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．     

Stability and bifurcation of an SIS epidemic model with treatment

An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.     

A numerical method for stationary shock problems with monotonic solutions

Numerical methods are considered for singularly perturbed quasilinear problems having interior-shock solutions. It is shown that the direct discretization on a layer-adapted mesh is ineffective for these problems. A special method is proposed for the case when the solution is monotonic: the problem is transformed by interchanging the dependent and independent variables, and it is then discretized on a uniform mesh. The method is analyzed both theoretically and numerically. It is shown that it can be effective, but that it is not entirely without problems. An approach for improving the method is suggested.     

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.     

Backward bifurcation of an epidemic model with standard incidence rate and treatment rate

An epidemic model with standard incidence rate and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infectives on the disease spread. It is assumed that treatment rate is proportional to the numbers of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infectives. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.     

On property of injectivity for real W*-algebras and JW-algebras

In this paper injective real W*-algebras are investigated. It is shown that injectivity is equivalent to the property of E (extension property). It is proven that a real W*-algebra is injective iff its hermitian part is injective, and it is equivalent to, that the enveloping W*-algebra is also injective. Moreover, it is shown that if the second dual space of a real C*-algebra is injective, then the real C*-algebra is nuclear.     

The Toroidal Embedding Arising From an Irrational Fan

A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasi-compact noetherian locally ringed space which is not a scheme. A divisor theory exists and a class group is defined. A second construction is also carried out which mimics the gluing construction of the usual toric variety, but which makes no reference to a lattice. The resulting scheme is separated but infinite dimensional. The Picard group is described in terms of the group of real valued locally linear support functions on the fan and the Brauer group is shown to be trivial. Many examples are given throughout the paper; in particular, it is shown that there is associated to a real hyperplane arrangement of full rank a toroidal embedding.     

一类具有垂直传染和预防接种的SEIR传染病模型的定性分析

建立并分析了一类对出生时没有被染病母体垂直传染的染病者的新生儿进行免疫接种的SEIR传染病模型.得到了疾病是否灭绝的阈值R0,当R0<1时,无病平衡点全局渐近稳定的.当R0>1时,地方病平衡点局部渐近稳定的,且疾病一致持续生存.     

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.     

One side cut accelerated random search

A new algorithm for bound constrained global optimization is presented. At each iteration the method uses a single feasible box containing a control point. A single random sample point is generated inside the box. If this new point is better it replaces the control point and the box is reset to the feasible region. Otherwise the box is shrunk so that it no longer contains the random sample point. If a minimal box size is reached the box is also reset to the feasible region. The method is shown to converge almost surely to an essential global minimizer. The method is very simple to implement. Numerical testing shows that the method is viable in practice. A simple modification to accelerated random search is also discussed.     

A transverse spinning double pendulum

A transverse spinning double pendulum is introduced. This pendulum is of interest as a simple mechanical system with two degrees of freedom with rotation which is autonomous. In addition to having physical origins, the pendulum is constructable for experimental observation. Our main interest in introducing and analyzing this system is that it is the simplest physical system with the codimension two singularity – in the linearization about the trivial solution – associated with coalescence of four zero eigenvalues. It is the dynamics of the nonlinear system in the neighbourhood of this singularity that is of interest. We study this problem using normal form theory. An algorithm for the Cushman–Sanders normal form is constructed and analyzed. A representative model for the truncated normal form is presented. This truncated normal form has seven parameters; it is not integrable in general and it is predicted that the dynamics associated with this model will be quite complex.     

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。     

J-semicommutative环的性质

环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J（R）,这里J（R）是环R的Jacobson根．环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don＇oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环．若R／J（R）是semicommutative环,则可得到R是J-semicommutative环．本文进一步论证了如果,是环月的一个幂零理想,且R／I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系     

一个解不等式约束非线性规划问题的有效方法

本文提出了一个解不等式约束非线性规划问题有效方法．在这个方法中,考虑解一个等价Ｋｕｈｎ－Ｔｕｃｋｅｒ条件的非线性方程组．这个方程组中ＮＣＰ函数的使用消去了对应于不等式约束的Ｌａｇｒａｎｇｅ乘子的非负性．截断牛顿方法被用来解这个非线性方程组．为了保证全局收敛性,一个强健的损失函数被选为寻查函数,同时方法中插入修正最速下降方向．本文证明了方法的分Ｑ－二阶收敛性,同时指出新方法可以有效地解稀疏大规模非线性规划问题。     

几种类型的K~*空间的特征

<正> §1.引言 假设非平坦的 n 维黎曼空间的曲率张量 R_(hijk)在每一点恒满足下列关系(?)其中(?)是某一向量场,同时也满足     

覆盖下近似算子的拓扑性质

在不限制U为有限论域的情况下,研究了覆盖下近似算子XL和CL的拓扑性质。证明了覆盖下近似算子XL是内部算子,而且由XL生成的拓扑TXL为包含由覆盖C本身作为子基生成的拓扑TC的最小Alexandrov拓扑。特别地,当U为有限论域时,TXL=TC.然而,覆盖下近似算子CL不是内部算子。当覆盖C为某拓扑的基时,CL是内部算子,且此时由CL生成的拓扑TCL与TC是同一个拓扑。若进一步要求U为有限论域,则TCL=TXL=TC,进而CL=XL.     

Jacobson-Chevalley稠密定理的一个推广

我们在[1]中证明了,一个半环(hemiring)关于它的Jacobson关系根的商同构于完全本原半环的亚直和。这使我们有兴趣对这个特殊的半环类——完全本原半环的结构作进一步的讨论。本文的主要结果是:一个半环是完全本原的当且仅当它是一个半模上的亚稠密自同态半环。这个定理给出了完全本原半环的结构,推广了Jacobson—Chevalley稠密定理。     

Traveling waves in a nonlocal dispersal population model with age-structure

This paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age-structure. If the birth function is monotone, then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness. It is proved that the traveling wavefront is strictly increasing and unique up to a translation. The asymptotic behavior of traveling wavefronts is also obtained. If the birth function is not monotone, the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi-monotonicity.     

(<Emphasis Type="Italic">T</Emphasis>, <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>) Policy Inventory Model for Deteriorating Items with Time Proportional Demand

An EOQ model is reconsidered here in which the demand rate is changing linearly with time and the deterioration is assumed to be a constant fraction of the onhand inventory. The planning horizon is finite and known and the replenishment periods are assumed to be constant. The problem is to find the optimal number of replenishments, which are instantaneous. When there is no deterioration, the model developed is related to the corresponding model for nondeteriorating items. An example followed by sensitivity analysis is given to illustrate the derived results.     

On hypothesis testing with a partitioned random alternative

It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on distributions.When m=1,it is done by the (traditional) hypothesis test.In this paper,a generalization to the case m > 1 is proposed.The fundamental difference with the case m=1 is that the new alternative hypothesis is a partition of m multiple claims and is data-dependent.Data is used to decide which claim in the partition is to be tested as the alternative.Thus,a random alternative is involved.The...