随机需求弹性及在经济分析中的应用

引入随机弹性的概念及随机弹性的相关性质，进而给出随机需求弹性．利用随机需求弹性分析了当消费群体的收入为随机变量时，其收入对需求量的变化和影响．给出了当收入服从某种分布时，需求量的弹性分布．     

Exposed points and extremal problems in H1 on a bidisc

An essential bounded function ? gives a continuous linear functional on the Hardy space H¹ on the bitorus. In this paper, we consider extremal problems on H¹ when ? is a rational function, ? is a product of one variable functions or ? = |f|/f for some outer function f in H¹ such that f(z, w) has a good property with respect to w for a.e. z. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Morphology,structure, and properties of in situ compatibilized linear low‐density polyethylene/polystyrene and linear low‐density polyethylene/high‐impact polystyrene blends

Blends of linear low‐density polyethylene (LLDPE) with polystyrene (PS) and blends of LLDPE with high‐impact polystyrene (HIPS) were prepared through a reactive extrusion method. For increased compatibility of the two blending components, a Lewis acid catalyst, aluminum chloride (AlCl₃), was adopted to initiate the Friedel–Crafts alkylation reaction between the blending components. Spectra data from Raman spectra of the LLDPE/PS/AlCl₃ blends extracted with tetrahydrofuran verified that LLDPE segments were grafted to the para position of the benzene rings of PS, and this confirmed the graft structure of the Friedel–Crafts reaction between the polyolefin and PS. Because the in situ generated LLDPE‐g‐PS and LLDPE‐g‐HIPS copolymers acted as compatibilizers in the relative blending systems, the mechanical properties of the LLDPE/PS and LLDPE/HIPS blending systems were greatly improved. For example, after compatibilization, the Izod impact strength of an LLDPE/PS blend (80/20 w/w) was increased from 88.5 to 401.6 J/m, and its elongation at break increased from 370 to 790%. For an LLDPE/HIPS (60/40 w/w) blend, its Charpy impact strength was increased from 284.2 to 495.8 kJ/m². Scanning electron microscopy micrographs showed that the size of the domains decreased from 4–5 to less than 1 μm, depending on the content of added AlCl₃. The crystallization behavior of the LLDPE/PS blend was investigated with differential scanning calorimetry. Fractionated crystallization phenomena were noticed because of the reduction in the size of the LLDPE droplets. The melt‐flow rate of the blending system depended on the competition of the grafting reaction of LLDPE with PS and the degradation of the blending components. The degradation of PS only happened during the alkylation reaction between LLDPE and PS. Gel permeation chromatography showed that the alkylation reaction increased the molecular weight of the blend polymer. The low molecular weight part disappeared with reactive blending. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1837–1849, 2003     

S_fS_(f-1)约化系数的解析表式

利用线性方程方法和解析延拓得到了导出置换群Sf Sf- 1约化系数解析表达式的一种简单的代数计算方法 .着重讨论了无重复度时Sf Sf- 1约化系数解析表达式的推导方法 .作为例子 ,给出了关于置换群内积 [f- 1,1]·[f- 1,1]和 [f - 1,1]·[f - 2 ,1,1]有关的所有Sf Sf- 1约化系数的解析表达式 .     

EXISTENCE OF STOCHASTIC EQUILIBRIUM WITH INCOMPLETE FINANCIAL MARKETS

This paper analyzes the aritrage-tree security markets and the general equilibrium ex-istence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to puraly financial securities. It isassume that trading takes place in the sequence of spot markets and futures markets for securi-ties payable in units of account. Unlimited short-selling in securities is allowed. Financial markets may be incomplete, some consumption streams may be impossible to obtain by any tradingstrategy. Securities may be individually precluded from trade at arbitrary states and dates. Thesecurity price process is arbitrage-free the dividend process if and only if there exists a stochaticstate price (present value) process : the present value of the security prices at every vertex isthe present value of their dividend and capital values over the set of immediate successors ; thecurrent value of each security at every vertex is the present value of its future dividend streamover all succeeding vertices. The existence of such an equilibrium is proved under the followingcondition: continuous, weakly convex, strictly monotone and complete preferences, strictlypositive endowmenta and dividends processes.     

Optimal vibration control of flexible spacecraft during a minimum-time maneuver

This paper is concerned with the simultaneous maneuver and vibration control of a flexible spacecraft. The problem is solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of vibration, as well as of perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies bang-bang control. On the other hand, the first-order control is a time-dependent linear quadratic regulator including integral feedback and prescribed convergence rate.This research was sponsored by USAF/ASD and AFOSR Research Grant F33615-86-C-3233 monitored by Drs. A. K. Amos and V. B. Venkayya, whose support is greatly appreciated.     

Active constraints,indefinite quadratic test problems,and complexity

The observation that at leasts constraints are active when the Hessian of the Lagrangian hass negative eigenvalues at a local minimizer is used to obtain two results: (i) a class of nearly concave quadratic minimization problem can be solved in polynomial time; (ii) a class of indefinite quadratic test problems can be constructed with a specified number of positive and negative eigenvalues and with a known global minimizer.The authors thank the reviewers for their constructive comments. The first author was supported by the National Science Foundation Grant DMS-85-20926 and by the Air Force Office of Scientific Research Grant AFOSR-ISSA-86-0091.     

The AR-property for Roberts' example of a compact convex set with no extreme points Part 2: Application to the example

In this second part of our paper, we apply the result of Part 1 to show that the compact convex set with no extreme points, constructed by Roberts (1977), is an AR.

     

Coherent trace-class operators in Hilbert couples

In this paper it is proved that the ideal of trace-class operators acting in a couple of Hilbert spaces coincides with the ideal of coherent trace-class operators. A new formula is derived for theK-functional in the couple of algebras of all bounded linear operators acting in a Hilbert couple, and new interpolation theorems are proved for trace class operators.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 866–872, June, 1998.This research was partially supported by the International Science Foundation and the Russian Government under grant JD 7100.