一个物理问题的建模及解答

对一个实际物理问题,构造相应的模型,得到描述其运动状态的常微分方程组.利用数学软件M ap le辅助,求解该方程组,从而准确刻画相应时刻物体的位置.     

Modelling Techniques for Simulation of Submarine Engagements

The process of designing complex, costly military systems benefits substantially from analyses of performance as predicted by some form of model of the system and its operating environment. In this paper, techniques are described that have been implemented in a suite of computer programs to represent the tactical situations that can develop between two opposing submarines. The kernel of the program suite is the Submarine Interactive Attack Model (SIAM). This is sufficiently versatile that a wide range of scenarios can be simulated, and meaningful statistics for expected submarine performance obtained. Emphasis is placed on the modelling of both the dynamic tactical situations that can evolve in underwater warfare and the tactical decision-making that influences the outcome of submarine operations. Although the techniques have been applied to a specific domain it is believed that they are applicable to a wide range of complex problems.     

水星近日点进动的建模与摄动解

本文针对水星近日点进动现象 ,结合广义相对论建立了奇摄动微分方程模型 ,并运用多重尺度法 ,求出了一般行星进动问题的摄动解 ,从而很好的解释了水星进动之谜和一般行星的进动问题 .     

Modelling the Effects of Prepaid Monetary Incentives on Mail-Survey Response

This paper presents a statistical model relating the impact of prepaid monetary incentives on response rates from mail surveys. The model supports the use of monetary incentives, but inclusion of incentive value made an insignificant contribution to the model. A cost-benefit model was developed to estimate the economic worth of incentives when a researcher is attempting to achieve a target sample size.     

Negative Effects of Modeling Techniques on Search Performance

Symmetries occur in many combinatorial problems, and a great deal of research has been done on symmetry breaking techniques for backtrack search. However, few results have been reported on the use of symmetry breaking with local search. On four classes of problem we find that adding symmetry breaking constraints to a model impairs local search performance, in terms of both execution time and search steps. We also find that implied constraints can impair backtrack search performance. These results show that modeling techniques and search heuristics should be combined with caution. They also motivate a novel modeling technique for local search: removing constraints to add new symmetries.     

Spline Techniques for the Numerical Solution of Singular Perturbation Problems

One-dimensional singularly-perturbed two-point boundary-value problems arising in various fields of science and engineering (for instance, fluid mechanics, quantum mechanics, optimal control, chemical reactor theory, aerodynamics, reaction-diffusion processes, geophysics, etc.) are treated. Either these problems exhibits boundary layer(s) at one or both ends of the underlying interval or they possess oscillatory behavior depending on the nature of the coefficient of the first derivative term. Some spline difference schemes are derived for these problems using splines in compression and splines in tension. Second-order uniform convergence is achieved for both kind of schemes. By making use of the continuity of the first-order derivative of the spline function, a tridiagonal system is obtained which can be solved efficiently by well-known algorithms. Numerical examples are given to illustrate the theory.     

Stochastic Global Optimization: Problem Classes and Solution Techniques

There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classification of essentially unconstrained global optimization problems into unimodal, easy, moderately difficult, and difficult problems is proposed. The problem features giving this classification are the chance to miss the region of attraction of the global minimum, embeddedness of the global minimum, and the number of minimizers. The classification of some often used test problems are given and it is recognized that most of them are easy and some even unimodal. Global optimization solution techniques treated are global, local, and adaptive search and their use for tackling different classes of problems is discussed. The problem of fair comparison of methods is then adressed. Further possible components of a general global optimization tool based on the problem classes and solution techniques is presented.     

Decomposition of Log Crepant Birational Morphisms between Log Terminal Surfaces

We prove that every log crepant birational morphism between log terminal surfaces can be decomposed into log flopping type divisorial contraction morphisms and log blowdowns. Repeating these two kinds of contractions, we reach a minimal log minimal surface from any log minimal surface.     

Log canonical thresholds of divisors on Grassmannians

Let L be the Plücker line bundle on the Grassmannian. Given D ∈ |kL|, we show that the log canonical threshold of D is at least . The main ingredients of the proof are Kapranov's result on the derived category of coherent sheaves on the Grassmannian, Nadel's vanishing theorem for multiplier ideal sheaves, and Demailly's vanishing theorem for vector bundles.     

Log canonical foliation singularities on surfaces

We give a classification of the dual graphs of the exceptional divisors on the minimal resolutions of log canonical foliation singularities on surfaces. As an application, we show the set of foliated minimal log discrepancies for foliated surface triples satisfies the ascending chain condition and a Grauert–Riemenschneider–type vanishing theorem for foliated surfaces with special log canonical foliation singularities.     

Log Structures on Generalized Semi-Stable Varieties

In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called semi-stable log structures exists if and only if the obstruction vanishes. In the case of no power, if the obstruction vanishes, then the semi-stable log structure is unique up to a unique isomorphism. So we obtain a kind of canonical structure on this family of morphisms.     

Complementary Modelling Approaches for Analysing Several Effects of Privatization on Electricity Investment

Through the impacts of higher required rates of return, debt, taxation changes and a new competitive structure for the industry, investment in electricity generating capacity has taken a shift to less capital-intensive technologies in the UK. This paper reports on the use of large-scale, long-term capacity planning models, of both an optimization and system dynamics nature, to reflect these separate factors, investigate their sensitivities and to generate future scenarios for the investment in the industry. Some new policy implications for the regulation of the industry become apparent, but the main focus of the paper is to develop some of the methodological changes required by the planning models to suit the privatized context.     

太阳帆塔轨道和姿态耦合动力学建模及辛求解

在建立太阳帆塔太阳能电站简化模型的基础上,将系统的动力学方程从Lagrange体系导入到了Hamilton体系,给出了带约束的Hamilton正则方程;进而采用祖冲之类算法和辛Runge-Kutta方法分析了太阳帆塔轨道和姿态耦合系统的动力学特性,并讨论了算法的保能量、保约束特性;最后,数值模拟了系统的动力学特性,说明了所提方法的有效性.     

Adjoint Linear Systems on Normal Log Surfaces

We prove a Reider type theorem for separating any cluster by an adjoint system to a pseudoeffective divisor on a normal surface. As a corollary we get a Reider type theorem for adjoint linear systems (to a nef Q-divisor) on normal log surfaces. This theorem is new even for smooth surfaces.     

一类具Rotenberg模型解的存在性

迁移方程是研究物质中的粒子运动所产生的微观效应综合所致的宏观迁移现象规律的一种模型,研究这类迁移方程对数学基础理论的发展有着非常重要的意义.在L_1空间中,运用线性算子理论,研究了种群细胞增生中具Rotenberg模型的迁移方程,采用所谓的豫解算子等法证明了种群细胞增生中具Rotenberg模型解的存在性.     

Micro-Mechanical Modelling of Anisotropic Time-Dependent Healing Effects in Rubber-like Materials

Filler-reinforced rubber-like materials demonstrate deformation induced softening, known as the Mullins effect. This softening can be reversible in a certain range (healing). The previously introduced concept of network evolution (NE) explains the Mullins effect as the result of a filler-polymer network rearrangement [1]. It is assumed that debonding of polymer chain segments from rigid aggregates does not effect the number of active segments. Furthermore, debonded chains are still active as a part of a longer chain. Now, considering the entropic vibration of polymer chains, entanglement of chains to the rough aggregate surfaces is assumed. This process inverse to the NE leads to a micro-mechanical model of time-dependent recovery of the deformation induced softening. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comments on The Co-emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection

We comment on the paper The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to ‚task-technique-theory’ in the light of a model of abstraction in context and suggest that this re-viewing brings mutual analytic benefits.     

Modelling the Effects of Pest Control with Development of Pesticide Resistance

In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive different...     

Financial Modelling on Microcomputers

The financial modelling packages for microcomputers can be considered as falling into one of three categories:- visual spread sheets, micro base structured models and structured models which are compatible across, and allow communications between, micros and mainframes. This paper describes the three types of package, discusses the pros and cons of each, and offers a guide to system selection.