同调谐振子的变形

实现了在保持本征值谱结构不变情况下同调谐振子的几种变形.这些变形包括三维各向同性谐振子径向方程、开普勒径向方程、Morse势s态等问题.每一个变形体系对应着同调参量g的确定取值.同调谐振子有一定的普遍适应性,具有丰富的内容. 关键词： 同调谐振子 同调参量 产生算符 湮没算符     

Interpretations of Quantum Theory in the Light of Modern Cosmology

The difficult issues related to the interpretation of quantum mechanics and, in particular, the “measurement problem” are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott’s problem.     

Optimal shape design of iron pole section of electromagnet

In this Letter, the classical problem of determining the optimal shape of the pole of an electromagnet is considered. In order to determine the optimal shape, we have extended a measure theory-based method. The problem of finding the optimal shape is reduced to one consisting of minimizing a linear form over a set of positive measures. To do so, an embedding procedure is applied. The resulting problem can be approximated by a finite-dimensional linear programming problem. The solution of the problem is used to construct a nearly optimal shape.     

The Pomraning-Eddington approximation to diffusion of light in turbid materials

The source-free diffusion problem of light in turbid media with generalized boundary conditions is considered. The intensity of light is considered as a sum of collimated and diffused radiance. In this way the problem is transformed to a source problem with a collimated source (problem 1). This problem is solved in terms of the corresponding source-free problem of simple boundary conditions (problem 2). The Pomraning-Eddington method is used to solve problem 2. Two coupled first-order differential equations are obtained involving the energy density and the radiation net flux. Weight functions are introduced in order to force the boundary conditions to be fulfilled. Numerical results are given and compared with previous calculations. The calculations show that the accuracy depends on the choice of the weight function.     

Computation of discrete transparent boundary conditions for the 2D Helmholtz equation

We present a family of non-local transparent boundary conditions for the 2D Helmholtz equation. The whole domain, on which the Helmholtz equation is defined, is decomposed into an interior and an exterior domain. The corresponding interior Helmholtz problem is formulated as a variational problem in a standard manner, representing a boundary value problem, whereas the exterior problem is posed as an initial value problem in the radial variable. This problem is then solved approximately by means of the Laplace transformation. The derived boundary conditions are asymptotically correct, model inhomogeneous exterior domains and are simple to implement.     

A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation

In this paper, a Cauchy problem of two-dimensional heat conduction equation is investigated. This is a severely ill-posed problem. Based on the solution of Cauchy problem of two-dimensional heat conduction equation, we propose to solve this problem by modifying the kernel, which generates a well-posed problem. Error estimates between the exact solution and the regularized solution are given. We provide a numerical experiment to illustrate the main results.     

对称分类在非线性偏微分方程组边值问题中的应用

研究了微分方程对称分类在非线性偏微分方程组边值问题中的应用.首先,利用偏微分方程(组)完全对称分类微分特征列集算法确定了给定非线性偏微分方程组边值问题的完全对称分类;其次,利用一个扩充对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解了常微分方程组初值问题的数值解.     

Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii) relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and (iii) symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution (half of the information specifying it when the solution is an unstructured bit string). Completing the physical representation shows that the number of computation steps (oracle queries) required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution.     

An iterative solution of the three-colour problem on a random lattice

We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and critical behaviour of the resulting matrix model. Based on a set of loop equations we develop an algorithm which enables us to solve the three-colour problem recursively.     

Review of force reconstruction techniques

An important engineering problem is the recovery of the input of a system given its output. This is a difficult problem to solve in that it is often an ill-defined problem. Such ill-posedness is problematic since noise becomes very influential and results in inaccurate or non-unique solutions. To combat this ill-posedness, additional constraints are typically applied to redefine the problem, leading to a well-defined problem with a unique solution. Current input reconstruction methods span the spectrum of analysis and computation, and we have grouped them into three categories: Direct, Regularization, and Probabilistic/Statistical. Each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem. Our primary interests lie in the behavior of mechanical systems and, as such, we have focused on the literature in these fields. However, applicability includes other fields with the same and similar governing equations.     

Lieben Mei symmetry and conserved quantities of the Rosenberg problem

The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.     

Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System

In this paper, we are concerned with the explicit construction of peakon solutions of the integrable twocomponent system with cubic non-linearity. We establish the spectral and inverse spectral problem associated to the Lax pairs of the system. The inverse problem is solved by the classical results of Stieltjes continued fractions, which also contributes a lot to the spectral problem. The explicit formulas are obtained from solutions of the inverse problem. The positivity of the spectral measures is implied by J. Moser's work on the Jacobi spectral problem.     

二维金属光子晶体的带结构研究

采用一种新的平面波展开法研究金属光子晶体的带结构，即在传统平面波展开法的基础上，将“原问题”拓展，引入一个“新问题”，通过求解“新问题”得到“原问题”的带结构，并论证了它们之间的关系.为了准确求解“新问题”，引入辅助函数，将其色散关系等价为一个积分微分本征方程，求解这个本征方程得到“新问题”的带结构，从而由此导出“原问题”的带结构.最后，以正方晶格二维金属光子晶体为例，进行数值计算，得到了满意的结果. 关键词： 金属光子晶体 平面波展开法 带结构 正方晶格     

Spectrum of a Problem of Elasticity Theory in the Union of Several Infinite Layers

The essential spectrum of the Dirichlet problem for the system of Lamé equations in a three-dimensional domain formed by three mutually perpendicular elastic layers occupies the ray [Λ_?,+∞). The lower bound Λ_? > 0 is the least eigenvalue (its existence is established) of the problem of elasticity theory in an infinite two-dimensional cross-shaped waveguide. It is proved that the discrete spectrum of the spatial problem is nonempty. Other configurations of layers and the scalar problem of the junction of quantum waveguides are also considered.     

A method of linearization for Painlevé equations: Painlevé IV, V

A method to linearize the initial value problem of the Painlevé equations IV, V is given. The procedure involves formulating a Riemann-Hilbert boundary value problem on intersecting lines for the inverse monodromy problem. This boundary value problem is reduced to a sequence of standard problems on single lines in a certain range of parameter space. Schlesinger transformations allow one to completely cover the parameter space. Special solutions are constructed from special cases of the Riemann problem as well.     

Universal Bounds for Eigenvalues of a Buckling Problem

In this paper, we investigate an eigenvalue problem for a biharmonic operator on a bounded domain in an n-dimensional Euclidean space, which is also called a buckling problem. We introduce a new method to construct ``nice' trial functions and we derive a universal inequality for higher eigenvalues of the buckling problem by making use of the trial functions. Thus, we give an affirmative answer for the problem on universal bounds for eigenvalues of the buckling problem, which was proposed by Payne, Pólya and Weinberger in [14] and this problem has been mentioned again by Ashbaugh in [1]. Research partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science. Research partially supported by SF of CAS     

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

太阳中微子问题研究进展

系统评述了国际上对太阳中微子研究的进展 ,说明了核物理实验对研究太阳中微子问题作出的贡献 ,对未来的中微子实验作了展望.The comparison between experimental results and theoretical predictions has yielded the solar neutrino problem. Over the years, the large communities of astrophysics and of nuclear physics took enormous efforts in solving this problem. The current progress on the study of solar neutrino problem is reviewed. Nuclear physics can make a significant contribution to this problem. The importance of the nuclear physics experiment is introduced. To minimize the uncertainties of neutrino detection has led to new...     

数字化机步旅抢修任务动态调度框架研究

针对一体化机动进攻作战中战场抢修任务动态分配缺乏定量化确定方法的问题,对数字化机步旅抢修任务动态调度的框架结构进行了研究。借鉴Hall三维结构方法论,从对象维、过程维和技术维3个维度建立了抢修任务动态调度的框架结构,并以此为基础,分析梳理出了抢修任务动态调度的7个核心子问题,总结了这些核心子问题的自身特性,为抢修任务动态调度的后续研究提供了宏观规划和微观指导。     

Rosenberg问题的对称性与守恒量

Rosenberg问题是一个典型而不太复杂的非完整系统问题.本文利用非完整系统的Noether对称性理论来求这个非完整力学问题的守恒量,进而得到问题的最终解.