Discrete quadratic curvature energies

We present a family of discrete isometric bending models (IBMs) for triangulated surfaces in 3-space. These models are derived from an axiomatic treatment of discrete Laplace operators, using these operators to obtain linear models for discrete mean curvature from which bending energies are assembled. Under the assumption of isometric surface deformations we show that these energies are quadratic in surface positions. The corresponding linear energy gradients and constant energy Hessians constitute an efficient model for computing bending forces and their derivatives, enabling fast time-integration of cloth dynamics with a two- to three-fold net speedup over existing nonlinear methods, and near-interactive rates for Willmore smoothing of large meshes.     

Linear variational principle for convex vector maximization

For infinitely dimensional convex vector maximization problems, it is proved that there exists, under certain conditions, an arbitrarily small additive perturbation of the performance criterion by a linear continuous operator such that the perturbed problem has efficient solutions. The study was sponsored by the Ukrainian State Fund for Basic Research __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 105–114, March–April 2007.     

Mesh Simplification Based on Super-Face and Genetic Algorithm in Reverse Engineering

Mesh simplification is one of the most important links in the context of reverse engineering. It is also an important consideration in computer graphics. This paper presents a novel and original method of triangular mesh reduction. A new concept of super-face is defined. In order to construct a super-face, a way to calculate the scattered point curvature is discussed. The growth of a seed point and the combination of different regions are also necessary for the construction of a super-face. When the hole left by the deletion of super-face is retriangulated a genetic algorithm is used that has been modified for our specific problem. Then the different weights to balance the optimisation of the new triangular mesh can be adjusted.     

基于波动方程的聚焦点控制照明叠前深度偏移

 基于波动方程的聚焦点控制照明叠前深度偏移技术借助于差分计算，把速度、密度等介质参数的影响体现在差分计算的矩阵方程中，能够自动适应速度场的任意变化，快速傅里叶变换的使用也加速了波场延拓的计算速度。因此此法兼具有限差分偏移方法和傅里叶偏移方法的优点，既可适应速度场的剧烈变化，又可保证对陡倾地层的成像效果，是目前针对复杂构造最有效的成像方法之一。对于单个聚焦点及其周围的成像步骤为：①采用矩形网格情况下绕射走时的有限差分计算方法生成合成算子；②应用合成算子来合成面炮震源和面波记录；③对合成的面炮震源和面波记录做傅里叶有限差分法波动方程叠前深度偏移，得到该聚焦点及其附近区域的成像结果。按照上述成像步骤，将震源波场和炮集记录依据相应的外推公式进行延拓，最终应用成像条件求取成像值。在地质目标处选取多个聚焦点，可以得到面向目标的控制照明偏移成像，在多个层位上选取多个聚焦点进行控制照明叠前深度偏移，可以得到整块区域的成像。通过对Marmousi模型的试算，取得了较好的效果。     

一种改进选择算子的遗传算法在泊松曲线沉降预测模型中的应用

选择算子是遗传算法的重要算子之一,它对于种群的多样性和算法的收敛性具有重要的影响。本文对轮盘赌选择算子进行改进,将适应值分组应用于种群个体的选择中,提出适应度分组轮盘赌,并将该方法用于泊松曲线沉降预测模型的优化。实验结果表明,该算法为泊松曲线沉降预测模型的参数估计提供一种有效的方法。     

An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow

In this paper we present a simple, general methodology for the generation of high-order operator decomposition (splitting) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described.     

Analysis of nonlinear electrical circuits using bernstein polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current (d.c.) operating points (either voltages or currents) of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.     

Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment

We study the group decision making problem under intuitionistic fuzzy environment. Based on entropy and cross entropy, we give two methods to determine the optimal weights of attributes, and develop two pairs of entropy and cross entropy measures for intuitionistic fuzzy values. Then, we discuss the properties of these measures and the relations between them and the existing ones. Furthermore, we introduce three new aggregation operators, which treat the membership and non-membership information fairly, to aggregate intuitionistic fuzzy information. Finally, several practical examples are presented to illustrate the developed methods.