拟阵Q6与W4可F-线性表示的构造

对拟阵Q6与W4可F-线性表示的构造进行了研究.用E(G)在R上的链群F0(G,R)表示G的圈拟阵M(G);用松弛拟阵M的极小圈超平面X的方法得到拟阵M'.得到主要结果为:(i)用链群表示了M(K4),M(W4);(ii)用松弛极小圈超平面的方法从M(K4)构造了Q6,从M(W4)构造了W4,找出了W4可线性表示的所有...     

“运价”为负的运输模型计算机求解问题的处理

为解决一些计算机软件求解"运价"既有正值又有负值运输模型时"不可求解"的问题,本文采用"运价同额增减法"决策模型转换的方法,将原模型的"运价"全部转换为正值后再用计算机软件求解,并分别编写了EXCEL求解模板和求解程序对该方法的计算加以印证。结果表明,采用该方法求解得出的最优解(最优决策方案)与原模型求得的最优解完全一样,而最优值(最优决策效果)减去虚增(或加上虚减)的部分就是原模型的最优值。采用这种方法能成功地解决一些计算机软件"不可求解"的问题。     

Existence and Regularity for Dynamic Viscoelastic Adhesive Contact with Damage

A model for the dynamic process of frictionless adhesive contact between a viscoelastic body and a reactive foundation, which takes into account the damage of the material resulting from tension or compression, is presented. Contact is described by the normal compliance condition. Material damage is modelled by the damage field, which measures the pointwise fractional decrease in the load-carrying capacity of the material, and its evolution is described by a differential inclusion. The model allows for different damage rates caused by tension or compression. The adhesion is modelled by the bonding field, which measures the fraction of active bonds on the contact surface. The existence of the unique weak solution is established using the theory of set-valued pseudomonotone operators introduced by Kuttler and Shillor (1999). Additional regularity of the solution is obtained when the problem data is more regular and satisfies appropriate compatibility conditions.     

An algorithm for the removal of noise and jitter in signals and its application to picosecond electrical measurement

The accuracy of data recorded by many measurement systems is limited both by uncertainty in the measured value as well as by uncertainty in the trigger input to the system which controls when a measurement is taken. The former effect, which appears as noise on the underlying signal, is due, in part, to the sampling process and can often be reduced to an acceptable level by averaging many measurements. Noise on the trigger input gives rise to uncertainty in time between the trigger and the measurement points. The effect, known as jitter, causes a distortion of the signal which cannot be removed by averaging.We describe and analyse the effects of noise and jitter on a waveform, and an algorithm for removing, or reducing, these effects is presented. The work is motivated by an application in picosecond electrical and optoelectronic metrology where a laser pulse is measured by a system consisting of a photodiode and sampling oscilloscope. Here, since the length of the pulse is so short, perhaps only tens of picoseconds in duration, the effect of jitter is as pronounced as that of measurement noise. Results obtained by applying the algorithm to simulated data obtained from this application are presented.     

Numerical method of mixed finite volume-modified upwind fractional step difference for three-dimensional semiconductor device transient behavior problems

Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L² norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.     

Automation and group structures in certain economic adjustment mechanisms

It is shown that the economic adjustment mechanism developed by Hurwicz and his associates has the structure of automata. It is then shown that certain price adjustment mechanisms, having an acceptability condition, impose a group structure upon the automaton. This condition is a bilinear invariance implied by a budget constraint. Then the automaton is defined by a subgroup, depending on agents' tastes, technologies and strategies, and by the representations of the subgroup imposed by the automaton.     

Completeness theorem for topological class models

A topological class logic is an infinitary logic formed by combining a first-order logic with the quantifier symbols O and C. The meaning of a formula closed by quantifier O is that the set defined by the formula is open. Similarly, a formula closed by quantifier C means that the set is closed. The corresponding models are a topological class spaces introduced by Ćirić and Mijajlović (Math Bakanica 1990). The completeness theorem is proved. This research was supported by the Ministry of Science, Technology and Development, Republic of Serbia, through Mathematical Institute, under grant 144013.     

货运列车的编组调度问题的研究

对于货运列车的编组调度问题,建立了以压缩中时和增加运量为双目标、多约束的0-1规划模型,采用逐步紧缩中时约束的方法得到了问题一的调度方案.在此基础上对装载特别物资的车辆施加更强的中时约束得到了问题二的调度方案.提出了列车匹配系数的概念并建立了列车最优配对原则,根据该原则对列车进行优化编组得到了问题三的调度方案.基于问题二的数据转换处理得到了问题四的调度方案.     

沪深股市收益的相关性

以概率作为相关度量指标,分整体相关性和尾部相关性对沪深两市收益进行考察。整体相关性采用概率方法中的变化协调形成的相关性作为度量,结果表明沪深两市收益在整体上具有一定的正相关性。对于尾部相关性,先用t分布分别拟事两市收益底分布,然后用蒙特卡洛模拟确定尾部的最优门限,进而求得尾部相关性,结果显示当市场剧烈波动时两市收益具有正的相关性,且比整体相关性强,尤其在暴跌的时候,两市具有很强的正相关性。     

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.     

Consciousness and the structuring property of typical data

The theoretical base for consciousness, in particular, an explanation of how consciousness is defined by the brain, has long been sought by science. We propose a partial theory of consciousness as relations defined by typical data. The theory is based on the idea that a brain state on its own is almost meaningless but in the context of the typical brain states, defined by the brain's structure, a particular brain state is highly structured by relations. The proposed theory can be applied and tested both theoretically and experimentally. Precisely how typical data determines relations is fully established using discrete mathematics. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Modelling,Synthesis, and Simulation of Supervisory Process Control Systems

Modelling, synthesis, and simulation issues of the supervisory systems in process control are investigated in the paper. Petri nets are used as a basic modelling framework for the supervisory part of the system. It is shown how the final verification effort can be minimised by applying formal synthesis methods. A straightforward approach to the industrial implementation of the developed solutions is suggested by means of sequential function chart representation. A batch process cell case study is used to illustrate the described concepts. Corresponding continuous and discrete event models of the process cell units are developed and a co-ordinating supervisor is designed by the method of place invariants. The system is simulated by the continuous simulation tool Matlab-Simulink, which is enhanced for simulation of the sequential control logic represented by sequential function chart.     

A fourth-order numerical method for the planetary geostrophic equations with inviscid geostrophic balance

The planetary geostrophic equations with inviscid balance equation are reformulated in an alternate form, and a fourth-order finite difference numerical method of solution is proposed and analyzed in this article. In the reformulation, there is only one prognostic equation for the temperature field and the velocity field is statically determined by the planetary geostrophic balance combined with the incompressibility condition. The key observation is that all the velocity profiles can be explicitly determined by the temperature gradient, by utilizing the special form of the Coriolis parameter. This brings convenience and efficiency in the numerical study. In the fourth-order scheme, the temperature is dynamically updated at the regular numerical grid by long-stencil approximation, along with a one-sided extrapolation near the boundary. The velocity variables are recovered by special solvers on the 3-D staggered grid. Furthermore, it is shown that the numerical velocity field is divergence-free at the discrete level in a suitable sense. Fourth order convergence is proven under mild regularity requirements. R. Samelson was supported by NSF grant OCE04-24516 and Navy ONR grant N00014-05-1-0891. R. Temam was supported by NSF grant DMS-0604235 and the research fund of Indiana University. S. Wang was supported by NSF grant DMS-0605067 and Navy ONR grant N00014-05-1-0218.     

集合环

本文用集环来表现模糊集，得到了表现定理的新形式，并证明了这种表现可以有限化，即用有限个经典集近似刻划模糊集并且这样的刻划是同态的。最后，证明了集对方法是集环表现的特殊情形。     

Exterior Minimum-Penalty Path-Following Methods in Semidefinite Programming

A semidefinite programming problem is a mathematical program in which the objective function is linear in the unknowns and the constraint set is defined by a linear matrix inequality. This problem is nonlinear, nondifferentiable but convex. It covers several standard problems, such as linear and quadratic programming, and has many applications in engineering. In this paper, we introduce the notion of minimal-penalty path, which is defined as the collection of minimizers for a family of convex optimization problems, and propose two methods for solving the problem by following the minimal-penalty path from the exterior of the feasible set. Our first method, which is also a constraint-aggregation method, achieves the solution by solving a sequence of linear programs, but exhibits a zigzagging behavior around the minimal-penalty path. Our second method eliminates the above drawback by following efficiently the minimum-penalty path through the centering and ascending steps. The global convergence of the methods is proved and their performance is illustrated by means of an example.     

On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest

We consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed.     

小垂度粘弹性索非线性响应及振动主动控制

研究具有初始应力的小垂度粘弹性索的非线性动态响应及振动主动控制。在假定索材料的本构关系为一般微分本构类型的基础上,建立小垂度粘弹性索的运动微分方程;应用Galerkin方法将其转化为可用Runge-Kutta数值积分方法求解的一系列三阶非线性常微分方程。在仅考虑面内的横向振动及忽略非线性的情况下得到了连续状态空间中的状态方程,将状态方程离散为差分方程形式,并用矩阵指数来逐步近似状态转移矩阵;基于二次性能指标的最小化得到了最优的控制力与状态向量。最后通过数值仿真研究说明了粘性参数对索动态响应的影响。     

面向不确定需求租户集的云服务智能匹配模型

为了解决云计算环境下由海量租户集和资源集间的不确定性因素引起的高质量云服务获取困难的问题,提出了一种描述动态异构租户集不确定性需求的方法.在此基础上,构建属性权重完全未知情况下的云服务智能匹配模型,排除了租户提交权值造成的偏差.神经网络以属性区间计算的相离度作为输入,服务满意度为输出来动态模拟租户集的不确定需求,运用萤火虫算法求解模型获取最优服务组合.最后,实例验证了神经网络的可靠性以及算法的有效性.实验结果表明,模型能有效获取高质量的云服务组合,优于传统的匹配方法.     

序数权重统一表示下的权重稳健性Hasse图分析

认识多种序数赋权方法的共性,有助于摆脱方法选择困扰,增强其实用效果。首先以线性函数为目标函数,以权重关系构造约束条件,建立线性规划。在此基础上证明了任意权重均可由线性规划的极值点集来表示,揭示了序数权重实质上是极值点的加权线性组合。进一步针对赋权方法稳健性不足的问题,利用极值点构建偏序关系,通过Hasse图增强权重排序的稳健性。实例分析表明,尽管序数权重不同,但与偏序方法相结合,均能得到类似的分析结果。     

Deletion-by-infeasibility rule for DC-constrained global optimization

In Ref. 1, a general class of branch-and-bound methods was proposed by Horst for solving global optimization problems. One of the main contributions of Ref. 1 was the opportunity of handling partition elements whose feasibility is not known. Deletion-by-infeasibility rules were presented for problems where the feasible set is convex, is defined by finitely many convex and reverse convex constraints, or is defined by Lipschitzian inequalities. In this note, we propose a new deletion-by-infeasibility rule for problems whose feasible set is defined by functions representable as differences of convex functions.This research was supported in part by the Hungarian National Research Foundation, Grant OTKA No. 2568.