一类变系数KdV方程的Painlevé分析和自Bcklund变换

利用符号计算对一类系数函数是x和t的函数的变系数K dV方程进行了Pa in levé分析,得到了该方程具有Pa in levé性质时系数函数必须满足的约束条件.利用Pa in levé截断法给出了该方程的一个自B ck lund变换,作为例子根据得到的自B ck lund变换给出了两组精确解.     

A multiobjective evolutionary algorithm for approximating the efficient set

In this article, a new framework for evolutionary algorithms for approximating the efficient set of a multiobjective optimization (MOO) problem with continuous variables is presented. The algorithm is based on populations of variable size and exploits new elite preserving rules for selecting alternatives generated by mutation and recombination. Together with additional assumptions on the considered MOO problem and further specifications on the algorithm, theoretical results on the approximation quality such as convergence in probability and almost sure convergence are derived.     

On Optimal Forecasting with Soft Computation for Nonlinear Time Series

In this paper we present a new approach on optimal forecasting by using the fuzzy set theory and soft computing methods for the dynamic data analysis. This research is based on the concepts of fuzzy membership function as well as the natural selection of evolution theory. Some discussions in the sensitivity of the design of fuzzy processing will be provided. Through the design of genetic evolution, the AIC criteria is used as the adjust function, and the fuzzy memberships function of each gene model are calculated. Simulation and empirical examples show that our proposed forecasting technique can give an optimal forecasting in time series analysis.     

非线性波方程准确孤立波解的符号计算

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.     

Quantum Algorithm for Hilbert's Tenth Problem

We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle—that is, if certain Hamiltonian and its ground state can be physically constructed according to the proposal—quantum computability would surpass classical computability as delimited by the Church—Turing thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.     

超临界CO2热力学性质的理论计算

应用BWR方程在温度为310～600 K、压强为75～300 bar范围内拟合的超临界CO2流体状态方程,计算了超临界状态下CO2体系的熵、热容和焓.研究表明,这些热力学函数具有明显的超临界特性;与文献值相比,超临界状态下CO2熵的相对误差小于0 .4%,而定压热容的相对误差稍大,为2.45%(T:330～360 K),其数据为进一步从理论上研究超临界CO2与金属铀表面反应的热力学行为奠定了基础.     

Interval estimation of mean response time for a G/M/1 queueing system: empirical Laplace function approach

Mean response time is an important performance measure for a queueing system. In this paper, we propose a consistent and asymptotically normal (CAN) estimator of the mean response time for a G/M/1 queueing system, which is based on the fixed point of empirical Laplace function. The confidence interval for the mean response time can be constructed by applying the proposed CAN estimator and its estimated variance. And we carried out a simulation study to perform the accuracy of the constructed confidence interval by calculating the coverage percentage and the relative average length of confidence interval. Detailed discussions of all simulation results for three various models of G/M/1‐type system are presented and some valuable conclusions are provided. Copyright © 2006 John Wiley & Sons, Ltd.     

Computers with Closed Timelike Curves Can Solve Hard Problems Efficiently

A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for the problem of factoring large numbers and argue that a similar approach can solve NP-complete and PSPACE-complete problems. I discuss the potential impact of quantum effects on this result.     

K_（1，r）－free图的次限制树多项式算法

设Ｇ＝（Ｖ，Ｅ）为一连通图，ｄ＞０整数．Ｇ中存在生成树Ｔ，使得Δ（Ｔ）小于ｄ吗？这一问题已被证明是ＮＰ－完全的，故不太可能有多项式解法．本文证明了当Ｇ是Ｋ１，ｒ－ｆｒｅ时，则有Ｏ（ｎ２）的算法求出Ｇ的生成树Ｔ，使Δ（Ｔ）≤ｒ，并用一个例子显示了这一结果是最好可能的     

利用暗本征态的绝热演化实现非几何条件相位移动:一种实现量子计算的新方法

利用绝热演化，文章提出一种新的方法以实现量子相位门，这种相位移动既非源于动力学过程，也非源于几何操纵，它来源于暗态本身的演化，基于绝热演化的优点，这种量子逻辑门对实验参量的起伏不敏感，与几何相位门相比，这种相位门更简单，并且保真度可得到进一步提高。文章对这种相位门做一简述。