The Comparative Statics of Constrained Optimization Problems

This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real‐valued function defined on R^l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R^l. We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle.     

一般散度型线性抛物方程Wp（1,0）弱解的存在性

利用Stampacchia内插定理,研究了一类带有混合边界条件的散度型线性抛物方程Wp1,0弱解的存在性.     

On Complete Convergence for Nonstationary ϕ-Mixing Random Variables

In this article, we study the complete convergence for non-stationary ?-mixing random variables, especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for ?-mixing random variables. Our result generalizes the corresponding one of Shao (1988 Shao, Q.M. (1988). A moment inequality and its applications. Acta Mathematica Sinica 31(6):736–747. [Google Scholar]) and improves the corresponding one of Peligrad (1985a Peligrad, M. (1985a). Convergence rates of the strong law for stationary mixing sequences. Z. Wahrsch. verw. Gebiete. 70:307–314.[Crossref], [Web of Science ®] , [Google Scholar]) and Wang (1987 Wang, D.C. (1987). The complete convergence of the sums for the stationary sequence of ?-mixing random variables. J. Syst. Sci. Mathemat. Sci. 7(4):352–359. [Google Scholar]).     

一类非线性混林发展系统的模型

讨论了一类非线性混林发展系统模型,利用特征理论、不动点定理和迭代技术,证明了这个问题古典解存在的唯一性。     

以{2~n-1,2~n,2~n+1}为基的余数系统2~n高性能缩放

数值缩放(scaling)的高效VLSI实现是基于余数系统(RNS)的DSP系统的关键问题之一。该文提出了有符号余数系统数值缩放通用算法,并结合基为{2n-1,2n,2n+1}的余数系统特性提出了其优化的2n缩放算法和VLSI实现结构,明确给出了在进行有符号RNS整数缩放时负数情况下所引入的修正常量计算方法。分析表明该方法较级联n个1bit缩放模块实现余数系统2n缩放具有更好的速度、面积和功耗特性,从而易于实现基于RNS的DSP系统。     

Fixed-width interval estimation of the minimum point of a regression function based on the Kiefer-Wolfowitz procedure

A version of the central limit theorem for the Kiefer-Wolfowitz procedure is stated. One constructs an asymptotically consistent fixed-width confidence interval for the minimum of a regression function. It is shown that the first moment of the corresponding stopping rule is finite. Both the construction and properties of the estimates of unknown parameters and an adaptive version of the procedure are presented.     

Testing equality of cause-specific hazard rates corresponding to m competing risks among K groups

In this paper, a class of tests is developed for comparing the cause-specific hazard rates of m competing risks simultaneously in K ( 2) groups. The data available for a unit are the failure time of the unit along with the identifier of the risk claiming the failure. In practice, the failure time data are generally right censored. The tests are based on the difference between the weighted averages of the cause-specific hazard rates corresponding to each risk. No assumption regarding the dependence of the competing risks is made. It is shown that the proposed test statistic has asymptotically chi-squared distribution. The proposed test is shown to be optimal for a specific type of local alternatives. The choice of weight function is also discussed. A simulation study is carried out using multivariate Gumbel distribution to compare the optimal weight function with a proposed weight function which is to be used in practice. Also, the proposed test is applied to real data on the termination of an intrauterine device.An erratum to this article can be found at