic attractors can be generated from the system within a wide range of parameter values. The shapes of spherical chaotic attractors can be impacted by the variation of parameters. Finally, a simpler 3D system and a more complex 3D system with the same capability of generating spherical chaotic attractors are put forward respectively.     

Optimal Delaunay Triangulations

The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.     

EXISTENCE OF MINIMIZING SOLUTIONS AROUND ＂EXTENDED STATES＂ FOR A NONLINEARLY ELASTIC CLAMPED PLANE MEMBRANE

The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo has justified the two-dimensional nonlinear “membrane“ equations for a plate made of a Saint Venant-Kirchhoffmaterial,