A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

Preparation of the individual compact single-chain globular particulates of Poly(N-isopropylacrylamide)

The compact single-chain (SC) particulates of Poly(N-isopropylacrylamide) (PNIPAM), which have been formed above its lower critical solution temperature in an aqueous solution containing the surfactant of sodium n-dodecyl sulfate (SDS), were recovered from the solution by freeze-drying. Under scanning electron microscopy, the compact particulate appears as a spherical or elliptical particulate individually dispersed in SDS, which acts as a solid solvent to prevent agglomeration. The conformation of the compact SC particulates of PNIPAM dispersed in SDS had been studied by the solid-state high-resolution ¹³C NMR spectroscopy. The ¹³C spin-lattice relaxation time T ₁ of the SC sample was determined in comparison with that of the original one. It was found that the T ₁ of the methyl carbon in the isopropyl group of the SC sample was about 45% higher than that in the original multichain sample, which revealed the differences in the motion of the methyl group in the different condensed states and illuminated the characteristic conformation of the compact SC globular particulates of PNIPAM.     

On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation

Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts.     

Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

邻氨基酚电聚合膜的研究

在酸性溶液中, 邻氨基酚(OAP)可电聚合成均匀的活性聚邻氮基酚膜(POAP), 膜有致密结构和“张开”结构。POAP膜的主要结构形式为: 与Ni~(2+)络合后, 形成POAP—Ni~(2+)膜, 其主要结构形式为:     

对流-扩散方程算子分裂方法的局部误差估计

考虑对流占优的对流扩散方程的算子分裂方法,给出了此方法的与小粘性参数无关的局部误差估计.     

超双曲型方程的Dirichlet问题

从紧算子的谱理论出发，给出了超双曲型方程（△x-△y）u＋λu＝f（x,y），x＝（x1，x2，…，xm），y＝（y1，y2，…，ym）的Dirichlet问题解的存在性和唯一性定理．     

非自伴算子代数的上同调群

设H是Hilbert空间,(?)是H上的子空间格且Vφ-只有有限个.当H=V{G:G是(?)的Vφ-生成子} 时.对一切自然数n,得到Hn(M(?),B(H))= 0,其中,(?)是(?)到(?)的格同态.特别地,取(?)为恒等映射时,对完全分配的子空间格(?)有Hn(alg(?),B(H))=0.设A是完全分配的CSL代数,M是任意含A的A- 模,则Hn (A,M)= 0.     

C－半群的位势算子

给出了Ｂａｎａｃｈ空间上指数有界Ｃ－半群的位势算子存在性定理及相关命题．     

Integral Representation Formulas in Polydomains

Representation formulas are given for solutions to second order systems in polydomains composed by as well the Laplace as the Bitsadze operator in the single variables. They result from iterations of the respective formulas for the one variable case. This procedure is also applied to mixed systems of first and second order equations.