Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Attrition through a partially coordinated area defense

An area defense consists of several groups that act independently, i.e., do not communicate with each other. Each group has a fixed number of defenders and a controller that allocates these defenders optimally against the individual attackers comprising an attack. We analyze the effectiveness of this partially coordinated defense against a simultaneous attack of known size in which all attackers are considered to be equally lethal. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Missile Strategy in a Post-Nuclear Age

While the arrival of nuclear weapons coincided roughly with the development of short, medium, intermediate, and eventually intercontinental missiles, the contribution of missile technology to the deterrence equation is often lost. If nuclear weapons were eliminated, even new generation missiles with conventional payloads could struggle to render effective deterrence. But some of the physical and psychological effects commonly ascribed to nuclear weapons could still be in play. And in a world without nuclear weapons, thinking about the use and control of force from the nuclear age would also deserve renewed attention.     

Optimal maintenance policies for serial,multi‐machine systems with non‐instantaneous repairs

We study optimal age‐replacement policies for machines in series with non‐instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost‐rate subject to a steady‐state throughput requirement and another that maximizes steady‐state throughput subject to a cost‐rate budget constraint. Under reasonable assumptions, the single‐machine cost‐optimal and throughput‐optimal solutions are unique and orderable, and the multi‐machine optimal solutions have appealing structure. Furthermore, we establish equivalence between the two formulations and provide an illustrative numerical example. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The Demand for Military Spending in Egypt

Egypt plays a pivotal role in the security of the Middle East as the doorway to Europe and its military expenditure reflects its involvement in the machinations of such an unstable region, showing considerable variation over the last 40?years. These characteristics make it a particularly interesting case study of the determinants of military spending. This paper specifies and estimates an econometric model of the Egyptian demand for military spending, taking into account important strategic and political factors. Both economic and strategic factors are found to play a role in determining military burden/spending, with clear positive effects of lagged military burden, suggesting some sort of institutional inertia, plus negative output and net exports effects. The strategic effect as a result of the impact of Israel’s military burden is mostly positive and significant, though its impact is reduced when the impact of important strategic events are taken into account. The military spending of Egypt’s allies Jordan and Syria generally seems to have had no effect on Egypt’s spending. These results are consistent over a range of econometric techniques.     

高速下的外压式空气轴颈轴承研究

本文基于有限元方法,针对不同的速度参数和离心率,采用一种直接的数字方法来计算多孔外压空气轴颈轴承的性能指标,并把模拟结果同参考资料上一种空气心轴轴颈轴承的计算进行了比较。     

采用空气轴承的大行程快速刀具伺服系统

随着对结构化超精密部件需要的不断增加,出现了加工具有高的表面光洁度以及形状精度的非旋转对称镜片的新技术。根据现有的快速刀具伺服系统,研制出了最大行程为16mm的新型快速刀具伺服系统(图1)。以前的快速刀具伺服系统采用了弹性导向机构,而现在的快速刀具伺服系统则采用了空气轴承,并且用了一个高频直线电机来驱动这个系统。由于采用了一个新的功率放大器,使得这个系统能够最高达到100Hz的频率以及1mm的振动幅度。这篇文章给出了这种新型快速刀具伺服系统的技术细节。     

Computational study of the multiechelon production planning problem

In this article we try to identify appropriate solution procedures for different types of multiechelon production planning problems. We conduct an extensive computational study on uncapacitated multiechelon production planning problems with serial and assembly types of bill-of-material structures. Problems are formulated as both single-source fixed charge network problems and as multicommodity flow problems with fixed charges. Solution procedures considered are branch and cut, Lagrangean relaxation (for the network formulation), and branch and bound (for the multicommodity formulation). Three hundred problems with various problem structures are tested. Our conclusions suggest the best approach for each type of problem structure. © 1997 John Wiley & Sons, Inc.     

A continuous-review inventory system with lost sales and variable lead time

Using a system-point (SP) method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous-review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long-run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 259–278, 1998