凝聚环上的Cotilting模

本文首先介绍了ｃｏ－＊－模的概念和刻划了凝聚环的一些性质，然后刻划了凝聚环上的ｃｏｔｉｌｔｉｎｇ模。     

关于局部Noether模

本文证明了如下结果：左 Ｒ－模 Ｍ是局部 Ｎｏｅｔｈｅｒ模当且仅当σ［Ｍ］中的任意Ｍ－内射左Ｒ－模的直和是一个有限余生成左Ｒ－模和一个拟连续（或连续,直内射）左Ｒ－模的直和．     

关于G－Matlis自反模的几点注记

本文证明，如果Ｒ是一个Ｎｏｅｔｈｅｒ完备半局部环，则Ｒ－模Ｍ是Ｎｏｅｔｈｅｒ（Ａｒｔｉｎ）模当且仅当对任意ＡｒｔｉｎＲ－模Ｎ，Hom _R(M, N)是Ａｒｔｉｎ（Ｎｏｅｔｈｅｒ）模．     

局部Noether模的相对连续性特征

设M是左R-模,本文证明了M是局部Noether的当且仅当σ[M]中的任意M-内射左R-模的直和是S∧2-连续的（S∧2-拟连续的）。     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

广义FP—内射模、广义平坦模与某些环

左（右）R－模A称为GFP－内射模，如果ExtR(M,A)=0对任－2－表现R－模M成立；左（右）R－模称为G－平坦的，如果Tor1^R(M,A)=0(Tor1^R(AM)=0)对于任一2－表现右（左）R－模M成立；环R称左（右）R－半遗传环，如果投射左（右）R－模的有限表现子模是投射的，环R称为左（右）G－正而环，如果自由左（右）R－模的有限表现子模为其直和项，研究了GFP－内射模和G－平坦模的一些性质，给出了它们的一些等价刻划，并利用它们刻划了凝聚环，G－半遗传环和G－正则环。     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.     

Multi‐dimensional Lotka–Volterra systems for carcinogenesis mutations

In the paper we consider three classes of models describing carcinogenesis mutations. Every considered model is described by the system of (n+1) equations, and in each class three models are studied: the first is expressed as a system of ordinary differential equations (ODEs), the second—as a system of reaction–diffusion equations (RDEs) with the same kinetics as the first one and with the Neumann boundary conditions, while the third is also described by the system of RDEs but with the Dirichlet boundary conditions. The models are formulated on the basis of the Lotka–Volterra systems (food chains and competition systems) and in the case of RDEs the linear diffusion is considered. The differences between studied classes of models are expressed by the kinetic functions, namely by the form of kinetic function for the last variable, which reflects the dynamics of malignant cells (that is the last stage of mutations). In the first class the models are described by the typical food chain with favourable unbounded environment for the last stage, in the second one—the last equation expresses competition between the pre‐malignant and malignant cells and the environment is also unbounded, while for the third one—it is expressed by predation term but the environment is unfavourable. The properties of the systems in each class are studied and compared. It occurs that the behaviour of solutions to the systems of ODEs and RDEs with the Neumann boundary conditions is similar in each class; i.e. it does not depend on diffusion coefficients, but strongly depends on the class of models. On the other hand, in the case of the Dirichlet boundary conditions this behaviour is related to the magnitude of diffusion coefficients. For sufficiently large diffusion coefficients it is similar independently of the class of models, i.e. the trivial solution that is unstable for zero diffusion gains stability. Copyright © 2009 John Wiley & Sons, Ltd.     

ML Estimation of the MultivariatetDistribution and the EM Algorithm

Maximum likelihood estimation of the multivariatetdistribution, especially with unknown degrees of freedom, has been an interesting topic in the development of the EM algorithm. After a brief review of the EM algorithm and its application to finding the maximum likelihood estimates of the parameters of thetdistribution, this paper provides new versions of the ECME algorithm for maximum likelihood estimation of the multivariatetdistribution from data with possibly missing values. The results show that the new versions of the ECME algorithm converge faster than the previous procedures. Most important, the idea of this new implementation is quite general and useful for the development of the EM algorithm. Comparisons of different methods based on two datasets are presented.     

Evaluating departures from fair representation

Computer–intensive estimates are introduced to evaluate departures from proportionality between the numbers of electors in a partition of a voting population and the numbers of representatives in the corresponding partition of the elected representation. At the first stage a pair of indices is proposed, one to evaluate the total strength of the departures and the other to indicate to what extent they are due to over–representation increasing (or decreasing) with the number of electors in a group. The properties of the indices are examined in suitably defined stochastic models which describe this type of over–representation. Since the values of the indices are strongly influenced by the distribution of electors in the given partition, a second stage of estimation is performed in order to get some [partition–free] information on the existence of a monotone size representation, and, if it exists, on its strength. The relevant transformation is based on intensive computer simulation in the introduced models. The methods proposed are applied to the results of the 1991 election of the Polish Scientific Research Council, which distributes funds among universities, scientific institutions and individual groups of researchers.     

Properties of Attainable Sets of Evolution Inclusions and Control Systems of Subdifferential Type

In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and the evolution operators that are the compositions of a linear operator and the subdifferentials of a time-dependent proper convex lower semicontinuous function. Alongside the initial inclusion, we consider a sequence of approximating evolution inclusions with the same perturbation and the evolution operators that are the compositions of the same linear operator and the subdifferentials of the Moreau–Yosida regularizations of the initial function. We demonstrate that the attainable set of the initial inclusion as a multivalued function of time is the time uniform limit of a sequence of the attainable sets of the approximating inclusions in the Hausdorff metric. We obtain similar results for evolution control systems of subdifferential type with mixed constraints on control. As application we consider an example of a control system with discontinuous nonlinearities containing some linear functions of the state variables of the system.     

基于韧性度的低轨卫星通信网络抗毁性度量及优化

低轨卫星通信网络的抗毁性是描述网络安全可靠的有效工具,在网络体系结构设计和路由策略等领域得到了广泛的应用。根据低轨卫星通信网络中卫星在轨道平面内移动,需要不断进行切换的特点,从建立抗毁性测度模型以及网络抗毁性优化两个角度来评估和提高网络抗毁性,提出一种基于韧性度的低轨卫星通信网络抗毁性度量方法。通过对移动模型以及切换模型的结构分析,对每种结构以一定概率出现的低轨卫星通信网络,应用韧性度函数,求得网络在某个时刻及某一段时间段内的抗毁性,并针对切换模型的不足之处进行优化,用赋权韧性度来体现优化的效果,得到了优化后的网络抗毁性。以铱星系统为应用实例进行仿真,结果表明:任意时刻网络的抗毁性跟拓扑结构的韧性度值有关,并且是一种线性关系,即随着韧性度的增加,其抗毁性也增加。通过对铱星通信系统切换模型的优化,网络的抗毁性与平均抗毁性都得到了提升,说明本文所构建模型的有效性和实用性。     

Irregularly shaped space-filling truncated octahedra

For any parent tetrahedron ABCD, centroids of selected sub-tetrahedra form the vertices of an irregularly shaped space-filling truncated octahedron. To reflect these properties, such a figure will be called an ISTO. Each edge of the ISTO is parallel to and one-eighth the length of one of the edges of tetrahedron ABCD and the volume of the ISTO is 3/16-th the volume of the tetrahedron. The ISTO is symmetric about the centroid of tetrahedron ABCD and each face is symmetric about a centre and has an opposite face that is parallel and congruent. The area of the faces of the ISTO is not proportional to that of the generating tetrahedron.     

夜盘交易对我国农产品期货市场影响的实证研究

随着我国农产品期货与国际市场的联动性进一步加强,为防止相关期货产品的隔夜风险和价格跳水问题,对部分农产品期货实行夜盘交易制度。为测度夜盘交易制度是否有益于农产品期货市场朝着稳定、理性的方向发展,本文采用了适合刻画金融序列波动性的GARCH族模型,实证检验得出GARCH、GARCH-M和EGARCH模型能够高度拟合农产品期货的价格序列并显著衡量夜盘交易对于我国农产品期货市场的影响。研究结论如下:第一、基于GRACH模型实证结果,夜盘交易制度变量的回归结果显著,该制度能减轻农产品期货的价格波动,且其影响是显著的;第二、EGARCH模型的回归结果同样显著,分别对比不同样本期的EGARCH模型实证结果可以得到,夜盘交易的开放减少了农产品期货市场的非对称性,使得市场趋向于理性的方向发展。     

基于零售商过度自信的存货质押博弈决策模型

存货质押是中小企业短期融资的有效手段,而企业对需求的过度自信会影响融资企业和银行的决策,从而影响到企业和银行的预期收益。针对过度自信环境下的存货质押决策问题,建立过度自信零售商和银行的存货质押博弈决策模型,采用Stackelberg博弈分析期望需求和需求波动性两方面过度自信对零售商销售努力、订货量和银行质押率的影响。研究表明:过度自信零售商融资更为激进,过度自信程度越高,对资金需求越大,投入销售努力越高,采购量越大,预期利润与实际利润之间的偏差越大;在低利润市场环境下,质押率随着过度自信的增加而降低,在高利润市场环境下,质押率会随着预测精度过度自信的增加而增加,随着期望需求过度自信的增加而下降。     

On the Index of Differential Operators on Manifolds with Conical Singularities

The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah–Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.