同心圆与直线剖分下的多元多项式插值

传统的插值方法一般是基于三角形或四边形剖分的，在应用上不易处理类似于呈圆形分布的问题，有一定的局限性．给出一种新的基于同心圆与直线剖分的插值方法，由于该剖分的节点分布是对称的，加之所构造的基函数是对称的，因而插值函数具有保对称性，且是多项式函数．数值实例表明，该插值方法对此类问题有很好的效果，并给出了相应的误差分析．另外，若剖分线退化为射线，该方法可适用更一般情形．     

基于同心圆与平行直线剖分的多元多项式插值

传统的插值方法一般是基于三角形功四边形剖分的，它们在应用上不易处理类似于呈圆形分布的问题，有一定的局限性，文中给出一种新的基于同心圆与平行直线剖分的插值方法，使用该方法构造的插值函数是保对称的，且是多项式函数，并在理论上给出一种误差估计方法，最后给出数值实例。     

CAD中确定平面凸多边形支撑线的一个实用算法

在ＣＡＤ中,快速有效地确定凸多边形的支撑线将直接影响到凸壳动态维持的效率。本文给出一种确定凸多边形形支撑线的有效算法,并利用折半查找技术对其进行了改进,使之具有更快的速度     

The Geometry of D-Decomposition of a Two-Dimensional Plane of Arbitrary Coefficients of the Characteristic Polynomial of a Discrete System

The D-decomposition of a two-dimensional plane of arbitrary coefficients of a discrete characteristic polynomial is studied. The geometry of the boundary curve is analyzed and its common properties with a linear discrete system of any order are described. Example are given.     

基于NoC系统级平面规划图的网格划分

常规基于片上网络(NoC)的网格划分没有考虑链路功耗,导致对具有内部链接结构的系统进行总功耗估计时会产生较大偏差。针对该问题,提出一种改进的网格划分方法,从IP核到路由的映射过程中产生相应NoC,并运用系统级平面规划图进行象征性网格划分。仿真结果表明,改进方法可降低链路功耗的同时,获得更低的总功耗和更小的碰撞区域。     

Robust D-Decomposition for a Polynomial Dependence of the Coefficients of a Polynomial on Two Parameters

Automation and Remote Control - A method for constructing the interval stability set of a polynomial with interval coefficients polynomially depending on two parameters is proposed. The method is...     

刍议高校平面设计如何提升实践教学层次

高校平面设计在实践教学中存在诸多问题：实践教学理论化,践行力度不高;教师指导实践的能力有待提高;实践教学制度不完善;考核方法欠科学。提升平面设计实践教学层次要作到：正确认识实践教学的意义,让实践指导老师更为专业化,健全实践教学制度,制定科学的考核方法。高校在培养平面设计专学生时应该多增加实践教学。     

Equivalence of Polynomial Identity Testing and Polynomial Factorization

In this paper, we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial f, the task of computing arithmetic circuits for the factors of f can be solved deterministically, given a deterministic algorithm for the polynomial identity testing problem (we require either a white-box or a black-box algorithm, depending on the representation of f).Together with the easy observation that deterministic factoring implies a deterministic algorithm for polynomial identity testing, this establishes an equivalence between these two central derandomization problems of arithmetic complexity.Previously, such an equivalence was known only for multilinear circuits (Shpilka & Volkovich, 2010).     

Kernel Polynomial Method on GPU

The simulation of lattice model systems for quantum materials is one of the most important approaches to understand quantum properties of matter in condensed matter physics. The main task in the simulation is to diagonalize a Hamiltonian matrix for the system and evaluate the electronic density of energy states. Kernel polynomial method (KPM) is one of the promising simulation methods. Because KPM contains a fine-grain recursive part in the algorithm, it is hard to parallelize it under the thread level parallelism such as on a supercomputer or a cluster computer. This paper focuses on methods to parallelize KPM on a massively parallel environment of GPU, aiming to achieve high parallelism for more speedups than the recent CPUs. This paper proposes two implementation methods called the full map and the sliding window methods, and evaluates the performances in the recent GPU platform. To enlarge available simulation sizes and at the same time to enhance the performance, this paper also describes additional optimization techniques depending on the GPU architecture.     

三角形域上C1连续的四次插值曲面

提出了一种在三角形域上构造C^1曲面的方法，该方法构造的曲面片由4个曲面加权平均产生，在三角形的边界上满足给定的边界曲线和一阶跨界导数．所构造的曲面可看作由一张基本曲面和三张过渡曲面构成．用三条曲线相交于一点且在交点处共面作为约束条件构造基本曲面，在三角形的内部具有较好形状和逼近精度．同边点法相比，文中方法产生的曲面形状更好；且该方法产生的曲面对四次多项式曲面是精确的，因而比Nielson的点边方法具有更高的插值精度．     

基于多项式重构的拒绝服务反向追踪方案

提出了利用代数方法反向追踪信息的方案,该方案把追踪重构问题当作多项式重构问题,使用代数编码理论技术提供鲁棒的传送和重构方法,是DoS攻击过程中的反向追踪问题的一种新的解决方法。     

Polynomial multiplication on systolic arrays

In this article, we show how the multiplication of polynomials can be performed in a pipelined fashion on a systolic array in linear time steps. The computational model consists of two linear systolic arrays with 2(n+1) processing elements used and (m+2n+2) running time steps needed, where m, n are the degrees of the two given polynomials, respectively. Since the same types of processing elements execute the same program, it is suitable for VLSI implementation. This algorithm is also proved to be correct.     

平面三站时差定位中的模糊研究

该文介绍了蜂窝网络无线定位技术的基本原理,给出了基于到达时间差的平面三站定位算法,并结合几何理论对平面三站时差定位算法进行了仿真,从而深入研究了时差定位中的模糊情况。     

Polynomial blending in a mesh hole-filling application

In this paper, a feature-preserving mesh hole-filling algorithm is realized by the polynomial blending technique. We first search for feature points in the neighborhood of the hole. These feature points allow us to define the feature curves with missing parts in the hole. A polynomial blending curve is constructed to complete the missing parts of the feature curves. These feature curves divide the original complex hole into small simple sub-holes. We use the Bézier-Lagrange hybrid patch to fill each sub-hole. The experimental results show that our mesh hole-filling algorithm can effectively restore the original shape of the hole.     

Celtic Stone Dynamics on a Plane with Viscous Friction

Automation and Remote Control - We consider the problem on the dynamics of a Celtic stone on a fixed horizontal plane. By analogy with [1], it is assumed that a classical viscous friction force is...     

On Locating a Semi-desirable Facility on the Continuous Plane

The paper considers a bicriteria model for locating a semi-desirable facility on the plane. One criterion is that of minimizing the sum of weighted distances between customers and facility, where distances are given by an arbitrary norm. The other criterion is that of maximizing the weighted Euclidean distance from the facility to the closest customer. The objective is to generate the set of efficient points, from which the decision maker must choose the preferred one. Two reformulations are considered: in one, the sum of weighted distances is minimized, subject to constraints requiring that each customer must have a weighted Euclidean distance to the facility of at least a given parameter; varying the parameter yields the efficient set. In the other, both criteria are viewed as minimization problems and a convex combination of them is minimized. Properties of the reformulations are given, and the reformulations are compared. Finally, a solution procedure is outlined.     

The Longest Path Problem has a Polynomial Solution on Interval Graphs

The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno (Proc. of the 15th Annual International Symp. on Algorithms and Computation (ISAAC), LNCS, vol. 3341, pp. 871–883, 2004), where they left the longest path problem open for the class of interval graphs, in this paper we show that the problem can be solved in polynomial time on interval graphs. The proposed algorithm uses a dynamic programming approach and runs in O(n ⁴) time, where n is the number of vertices of the input graph.     

Sharp Bounds on Interval Polynomial Roots

An algorithm is developed for computing sharp bounds on the real roots of polynomials with interval coefficients. The procedure is introduced by studying interval quadratic equations.