用预邻域系算子、预开邻域基算子和预基确定预拓扑

目的将拓扑空间的邻域系、开邻域基与基的性质和定理推广到预拓扑空间上。方法运用拓扑与格论的方法。结果得到五对完备格同构。结论将拓扑空间的邻域系、开邻域基与基的性质和定理推广到预拓扑空间上是成功的。

用L-预远域系算子、L-预外部算子或L-预边界算子确定L-预拓扑

给定集合X,设T(X)是X上的L-预拓扑的全体。本文证明了可以在R(X)(X上的L-预远域系算子的全体)、E(X)(X上的L-预外部算子的全体)和B(X)(X上的L-预边界算子的全体)上定义适当的序关系,使它们在一定条件下成为与(T(X),)同构的完备格。因此一个给定集合X上的L-预拓扑可以由X上的L-预远域系算子、L-预外部算子或L-预边界算子确定。

基于泛系粗糙集等价算子上的粒计算模型(英文)

标准粗糙集使用等价类作为粒来描述概念。本文弱化对等价关系的要求,将更广泛的粒计算模型建立到泛系粗糙集上去。本文通过对全域的分割和覆盖来诱导出泛系粗糙集上的粒计算模型。

基于粗糙集与泛系等价算子的特征选择

传统特征选择方法选出的特征子集存在冗余,并且不具备较好的代表性。针对该问题,提出基于粗糙集与泛系等价算子的特征选择方法。利用基于最小词频的文档频提取初始特征,通过泛系等价算子对粗糙集进行扩展,并给出属性约简算法消除冗余,从而获得较具代表性的特征子集。实验结果表明,该方法具有较高的准确率和召回率。

基于泛系等价算子的粗集概念扩展

利用泛系中的等价算子把一般的二元关系转化为等价关系,提出了泛系粗集的概念,使粗集可以处理基于非等价关系的问题,扩展了粗集的应用范围,为信息不完全问题的处理提供了思路,并讨论了几种特定等价算子的特点.

邻域系算子格及其性质

对拓扑学中邻域系的性质进行了研究,提出了一般集合X上的邻域系算子的概念.借助格论的思想,在邻域系算子族N(X)中引入二元运算∩,∪,构造了邻域系算子格(N(X),∩,∪),并对其性质进行了研究.证明了(N(X),∩,∪)是一个完备格,它所诱导的序是由邻域系算子在各点结果的包含序决定的.并证明了(N(X),∩,∪)不满足分配性.

邻域系算子范畴及相关性质

对拓扑空间中的邻域系性质进行了进一步研究.提出了邻域系算子和邻域连续映射的概念,定义了邻域系算子范畴,讨论了该范畴上的余积和乘积,并证明了邻域系算子范畴与拓扑范畴是同构的2个范畴.

一些泛系算子的逆问题

本文主要给出了泛系算子方程ε_4(f)=(fof^(-1)U1)=ε,ε_5(f)=(f^(-1)ofU-I)=ε与δ_4=(fof^(-1)UI)~t=δ,δ_5=(f^(-1)foU1)~t=δ存在解的充分必要条件,而且当ε、δ有限时,讨论了方程的完全解集与解的数目等问题。

PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

Research on Rice Panicle L-system Model Based on Substructure Algorithm

In order to decrease model complexity of rice panicle for its complicated morphological structure,an interactive L-system based on substructure algorithm was proposed to model rice panicle in this study.Through the analysis of panicle morphology,the geometrical structure models of panicle spikelet,axis and branch were constructed firstly.Based on that,an interactive panicle L-system model was developed by using substructure algorithm to optimize panicle geometrical models with the similar structure.Simulation results showed that the interactive L-system panicle model based on substructure algorithm could fast construct panicle morphological structure in reality.In addition,this method had the well reference value for other plants model research.

关于不变平行闭子空间的一个注记(英文)

利用完全正映射与相似 同态问题的关系 ,给出了满足特殊条件具有相同算子值的两个算子 。

基于二进小波变换的图像增强技术

文章给出了图像的二进小波分解与重构,通过理论分析和实验研究了基于二进小波变换的图像子带增强算法,重点是二进小波基的选取以及图像分解层次对图像中目标边缘增强的影响研究。二进小波变换提供平移不变表示,导致完备的高频分量适于图像增强,实验结果表明,二进小波变换增强方法可以减少噪声的放大,在增强图像微小细节和避免放大噪声两方面获得令人满意的结果。

General Quantum Interference Principle and Duality Computer

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.

IMPROVEMENT OF MATRIX REPRESENTATION METHOD IN NORMAL FORM THEORY

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.

Completeness of Eigenfunction Systems for Off-Diagonal Infinite-Dimensional Hamiltonian Operators

For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.

Decomposable Algorithm for Large Dynamic Programming

An approach about large dynamic programming based on discrete linear system with a quadratic index function is proposed by importing two Lagrange multipliers.

Particle contamination, the disruption of electronic connectors in the signal transmission system

Particle pollution in air, also sometimes known as fine dust contamination, may cause electric contact failure. Recent research further proved that the fine particle is becoming a major disruption of the electronic connectors in signal transmission system. This paper specifies the connector contact in mobile phone application. To study the contact failure of mobile phone, a series of inspections and analytical research methods are introduced. Special features that cause the contact failure are summarized. Particle accumulation is the main problem; organic material such as lactates from sweat of the human body may act as adhesives to stick the separate particles together and make them adhere on the contact surface; chemical properties of dust cause serious local corrosion. The corrosion products may trap the particles and firmly attach on the contact surface; micro motion frequently occurs at the contact interface. Hard particle can be embedded into the surface, and soft particle could be squeezed and inserted into the contact; silicon compounds in dust play the most important role in forming high resistance regions that lead to failure; deposition of particles depends on the amount of materials, static electricity attracting force and gravity force applied on the particles. Current dust test can hardly reflect the serious contact failure. It is difficult to simulate the complexity of contact failure caused by particle contamination. Thus alternative ways of simulation experiment and improvement of contact reliability are proposed.

Computation of the Simplest Normal Forms for Resonant Double Hopf Bifurcations System Based on Lie Transform

The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.

Relativistic Spin Operators

A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new operator, field quanta spin is defined and in terms of the generators of Poincaré group the moving spin of field system is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.

On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations

The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy＇s principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.