Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.     

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.     

LIMIT CYCLES FOR A CLASS OF NONPOLYNOMIAL PLANAR VECTOR FIELDS(II)

In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the critical point of such nonpolynomial planar vector felds to be the focus or center. Then, using Dulac criterion, we establish some sufcient conditions for the nonexistence of limit cycles of this nonpolynomial planar vector felds. And then, according to Hopf bifurcation theory, we analyze some sufcient conditions for bifurcating limit cycles from the origin. Finally, by transforming the nonpolynomial planar vector felds into the generalized Li′enard planar vector felds, we discuss the existence, uniqueness and stability of limit cycles for the former and latter planar vector felds. Some examples are also given to illustrate the efectiveness of our theoretical results.     

Reflected SPDEs Driven by Fractional Noises

In this paper,we study the stochastic partial differential equation with two reflecting smooth walls h^1 and h^2,driven by a fractional noise,which is fractional in time and white in space.The large deviation principle for the law of the solution to this equation,will be established through developing a classical method.Furthermore,we obtain the H?lder continuity of the solution.     

Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.     

立体几何中的活跃分子——直角四面体

三条侧棱两两相互垂直的四面体是一种特殊的四面体,我们称之为直角四面体,它具有以下性质:(1)任何一条侧棱垂直另两个侧棱构成的平面;(2)三个侧面两两垂直;(3)顶点在底面上的射影是底面三角形的垂心等,立体几何中很重要的概念和定理.都能从这个直角四正面体中衍生,因此深入研究直角四面体,对于把握空间图形中直线和平面的关系,尤为重要.下面利用直角四面体的性质简解两道商考题.……     

Induced generalized exact boundary synchronizations for a coupled system of wave equations

Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.     

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.     

Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.     

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.     

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.