Variable resolution triangulations

A comprehensive study of multiresolution decompositions of planar domains into triangles is given. A general model is introduced, called a Multi-Triangulation (MT), which is based on a collection of fragments of triangulations arranged into a directed acyclic graph. Different decompositions of a domain can be obtained by combining different fragments of the model. Theoretical results on the expressive power of the MT are given. An efficient algorithm is proposed that can extract a triangulation from the MT, whose level of detail is variable over the domain according to a given threshold function. The algorithm works in linear time, and the extracted representation has minimum size among all possible triangulations that can be built from triangles in the MT, and that satisfy the given level of detail. Major applications of these results are in real-time rendering of complex surfaces, such as topographic surfaces in flight simulation.     

平顶高斯光束的模相关系数和模分解理论

利用部分相干光理论,推导出柱坐标系下平顶高斯光束模相关系数的解析表达式,基于推导出的Ｍ＾２因子的推广公式,建立了平顶高斯光束的模分解理论。     

Matrix inverse problem and its optimal approximation problem for R-skew symmetric matrices

Let R ∈ C^n×n be a nontrivial involution, i.e., R² = I and R ≠ ±I. A matrix A ∈ C^n×n is called R-skew symmetric if RAR = −A. The least-squares solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are firstly derived, then the solvability conditions and the solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are given. The solutions of the corresponding optimal approximation problem with R∗ = R for R-skew symmetric matrices are also derived. At last an algorithm for the optimal approximation problem is given. It can be seen that we extend our previous results [G.X. Huang, F. Yin, Matrix inverse problem and its optimal approximation problem for R-symmetric matrices, Appl. Math. Comput. 189 (2007) 482-489] and the results proposed by Zhou et al. [F.Z. Zhou, L. Zhang, X.Y. Hu, Least-square solutions for inverse problem of centrosymmetric matrices, Comput. Math. Appl. 45 (2003) 1581-1589].     

三缺位杂多化合物K_8［P_2W_（18）Mo_2Co_2（H_2O）_2O_（68）］·MoO_6·15H_2O的合成、结构及催化H_2O_2分解研究

合成了杂多化合物Ｋ８［Ｐ２Ｗ（１８）Ｍｏ２Ｃｏ２（Ｈ_２Ｏ）２Ｏ（６８）］·ＭｏＯ６·１５Ｈ２Ｏ，依据ＸＲＤ、ＩＲ、ＵＶ－Ｖｉｓ及ＸＰＳ确定了其晶体结构和配位原子价态，考察了该化合物催化Ｈ２Ｏ２分解的动力学行为。     

CATALASE MIMIC WITH Fe (II) METALLOMICELLE

The effect of Fe (II) metallomicelle as a model of catalase, which was formed by adding surfactants (CTAB, SDS, LSS, Brij35) in Fe (II) -trien complex of molar ratios 1: 500 on the decomposition of hydrogen peroxide was investigated at 20°C and 30°C in pH 10 using KI-color and UV Spectrophotometry. A kinetic model for metallomicellar catalysis was proposed. The association constant of the ternary complex K and the rate constant of the decomposition of hydrogen peroxide k3 were obtained. The results indicate that the metallomicelles making up of Fe (II) metal complex and cationic or nonionic surfactants have obvious catalysis on the decomposition of hydrogen peroxide, but the metallomicelles making up of Fe (II) metal complex and anionic or zwitterionic surfactants have inhibition on this reaction.     

A new approach to solution of the maxwell equations

The decomposition method [1–5] is applied to the Maxwell equations to obtain analytic approximations.     

On the Small Time Asymptotics of Diffusion Processes on Path Groups

In this paper, we obtain the Varadhan type small time asymptotics for diffusion processes on path groups.     

Kinetics of the thermal decomposition of dinitramide

The kinetic regularities of the thermal decomposition of dinitramide in aqueous solutions of HNO₃, in anhydrous acetic acid, and in several other organic solvents were studied. The rate of the decomposition of dinitramide in aqueous HNO₃ is determined by the decomposition of mixed anhydride of dinitramide and nitric acid (N₄O₆) formed in the solution in the reversible reaction. The decomposition of the anhydride is a reason for an increase in the decomposition rates of dinitramide in solutions of HNO₃ as compared to those in solutions in H₂SO₄ and the self-acceleration of the process in concentrated aqueous solutions of dinitramide. The increase in the decomposition rate of nondissociated dinitramide compared to the decomposition rate of the N(NO₂)₂ ⁻ anion is explained by a decrease in the order of the N−NO₂ bond. The increase in the rate constant of the decomposition of the protonated form of dinitramide compared to the corresponding value for neutral molecules is due to the dehydration mechanism of the reaction. For Part 1, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 41–47, January, 1998.     

Min-cut clustering

We describe a decomposition framework and a column generation scheme for solving a min-cut clustering problem. The subproblem to generate additional columns is itself an NP-hard mixed integer programming problem. We discuss strong valid inequalities for the subproblem and describe some efficient solution strategies. Computational results on compiler construction problems are reported.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.This research was supported by NSF grants DMS-8719128 and DDM-9115768, and by an IBM grant to the Computational Optimization Center, Georgia Institute of Technology.