代数体函数及其导数的涉及重值的Borel方向

该文研究了有限正级代数体函数涉及重值的Borel方向的存在范围, 并得到了有限正级代数体函数及其导数存在公共的涉及重值的Borel方向的判定方法.     

基于R／S分析法的股市走势分析

本文根据上证综合指数和深圳成分股2003年1月2日到2006年5月17日的收盘价及换手,对上证综合指数和深圳成分股的收盘价趋势进行了分析。用R／S分析法对收盘价趋势进行了分析,为分析历史数据对收盘价的影响,引入了关联尺度函数,通过求解出上证综合指数和深圳成分股的赫斯特（Hurst）指数,可以求出其关联尺度。根据赫斯特指数及关联尺度,我们分析出了收盘价是一个有偏的随机游动,并给出了上证综合指数和深圳成分股走势的相关结论。     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

Approximate hierarchical facility location and applications to the bounded depth Steiner tree and range assignment problems

The paper concerns a new variant of the hierarchical facility location problem on metric powers (HFL_β[h]), which is a multi-level uncapacitated facility location problem defined as follows. The input consists of a set F of locations that may open a facility, subsets D₁,D₂,…,D_h−1 of locations that may open an intermediate transmission station and a set D_h of locations of clients. Each client in D_h must be serviced by an open transmission station in D_h−1 and every open transmission station in D_l must be serviced by an open transmission station on the next lower level, D_l−1. An open transmission station on the first level, D₁ must be serviced by an open facility. The cost of assigning a station j on level l1 to a station i on level l−1 is c_ij. For iF, the cost of opening a facility at location i is f_i0. It is required to find a feasible assignment that minimizes the total cost. A constant ratio approximation algorithm is established for this problem. This algorithm is then used to develop constant ratio approximation algorithms for the bounded depth Steiner tree problem and the bounded hop strong-connectivity range assignment problem.     

A note on some quadrature based three-step iterative methods for non-linear equations

In a recent paper [N.A. Mir, T. Zaman, Some quadrature based three-step iterative methods for non-linear equations, Appl. Math. Comput. 193 (2007) 366-373], some new three-step iterative methods for non-linear equations have been proposed. In this note, we show that the Algorithm 2.2 and Algorithm 2.3 given by the authors have twelfth-order and ninth-order convergence respectively, not seventh-order one as claimed in their work.     

Evaluating a warm standby system with components having proportional hazard rates

This paper investigates the heterogeneity of components with proportional hazard rates in a redundant system. The total number of those standbys surviving the failure time of some active component is derived, and the algorithm to determine the optimal number of standbys is also discussed.     

Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations

Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation is used to describe the propagation of a diffraction sound beam in a nonlinear medium. We give a new algebraic method of solving these equations by using certain finite-dimensional stable range of the nonlinear terms and obtain large families of new explicit exact solutions parameterized by several functions for them. These parameter functions enable one to find the solutions of some related practical models and boundary value problems. Research supported by China NSF 10871193.     

A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components

In this paper, we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components. For maximizing the overall system reliability under limited resource constraints, the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced GA for integer variables with interval fitness function, tournament selection, uniform crossover, uniform mutation and elitism. As a special case, considering the lower and upper bounds of the interval valued reliabilities of the components to be the same, the corresponding problem has been solved. The model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature. Finally, sensitivity analyses have been shown graphically to study the stability of our developed GA with respect to the different GA parameters.     

Modified Newton’s method for systems of nonlinear equations with singular Jacobian

It is well known that Newton’s method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of this method for nonlinear systems whose Jacobian matrix is singular. We prove, under certain conditions, that this modified Newton’s method has quadratic convergence. Moreover, different numerical tests confirm the theoretical results and allow us to compare this variant with the classical Newton’s method.     

短焦段数字电影变焦放映镜头的设计

为了填补国内短焦段数字电影变焦放映镜头的空白及满足国内数字电影市场对大投射比镜头的需求,本文采用机械补偿式变焦原理,利用ZEMAX光学设计软件自主研发设计出一款适用于0.65英寸、单数字光处理器、1.3K数字电影放映机的短焦段连续变焦数字电影放映镜头.镜头包括前固定组、变倍组、补偿组和后固定组,由8组10片玻璃球面透镜组成,其中变倍组由一片负透镜构成,补偿组由两组双胶合透镜组构成.镜头总长170mm,全口径70mm,变焦范围为14.5～18.2mm,相对孔径为1/2,投射比范围为0.99∶1～1.23∶1,后工作距离为32.6mm.镜头凸轮曲线的设计采用等间隔变焦的方法,设计出了平滑稳定、斜率适宜、压力角小的凸轮曲线,具有加工方便、加工准确度高、变倍组升角容易控制且焦距变化均匀的优点.整个镜头结构简单、体形小、重量轻、成本低.