An Extension of the Lanchester Square Law to Inhomogeneous Forces with an Application to Force Allocation Methodology

This paper extends the classic Lanchester representation of a battle between an Attacker and a Defender to the case where the former possesses two weapon types, and the latter one. The Defender's force levels can be reduced by both types of Attacker weapons but at different attrition rates. The converse also applies. Victory is assumed to be by total annihilation of the Defender, towards which the battle progresses in one of two ways: where the Attacker is left with some of both weapon types, or where he retains some of one type only. The analysis is then extended to cover the optimization problem of minimizing the Attacker's initial resources. The implications for casualties are also discussed.     

悬臂梁在倾斜载荷作用下的弹塑性大挠度分析

作为Plastica理论[12]的应用,本文分析了理想弹塑性矩形截面梁在自由端承受倾斜集中力作用时塑性区扩展阶段的大挠度变形.着重讨论了集中力的倾角对弯曲形状、载荷—挠度关系及塑性区长度的影响.结果用解析解和数值解同时给出.     

Approximation of the Equilibrium Distribution via Extreme Value Theory: an Application to Insurance Risk

Methodology and Computing in Applied Probability - We use the excess over a threshold method (see e.g. Embrechts et al. 1997) to approximate the tails of equilibrium distributions (integrated tail...     

C_0复杂度的改进及其在证券市场中的应用

系统地分析了Lemple-Ziv复杂性度量方法的应用过程中,将实际信号(时间序列)转变成符号序列的诸多方法中存在的一些问题,提出了更合理兼容法.该方法可以有效地刻划各种时间序列的复杂度.文章最后动态地分析了中国证券市场的复杂性.     

Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation

The purpose of the present work is to implement well-known statistical decision and game theory strategies into multiobjective stochastic control problems of fluid dynamics. Such goal is first justified by the fact that deterministic (either singleobjective or multiobjective) control problems that are obtained without taking into account the uncertainty of the model are usually unreliable. Second, in most real-world problems, several goals must be satisfied simultaneously to obtain an optimal solution and, as a consequence, a multiobjective control approach is more appropriate. Therefore, we develop a multiobjective stochastic control algorithm for general fluid dynamics applications, based on the Bayes decision, adjoint formulation and the Nash equilibrium strategies. The algorithm is exemplified by the multiobjective stochastic control of a periodic Burgers equation.     

主客观赋权合成指标权重及其在公共卫生综合评价中的应用

目的:探讨综合评价中指标权重的确定.方法:将相似权法和属性AHM赋权法相结合来确定指标权重,并应用于公共卫生质量的综合评价.结果:实现了对太原市5所普通旅店的聚类与排序;结论:主客观赋权合成指标权重,既充分利用了样本资料的统计信息,又反映了专家的理论知识和经验,可得到较为客观、合理的指标权重,将此权重用于综合评价,其结果准确可靠.     

An Evaluation of a Master's Degree in K‐8 Mathematics and Science: Classroom Practice

“Evaluation as a particular kind of investigated discipline is distinguished from, for example, traditional empirical research in the social sciences or from literary criticism, criminalistics, or investigative reporting, partly by its extraordinary multidisciplinarity” ( Scrivens, 1991 , p. 141). It is this unique multidisciplinary feature of evaluation that adds usefulness when determining the effectiveness of programs seeking to integrate mathematics and science teaching and learning across elementary and middle grade levels. In 2005, a K‐8 mathematics and science program celebrated its 15th year of service. The program was the result of education, business, and community partnership efforts focused on improving mathematics and science teaching and learning in schools throughout a metropolitan region in the southeastern United States. To date, over 350 K‐8 teachers have completed a master's degree through this mathematics and science education program. The director realized that an evaluation of the program would likely provide insights that would benefit not only the efforts of the program but the broader mathematics and science teaching and learning community. Hence, the National Science Foundation (award No. 9815931), which had provided start‐up funds for the program responded to this need and provided funding for a longitudinal evaluation of the program. The evaluation was conducted from 1999 to 2004. This article focuses on the evaluation results for years 1 and 2 and addresses the question related to changes in teachers' classroom practice.     

A Time-Independent Approach for the Study of the Spectral Shift Function and an Application to Stark Hamiltonians

In this paper we develop a time-independent approach for the study of the spectral shift function (SSF for short). We apply this method for the perturbed Stark Hamiltonian. We obtain a weak and a Weyl-type asymptotics with optimal remainder estimate of the SSF of the operator pair (P = P₀ + V(x), P₀ = ? h²Δ +x₁), x = (x₁,…, x_n) where V(x) ∈ 𝒞^∞(?ⁿ, ?) decays sufficiently fast at infinity, and h is a small positive parameter. Near a non-trapping energy λ, we give a pointwise asymptotic expansions in powers of h of the derivative of the SSF, and we compute explicitly the two leading terms.     

An Upper Bound for the Excessive Index of an r‐Graph

We construct a family of r‐graphs having a minimum 1‐factor cover of cardinality (disproving a conjecture of Bonisoli and Cariolaro, Birkhäuser, Basel, 2007, 73–84). Furthermore, we show the equivalence between the statement that is the best possible upper bound for the cardinality of a minimum 1‐factor cover of an r‐graph and the well‐known generalized Berge–Fulkerson conjecture.     

Stable Solutions to Homogeneous Difference-Differential Equations with Constant Coefficients: Analytical Instruments and an Application to Monetary Theory

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we present a general method for determining the stability of any solution to a homogeneous linear difference-differential equation with constant coefficients and advancing arguments.     

逆谱理论新方法中A-函数和势函数依赖关系的稳定性研究

对于一维Schrdinger算子,本文基于Simon给出的惟—性定理(势函数由A-函数惟一确定)证明了势函数连续依赖于A-函数;反过来,若势函数q∈L~1(0,∞),给出了A-函数也连续依赖于势函数的结论.     

Quadruple Trigonometrical Series Equations and Their Application to an Inclusion Problem in the Theory of Elasticity

Closed form solution of quadruple series equations involving cosine kernels has been obtained by reducing the series equations into triple Abel's type integral equations which in turn are reduced to a single integral equation. Making use of finite Hilbert transforms the solution of the single integral equation is obtained in closed form. This solution is used to solve an electrostatic problem. The results of this paper have also been used in a two-dimensional elastostatic problem under anti-plane shear and the effect of rigid line inclusions with thickness on the Griffith cracks has been examined. The expressions for shear stress and stress intensity factor at the tip of the crack are obtained. Finally, some numerical results for the stress intensity factor and shear stress distribution are obtained.     

The Application of the Engineering Design Process to Curriculum Revision: A Collaborative Approach to STEM Curriculum Refinement in an Urban District

This study describes how student unit assessment data helped support ongoing curriculum revisions in the Baltimore City School District. This project is situated in the STEM Achievement in Baltimore Elementary Schools (SABES) project, which is a National Science Foundation funded multi‐year Math Science Partnership between the Johns Hopkins University and the Baltimore City School District. The project focuses on improving STEM education in grades three through five. The study modeled the process of curriculum revision after the engineering design process. One of the units developed by the partnership was analyzed using this revision process. Areas of unit revision and modification were identified utilizing the analysis of pre‐ and post‐assessment data from the implementation of the unit. Constraints represented by standards, unit objectives, and student‐reading levels further informed the revision process. The process resulted in modifications to aspects of the unit and assessment. Findings from this work will help inform collaborative curriculum initiatives between institutions of higher education public school districts.     

An Extension of a Convolution Inequality forG-Monotone Functions and an Approach to Bartholomew's Conjectures

A variety of convolution inequalities have been obtained since Anderson's theorem. ?In this paper, we extend a convolution theorem forG-monotone functions by weakening the symmetry condition ofG-monotone functions. Our inequalities are described in terms of several orderings obtained from a cone. It is noteworthy that the orderings detect differences in directions. A special case of the orderings induces a majorization-like relation on spheres. Applying our inequality, Bartholomew's conjectures, which concern directions yielding the maximum power and the minimum power of likelihood ratio tests for order-restricted alternatives, are partly settled.     

On the Stochastic Theory of Compartments: The General Time-dependent Two-compartment Reversible System with an Application to Manpower Planning

In this paper a general time-dependent stochastic model for the analysis of the two-compartment reversible system with non-homogeneous Poisson inputs and arbitrary residence times in each of the compartments is presented. The transition probabilities are suitably modified in order to be useful for estimation purposes of the parameters of the model. Various results are derived in terms of the distributions of the residence times only and are expressed in the form of convolution integrals which are readily evaluated by means of known computational algorithms. Finally, the theoretical results are applied to examples from the literature on manpower planning and some practical implications for the personnel and labour fields are considered.     

Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models

This study considers the problem of control and synchronization between fractional‐order and integer‐order, N‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results are exemplified by two significant biochemical models, namely, the fractional‐order Lengyel‐Epstein model and the Gray‐Scott model. To illustrate the effectiveness of the proposed scheme, numerical simulations are performed in one and two space dimensions using Homotopy Analysis Method (HAM).