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     

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.     

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   

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.     

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.     

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。     

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     

An extension of an inequality for ratios of gamma functions

In this paper, we prove that for $x+y>0$ and $y+1>0$ the inequality $\frac{{[\Gamma (x+y+1)/\Gamma (y+1)]}^{1/x}}{{[\Gamma (x+y+2)/\Gamma (y+1)]}^{1/(x+1)}}<{\left(\frac{x+y}{x+y+1}\right)}^{1/2}$ is valid if $x>1$ and reversed if $x<1$ and that the power $\frac{1}{2}$ is the best possible, where $\Gamma \left(x\right)$ is the Euler gamma function. This extends the result of [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2) (2009) 967–970] and resolves an open problem posed in [B.-N. Guo, F. Qi, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math. 7 (2) (2003) 239–247].     

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.     

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.     

The zero-one law for a complete orthonormal system

A complete orthonormal system of functions $\Theta ={\left\{{\theta }_n\right\}}_{n=1}^{\infty }\text{,}{\theta }_n\in L_{[0\text{,}1]}^{\infty }$ is constructed such that ${\sum }_{n=1}^{\infty }{a}_n{\theta }_n$ converges almost everywhere on $[0\text{,}1]$ if ${\left\{a_n\right\}}_{n=1}^{\infty }\in l^2$ and ${\sum }_{n=1}^{\infty }{a}_n{\theta }_n$ diverges a.e. for any ${\left\{a_n\right\}}_{n=1}^{\infty }?l^2$. We also show that for any complete ONS ${\left\{f_n\right\}}_{n=1}^{\infty }$ of functions defined on $[0\text{,}1]$ there exists a fixed non decreasing subsequence ${\left\{n_k\right\}}_{k=1}^{\infty }$ of natural numbers such that for any $f\in L_{[0\text{,}1]}^0$ and some sequence of coefficients ${\left\{b_n\right\}}_{n=1}^{\infty }$,

$\sum _{n=1}^{n_k}{b}_n{f}_n\to f\text{a.e. when}k\to \infty \text{.}$

To cite this article: K. Kazarian, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Mordell type exponential sum estimates in fields of prime order

We establish a Mordell type exponential sum estimate (see Mordell [Q. J. Math. 3 (1932) 161–162]) for ‘sparse’ polynomials $f(x)={\sum }_{i=1}^r{a}_i{x}^{k_i}\text{,}(a_i\text{,}p)=1\text{,}p$ prime, under essentially optimal conditions on the exponents $1?k_i<p?1$. The method is based on sum–product estimates in finite fields ${\mathbb{F}}_p$ and their Cartesian products. We also obtain estimates on incomplete sums of the form ${\sum }_{s=1}^t{e}_p({\sum }_{i=1}^r{a}_i{\theta }_i^s)$ for $t>p^{?}$, under appropriate conditions on the ${\theta }_i\in {\mathbb{F}}_p^{*}$. To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Enumeration formulas for standard Young tableaux of nearly hollow rectangular shapes

This paper considers the enumeration problem of a generalization of standard Young tableau (SYT) of truncated shape. Let $\lambda ?\mu |\left\{(i_0,j_0)\right\}$ be the SYT of shape $\lambda$ truncated by $\mu$ whose upper left cell is $(i_0,j_0)$, where $\lambda$ and $\mu$ are partitions of integers. The summation representation of the number of SYT of the truncated shape $(n+k+2,{(n+2)}^{m+1})?\left(n^m\right)|\left\{(2,2)\right\}$ is derived. Consequently, three closed formulas for SYT of hollow shapes are obtained, including the cases of (i). $m=n=1$, (ii). $k=0$, and (iii). $k=1,m=n$. Finally, an open problem is posed.     

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.     

Universality in the bulk holds close to given points

Let $\mu$ be a measure with compact support. Assume that $\xi$ is a Lebesgue point of $\mu$ and that ${\mu }^{\prime }$ is positive and continuous at $\xi$. Let $\left\{A_n\right\}$ be a sequence of positive numbers with limit $\infty$. We show that one can choose ${\xi }_n\in [\xi ?\frac{A_n}{n},\xi +\frac{A_n}{n}]$ such that $\underset{n\to \infty }{lim}\frac{K_n({\xi }_n,{\xi }_n+\frac{a}{{\stackrel{?}{K}}_n({\xi }_n,{\xi }_n)})}{K_n({\xi }_n,{\xi }_n)}=\frac{sin\pi a}{\pi a}\text{,}$ uniformly for $a$ in compact subsets of the plane. Here $K_n$ is the $n$th reproducing kernel for $\mu$, and ${\stackrel{?}{K}}_n$ is its normalized cousin. Thus universality in the bulk holds on a sequence close to $\xi$, without having to assume that $\mu$ is a regular measure. Similar results are established for sequences of measures.