两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

AR（p）模型中的缺失数据估计

运用EM算法,对含有缺失数据的AR（p）模型进行参数估计,通过最大似然准则就非左端缺失的情况进行插补.最后,用蒙特卡洛方法给出实验分析,表明如下结果：（i）误差与AR模型的阶数正相关,与缺失比例正相关;（ii）当AR模型的特征根模长相对较小时,误差与数据长度负相关,且误差被控制在了标准差的30％以内;（iii）当模长中等时,误差基本控制在1个标准差左右;（iv）当模长较大时,误差与数据长度正相关,而且误差也相对较大.     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

ＰＯＩＮＴＥＤＲＥＰＲＥＳＥＮＴＡＴＩＯＮＳＯＦＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＬＩＥＡＬＧＥＢＲＡＳ￥ＸＵＸＩＡＮＧＡｂｓｔｒａｃｔ：ＡｃｏｎｔｒａｖａｒｉｅｄｂｉｌｉｎｅａｒｐａｉｒｉｎｇＸｏｎｅｖｅｒｙＭ（ρ）×Ｍ（ρθ）ｉｓｄｅｔｅｒｍ...     

Polynomial-time algorithms for regular set-covering and threshold synthesis

A set-covering problem is called regular if a cover always remains a cover when any column in it is replaced by an earlier column. From the input of the problem - the coefficient matrix of the set-covering inequalities - it is possible to check in polynomial time whether the problem is regular or can be made regular by permuting the columns. If it is, then all the minimal covers are generated in polynomial time, and one of them is an optimal solution. The algorithm also yields an explicit bound for the number of minimal covers. These results can be used to check in polynomial time whether a given set-covering problem is equivalent to some knapsack problem without additional variables, or equivalently to recognize positive threshold functions in polynomial time. However, the problem of recognizing when an arbitrary Boolean function is threshold is NP-complete. It is also shown that the list of maximal non-covers is essentially the most compact input possible, even if it is known in advance that the problem is regular.     

Optimal damping ratio for linear second-order systems

In this paper, it is shown that the optimal damping ratio for linear second-order systems that results in minimum-time no-overshoot response to step inputs is of bang-bang type. The optimal damping ratio is zero at the outset and is switched to some maximum value at an appropriate instant of time. The switching time is shown to be a function of the maximum damping ratio and the system natural frequency. Furthermore, it is shown that the larger the maximum damping ratio is, the shorter it takes for the system to reach the desired set point. Finally, it is shown that, if the optimal damping ratio is switched as a function of the system state, then the minimum-time no-overshoot criterion is satisfied, irrespective of the magnitude of the uncertainty in the value of the system natural frequency.     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

The Fraenkel‐Carnap question for Dedekind algebras

It is shown that the second‐order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second‐order theory is categorical. It follows that the second‐order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second‐order theory of a Dedekind algebra is quasi‐finitely axiomatizable iff the algebra is quasi‐finitely characterizable.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

Nontrivial Attractors in a Model Related to the Three-Body Quantum Problem

A model of a quantum mechanical system related to the three-body problem is studied. The model is defined in terms of a symmetric pseudo-differential operator (PDO) with unbounded symbol. The entire family of self-adjoint extensions of this operator is studied using harmonic analysis. A regularization procedure for this PDO is introduced and the spectral properties of the operators obtained in this way are investigated. The limit behavior of the regularized operators when the regularization parameter is removed is analyzed and a nontrivial attractor is exhibited.     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

Compromise solutions and estimation of the noninferior set

A general framework is presented in which the relation of the set of noninferior points and the set of compromise solutions is studied. It is shown that the set of compromise solutions is dense in the set of noninferior points and that each compromise solution is properly noninferior. Also, under convexity of the criteria space, a characterization of the properly noninferior points in terms of the compromise solutions is presented. In this characterization, the compromise solutions depend continuously on the weights. Use of the maximum norm is studied also. It is shown that a subset of these max-norm solutions, obtained by taking certain limits of compromise solutions, is dense and contained in the closure of the set of noninferior points.     

Milnor方图中的w-凝聚性

整环R称为ω-凝聚整环,是指R的每个有限型理想是有限表现型的.本文证明了ω-凝聚整环是v-凝聚整环,且若(RDTF,M)是Milnor方图,则在Ⅰ型情形,R是ω-凝聚整环当且仅当D和T都是ω-整环,且T_M是赋值环;对于Ⅱ-型情形,R是ω-凝聚整环当且仅当D是域,[F:D]<∞,M是R的有限型理想,T是ω-凝聚整环,且R_M是凝聚整环.     

A modified (S − 1, S) inventory system for deteriorating items with Poisson demand and non-zero lead time

An inventory system is considered for continuous decaying items with non-zero lead time and stochastic demand when shortages are allowed and all unsatisfied demands are backlogged. In this research we consider orders as separate packages where replenishment is one-for-one and a modified base stock policy is applied. In this paper, a penalty cost is introduced for stochastic inventory models with decaying items when less than one unit of the product is delivered to the customers. The objective of the warehouse is to maximize his average profit. Since the concavity analysis of the model is extremely complicated, an upper bound is introduced and an algorithm is presented for finding the optimal solution. Finally, a numerical example is presented and sensitivity analysis is carried out for a number of important parameters.     

Waves in an Inhomogeneous Tube with a Flowing Two-Phase Fluid

Results of theoretical and mathematical justification of the problem on a pulsating flow of a two-phase barotropic bubbly fluid enclosed in an elastic semi-infinite cylindrical tube inhomogeneous along its length are presented. Linear one-dimensional equations are used. It is assumed that the tube is rigidly attached to the surrounding medium and therefore its displacement in the axial direction is absent. At infinity, the tube material is assumed to be homogeneous. To describe the pressure, flow rate, and displacement of the fluid, a pulsating pressure is given at the tube end. The problem stated is reduced to a singular Sturm-Liouville boundary-value problem, which in turn is reduced to a Volterra-type integral equation. This equation is solved by the method of successive approximations. By assuming that the corresponding potential is integrable, it is proved that these approximations converge to the exact solution of the problem. It is shown that this assumption also covers the very important practical case of piecewise inhomogeneity. For numerical realization, we consider a homogeneous tube with flowing water containing a small amount of bubbles. The effect of the volume content of bubbles on wave characteristics is revealed. In particular, it is stated that, for the oscillation regime selected, an increased bubble volume content decreases the wave velocity and considerably increases the flow speed (rate).     

一个复合系统边界反馈的Riesz基性质

该文考虑一端固定 ,一端具负荷的梁的振动问题 .证明了线性反馈的闭环系统是一个 Riesz谱系统 ,即系统存在一列广义本征函数列构成状态空间的 Riesz基 .从而系统的谱确定增长条件成立 .在此过程中 ,简单的导出了系统本征值的渐近展开式 .并因此推论出系统的指数稳定性的条件     

Logic optimality for multi-objective optimization

Pareto dominance is one of the most basic concepts in multi-objective optimization. However, it is inefficient when the number of objectives is large because in this case it leads to an unmanageable number of Pareto solutions. In order to solve this problem, a new concept of logic dominance is defined by considering the number of improved objectives and the quantity of improvement simultaneously, where probabilistic logic is applied to measure the quantity of improvement. Based on logic dominance, the corresponding logic nondominated solution is defined as a feasible solution which is not dominated by other ones based on this new relationship, and it is proved that each logic nondominated solution is also a Pareto solution. Essentially, logic dominance is an extension of Pareto dominance. Since there are already several extensions for Pareto dominance, some comparisons are given in terms of numerical examples, which indicates that logic dominance is more efficient. As an application of logic dominance, a house choice problem with five objectives is considered.     

弱空间式Locale

空间式locale范畴SLoc是locale范畴Loc的余反射满子范畴,但对locale乘积不封闭．本文引入弱空间式locale,证明弱空间式locale范畴WSloc为范畴Loc的余反射满子范畴,且对locale秉积封闭．还证明了一个locale A是空间式的当且仅当它的枝映射localeN(A)是弱空间式的;一个空问式locale的每一个子locale都是空间式的当且仅当它的每一个子locale是弱空间式的．最后,证明了弱空间式性在定向函子下保持不变．     

广义混合非线性Schr？dinger方程的拟谱方法

本文讨论了广义混合非线性Schrodinger方程的周期初值问题,构造了守恒的半离散Fourier拟谱格式,对其近似解进行了先验估计,并证明了格式的收敛性.证明了该方程存在孤立子解,并给出其孤立子解的精确表达式.研究了线性化方程的稳定性问题,即在初值有扰动的情况下,该方程只有振荡解和鞍点.最后,通过数值例子验证了格式的可信性,数值计算表明,本格式时间方向可取大步长且是长时间稳定的,我们还计算了孤立子解,并绘出了在初值有扰动的情况下,相空间的轨线图.