离散几何的两个铺砌问题

利用图论和代数的方法研究离散几何中的两个铺砌问题:1)给出1×2长方形铺砌多米诺骨牌的充分必要条件;2)对高维空间盒子的情形,给出m_1×m_2×…×m_n砖能够铺砌a_1×a_2×…×a_n盒子的一些必要条件和充要条件.     

Relativistic dynamics for spin-zero and spin-half particles

The classical and quantum mechanics of a system of directly interacting relativistic particles is discussed. We first discuss the spin-zero case, where we basically follow Rohrlich in introducing a set of covariant centre of mass (CM) and relative variables. The relation of these to the classic formulation of Bakamjian and Thomas is also discussed. We also discuss the important case of relativistic potentials which may depend on total four-momentum squared. We then consider the quantum mechanical case of spin-half particles. The negative energy difficulty is solved by introducing a number of first class constraints which fix the spinor structure of physical solutions and ensure the existence of proper CM and relative variables. We derive the form of interactions consistent with Lorentz invariance, space inversion, time reversal and charge conjugation and with the above mentioned first class constraints and find that it is analogous to that for the non-relativistic case. Finally the relationship of the present work with some previous work is briefly discussed.     

Numerical examples of the behavior of REQP on nonlinear programming problems involving linear dependence among the constraint normals

This report illustrates, by means of numerical examples, the behavior of the constrained minimization algorithm REQP in situations where the active constraint normals are not linearly independent. The examples are intended to demonstrate that the presence of the penalty parameter in the equations for calculating the Lagrange multiplier estimates enables a useful search direction to be computed. This is shown to be true, whether the dependence among the constraint normals occurs at the solution or in some other region.     

Brownian motion on a manifold

The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due to a physical agency that forces the motion to remain on a manifold, or they represent conserved quantities of the equation of motion themselves. Also the Brownian motion is described either by a Smoluchowski diffusion equation or by a Kramers equation. The four cases lead to the following conclusions, (i) Smoluchowski diffusion with a conserved quantity reduces to a diffusion equation on the manifold; (ii) The same is true for diffusion with a physical constraint in three dimensions, but in more dimensions it may happen thatno autonomous equation on the manifold results; (iii) A Kramers equation with a conserved quantity reduces to an equation on the manifold, but in general not of the form of a Kramers equation; (iv) The Kramers equation with a physical constraint reduces to an autonomous Kramers equation on the manifold only for a special shape of that constraint. Throughout, only a certain type of physical constraints has been envisaged, and global questions are ignored. Finally, the customary heuristic construction of a Fokker-Planck equation for a mechanical system on a manifold is demonstrated for the case of Brownian rotation of a rigid body, and its shortcomings are emphasized.     

Characteristics of Good Meta-Heuristic Algorithms for the Frequency Assignment Problem

Most writers on frequency assignment algorithms have described the details of a single algorithm, and evaluated the algorithm on selected data sets. There has been relatively little emphasis on describing the common features that are important if an algorithm is to have good performance. This paper describes the key features, with particular emphasis on algorithms for weighted fixed spectrum problems. The use of algorithms handling weighted constraints has become increasingly common in recent years. The advantages and disadvantages of weighting constraints are demonstrated.     

On convergence properties of a least-distance programming procedure for minimization problems under linear constraints

In Ref. 1, Bazaraa and Goode provided an algorithm for solving a nonlinear programming problem with linear constraints. In this paper, we show that this algorithm possesses good convergence properties.This paper was written under the guidance of Associate Professor C. Y. Wang. The author takes great pleasure in thanking him.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739–760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example. The first author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science and SRF for ROCS, SEM. The second author’s work was supported in part by the United Kingdom Engineering and Physical Sciences Research Council grant. The third author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.     

On Some Feasibility Conditions in MPEC

This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].     

基于激光点云多条件约束的相机检校方法

为了克服相机检校对二维/三维检校场的依赖,提出一种基于激光点云多条件约束的相机检校方法。该方法通过对相机获取的多视影像进行光束法平差获得初始相机参数;利用影像点云与其最邻近的激光点云之间的位置关系,以共线方程为基础模型,建立多条件约束的相机检校数学模型;使用不等式约束的最小二乘方法平差迭代解算相机参数。将本文方法与基于三维控制场的检校精度进行了实验对比分析,结果表明本文方法与基于三维控制场的检校精度相当,两者反投影平均误差相差小于0.1 pixel,验证了本文方法在没有传统检校场的情况下进行相机检校的可行性。