Finding an Euclidean anti--centrum location of a set of points

An obnoxious facility is to be located inside a polygonal region of the plane, maximizing the sum of the k smallest weighted Euclidean distances to n given points, each protected by some polygonal forbidden region. For the unweighted case and k fixed an O(n²logn) time algorithm is presented. For the weighted case a thorough study of the relevant structure of the multiplicatively weighted order-k-Voronoi diagram leads to the design of an O(kn³+n³logn) time algorithm for finding an optimal solution to the anti-t-centrum problem for every t=1,…,k, simultaneously.     

基于CCl101的分布式节能测控网络设计

设计并实现了一种基于无线收发器芯片CCll01的测控网络,简要介绍了网络中链路层协议的工作机制及相应硬件电路设计;详细分析了使用CCll01进行无线通信时的节能设计和防冲突设计原理,计算并给出了CCll01的有关内部寄存器的取值,同时也说明了使用PIC单片机PICl8F66J60进行局域网互连的软硬件设计方法;介绍了最终系统的实现情况及应用前景。     

非线性延迟积分微分方程单支方法的散逸性

本文研究了非线性延迟积分微分方程单支方法的散逸性．把G（c3P30）-代数稳定的单支方法应用到以上方程中,得到了在有限维空间和无限维空间的散逸性结果．文章最后,数值试验验证了本文的结论．     

Ten commandments for good default expression simplification

This article provides goals for the design and improvement of default computer algebra expression simplification. These goals can also help users recognize and partially circumvent some limitations of their current computer algebra systems. Although motivated by computer algebra, many of the goals are also applicable to manual simplification, indicating what transformations are necessary and sufficient for good simplification when no particular canonical result form is required.After motivating the ten goals, the article then explains how the Altran partially factored form for rational expressions was extended for Derive and for the computer algebra in Texas Instruments products to help fulfill these goals. In contrast to the distributed Altran representation, this recursive partially factored semi-fraction form:

•

does not unnecessarily force common denominators,

•

discovers and preserves significantly more factors,

•

can represent general expressions, and

•

can produce an entire spectrum from fully factored over a common denominator through complete multivariate partial fractions, including a dense subset of all intermediate forms.

     

Global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux

In this paper, by constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions, which generalize the recent results of, for instance, Cui [Z. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008) 3201–3208], Zhou–Mu [J. Zhou, C. Mu, Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007) 1185–1197] etc.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

On a new class of analytic functions associated with conic domain

The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain.     

An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

In this paper, we investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function f and the step size λ_k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.     

Step sequence planning for a biped robot by means of a cylindrical shape model and a high-resolution 2.5D map

A novel step sequence planning (SSP) method for biped-walking robots is presented. The method adopts a free space representation custom-designed for efficient biped robot motion planning. The method rests upon the approximation of the robot shape by a set of 3D cylindrical solids. This feature allows efficient determination of feasible paths in a 2.5D map, comprising stepping over obstacles and stair climbing. A SSP algorithm based on A^∗-search is proposed which uses the advantages of the aforementioned environment representation. The efficiency of the proposed approach is evaluated by a series of simulations performed for eight walking scenarios.