The construction of infinite families of any k-tight optimal and singular k-tight optimal directed double loop networks

The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed.     

Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

圆感应同步器数显表检测方法研究

介绍了圆感应同步器数显表测角系统的工作原理,以及在静态和动态测角方法。提出了两种提高动态测量精度的方法。实验数据验证了方法的合理性。     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376     

正相协列乘积和的重对数律与强大数律

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实,并讨论了定理2中一个条件的必要性．     

B值鞅型序列的一些极限定理

本文讨论了一些B值鞅型序列的强大数定律 ,弱大数定律 ,Lr收敛性及完全收敛性 ,推广了许多熟知的结果 .     

跳远中人体髋部的合理位置对起跳的作用

运动员的起跳动作是跳远技术的核心，而起跳中人体髋部应处的合理位置又是加大起跳力量的关键，为了采用科学的训练方法，提高运动成绩，运用动力学方法分析了人体髋部位移在跳远运动中的作用。