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．     

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     

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.     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

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

Note of the enumeration formula of standard Young tableaux of truncated shape (nm)∖(2)

In this paper integration method is used to derive the enumeration formulas of the standard Young tableau (SYT) of truncated shape. An integration representation of the number of SYT of truncated shape $\left(n^m\right)\setminus \left(2\right)$ is given, which implies a positive proof of the conjecture of Adin et al. on the number of SYT of truncated shape $\left(n^n\right)\setminus \left(2\right)$. Furthermore, the enumeration formulas of the numbers of SYTs of truncated shapes $\left(n^{n-k}\right)\setminus \left(2\right)$ and $\left(n^{n-k}\right)\setminus (1,1)$$(k=1,2)$ have been obtained.     

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。     

基于规模的企业竞争力蜘蛛图法评价研究

科学合理的规模结构不仅是实现规模经济的基本条件,而且是提高经济效益、降低交易成本、获得较高的企业竞争力的重要保证.基于规模理论,从生产规模、资本规模、市场规模以及效益规模四大因素入手,提出了一套基于规模的企业竞争力评价指标体系,运用蜘蛛图法建立了基于规模的企业竞争力评价模型,并结合具体的数据分析说明了企业竞争力的大小强弱.此种方法具有直观形象、定量化、可操作性强的特点.     

极大子因子

若N是一个Ⅱ1型因子,G是一个有限群且在N上有一个真外作用α,则当G的阶是素数对,N是Ⅱ1型因子M=N(?)αG的极大子因子．另一方面,假设 N(?) M是Ⅱ1型因子的一个包含,M(?)M1是N(?)M的基本构造,[M:N]= p∈N是素数,N’∩ M=CI,N’∩M1是交换的,N,(?)M深度为2,则N是M的极大子因子．     

关于拟平坦模的几个注记

本文所有的环均指有单位元的环,模均指酉模。左R-模M称为拟内射的,如果对任意N相似文献   

A characterization of a class of hyperplanes of DW(2n−1,F)

A hyperplane of the symplectic dual polar space $DW(2n?1,\mathbb{F})$, $n\ge 2$, is said to be of subspace-type if it consists of all maximal singular subspaces of $W(2n?1,\mathbb{F})$ meeting a given $(n?1)$-dimensional subspace of $\text{PG}(2n?1,\mathbb{F})$. We show that a hyperplane of $DW(2n?1,\mathbb{F})$ is of subspace-type if and only if every hex $F$ of $DW(2n?1,\mathbb{F})$ intersects it in either $F$, a singular hyperplane of $F$ or the extension of a full subgrid of a quad. In the case $\mathbb{F}$ is a perfect field of characteristic 2, a stronger result can be proved, namely a hyperplane $H$ of $DW(2n?1,\mathbb{F})$ is of subspace-type or arises from the spin-embedding of $DW(2n?1,\mathbb{F})?DQ(2n,\mathbb{F})$ if and only if every hex $F$ intersects it in either $F$, a singular hyperplane of $F$, a hexagonal hyperplane of $F$ or the extension of a full subgrid of a quad.     

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.     

Solving linear program as linear system in polynomial time

A physically concise polynomial-time iterative-cum-non-iterative algorithm is presented to solve the linear program (LP) $Min{c}^{t}x\text{subject to}Ax=b,x\ge 0$. The iterative part–a variation of Karmarkar projective transformation algorithm–is essentially due to Barnes only to the extent of detection of basic variables of the LP taking advantage of monotonic convergence. It involves much less number of iterations than those in the Karmarkar projective transformation algorithm. The shrunk linear system containing only the basic variables of the solution vector $x$ resulting from $Ax=b$ is then solved in the mathematically non-iterative part. The solution is then tested for optimality and is usually more accurate because of reduced computation and has less computational and storage complexity due to smaller order of the system. The computational complexity of the combination of these two parts of the algorithm is polynomial-time $O\left(n^3\right)$. The boundedness of the solution, multiple solutions, and no-solution (inconsistency) cases are discussed. The effect of degeneracy of the primal linear program and/or its dual on the uniqueness of the optimal solution is mentioned. The algorithm including optimality test is implemented in Matlab which is found to be useful for solving many real-world problems.     

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.     

Strongly Regular Rings and SF-rings

in this paper, new characteristic properties of strongly regular rings are' given.Relations between certain generalizations of duo rings are also considered. The followingconditions are shown to be equivalent: (1) R is a strongly regular ring; (2) R is a left SFring such that every product of two independent closed left ideals of R is zero; (3) R is aright SF-ring such that every product of two independent closed left ideals of R is zero; (4)R is a left SF-ring whose every special left annihilator is a quasi-ideal; (5) R is a right SFring whose every special left annihilator is a quasi-ideal; (6) R is a left SF-ring whose everymaximal left ideal is a quasi-ideal; (7) R is a right SF-ring whose every maximal left ideal isa quasi-ideal; (8) R is a left SF-ring such that the set N(R) of all nilpotent elements of R isa quasi-ideal; (9) R is a right SF-ring such that N(R) is a quasi-ideal.     

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.     

On the constructive characterization of threshold functions

In this paper, the structure of the set of threshold functions and complexity problems are considered. The notion of the signature of a threshold function is defined. It is shown that if a threshold function essentially depends on all of its variables, then the signature of this function is unique. The set of threshold functions is partitioned into classes with equal signatures. A theorem characterizing this partition is proved. The importance of the class of monotone threshold functions is emphasized. The complexity of transferring one threshold function specified by a linear form into another is examined. It is shown that in the worst case this transfer would take exponential time. The structure of the set of linear forms specifying the same threshold function is also examined. It is proved that for any threshold function this set of linear forms has a unique basis in terms of the operation of addition of linear forms. It is also shown that this basis is countable.     

On the unimodality of independence polynomials of very well-covered graphs

The independence polynomial $i(G,x)$ of a graph $G$ is the generating function of the numbers of independent sets of each size. A graph of order $n$ is very well-covered if every maximal independent set has size $n∕2$. Levit and Mandrescu conjectured that the independence polynomial of every very well-covered graph is unimodal (that is, the sequence of coefficients is nondecreasing, then nonincreasing). In this article we show that every graph is embeddable as an induced subgraph of a very well-covered graph whose independence polynomial is unimodal, by considering the location of the roots of such polynomials.     

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.     

Basins of attraction of equilibrium points of second order difference equations

We investigate the basins of attraction of equilibrium points and period-two solutions of the difference equation of the form $x_{n+1}=f(x_n,x_{n?1})\text{,}n=0,1,\dots \text{,}$ where $f$ is decreasing in the first and increasing in the second variable. We show that the boundaries of the basins of attraction of different locally asymptotically stable equilibrium points are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium points.     

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。