An inner product lemma

Given the operator product BA in which both A and B are symmetric positive‐definite operators, for which symmetric positive‐definite operators C is BA symmetric positive‐definite in the C inner product 〈x, y〉C? This question arises naturally in preconditioned iterative solution methods, and will be answered completely here. Copyright © 2004 John Wiley & Sons, Ltd.     

中国邮路问题的一个解法

本给出中国邮路问题的一个解法。虽然它仍只是初始方案，但因考虑了问题的足够信息，因而这种方案至少拉近了与最优解的距离。     

一种基于图论与熵的专家判断客观可信度的确定方法

本文给出一种群决策中确定专家判断可信度的方法，其主要思路是首先通过图论中最小生成树的方法提取专家判断矩阵的全部信息，其次，使用相对熵指标确定获得专家判断的最终结果，并同时衡量专家自身判断的统一程度，从而确定专家判断的相对客观可信度。最后，文章给出一个典型的算例以说明该方法的可行性和有效性。     

期货经纪公司保证金的一种确定方法

本文基于马尔可夫链在存储论中的应用，结合Ergodic定理，得到确定期货经纪公司保证金的Ergodic模型，即一个双目标规划问题，然后应用乘积最大化准则，将该模型转化为单目标规划问题来求解。该方法考虑期货经纪公司承担的风险和对投资者的吸引程度，为保证金的确定提供新的思路。     

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB B A) =φ(A)φ(5) φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU for all A or φ(A) = cUA U for all A; φsatisfies φ(AB A) = φ(A)φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA V for all A, where A denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U U = c-1I and V V = cI for some nonzero real number c.     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

Searching in trees

In (Discrete Math. 17 (1977)181) Rivest introduced the search complexity of binary trees and proved that among all binary trees with a fixed search complexity the smallest ones are the so-called Fibonacci trees. This result is extended for q-trees. The structure of the smallest q-trees is again Fibonacci-like but more complicated than in the binary case. In addition an upper bound for the asymptotic growth of these trees is given.     

A greedy algorithm for multicut and integral multiflow in rooted trees

We present an O(min(Kn,n²)) algorithm to solve the maximum integral multiflow and minimum multicut problems in rooted trees, where K is the number of commodities and n is the number of vertices. These problems are NP-hard in undirected trees but polynomial in directed trees. In the algorithm we propose, we first use a greedy procedure to build the multiflow then we use duality properties to obtain the multicut and prove the optimality.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

High power CW solid-state multilaser system

A laser system containing four CW Nd:YAG double-rod lasers, transforming optics and a fibre with input-output optics has been designed and investigated. It is shown that reduction of the beam parameter product of the non-Gaussian beams in the image space of the lens has made it possible to collect the emission of four lasers to the same fibre. Independent laser operation has provided the output power control in the range of 10–900 W with a stable light spot size on the input end of the fibre.