Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

低负荷维氏硬度法的负荷选择

本文按照维氏硬度测定的技术条件,将基本公式H_v=1854P/D~2加以变换,从而得到一些较为简单的数学关系式.利用这些关系式,可以对不同金属薄带材料,很容易计算出较合理的负荷大小,既能保证不被"打穿",也使视场内有一个适合观测的压痕图象.     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.     

水准折光及双波长激光效应

本文从“同温度层不完全平行于地面,且在变化”的“任意分层”假设出发,导出了水准折光修正公式,并利用光的色散效应在10~(-6)的精度要求下,求得r=r_T=h_1/h_2=(n_(01)-1)/(n_(02)-1)=常数最后指出,研制双波长激光水准仪的必要性和可能性,并提出了研制此种仪器的技术参数.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

The elimination of fast variables in complex chemical reactions. III. Mesoscopic level (irreducible case)

The master equation for a complex chemical reaction cannot always be reduced to a simpler master equation, even if there are fast and slow individual reaction steps. Nevertheless the elimination of intermediates can be carried out with the help of the-expansion. This is illustrated with a well-known complex reaction: the dissociation of N₂O₅. It is shown that the intrinsic fluctuations in the N₂O₅ decay are larger than those implied by the master equation suggested by the macroscopic rate law.     

The Büttiker-Landauer model generalized

Büttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V ₀(x)+V ₁(x)cos t. In the process, we confirm that Büttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.This paper is dedicated to E. G. D. Cohen.     

Ti－Si沸石的催化氧化性能Ⅱ．环己醇的氧化及环己酮的肟化

Ｔｉ－Ｓｉ沸石的催化氧化性能Ⅱ．环己醇的氧化及环己酮的肟化夏清华，王公慰，应慕良，郑禄彬（中国科学院大连化学物理研究所，大连１１６０１２）关键词Ｔｉ－Ｓｉ沸石催化剂，Ｈ_２Ｏ_２氧化剂，环己醇氧化，环己酮肟化．１．前言环己酮肟是生产ε－己内酰胺的关键中...     

钌催化二氧化碳加氢合成甲酸的研究

钌催化二氧化碳加氢合成甲酸的研究张俊忠，李忠，王辉，王常有（太原工业大学煤化所Ｃ１室，太原０３００２４）关键词ＣＯ_２催化加氢，甲酸合成，钌络合催化剂１．前言由于ＣＯ２对环境、气候和生态等方面带来愈加恶劣的影响以及碳资源的日益短缺，近年来对ＣＯ２开发?..