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．     

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.     

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.     

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     

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.     

List star chromatic index of sparse graphs

A star edge-coloring of a graph $G$ is a proper edge coloring such that every 2-colored connected subgraph of $G$ is a path of length at most 3. For a graph $G$, let the list star chromatic index of $G$, $c{h}_s^{\prime }\left(G\right)$, be the minimum $k$ such that for any $k$-uniform list assignment $L$ for the set of edges, $G$ has a star edge-coloring from $L$. Dvo?ák et al. (2013) asked whether the list star chromatic index of every subcubic graph is at most 7. In Kerdjoudj et al. (2017) we proved that it is at most 8. In this paper we consider graphs with any maximum degree, we proved that if the maximum average degree of a graph $G$ is less than $\frac{14}{5}$ (resp. 3), then $c{h}_s^{\prime }\left(G\right)\le 2\Delta \left(G\right)+2$ (resp. $c{h}_s^{\prime }\left(G\right)\le 2\Delta \left(G\right)+3$).     

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 sufficient condition for DP-4-colorability

DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-choosable. Furthermore, Jin et al. (2016) showed that for each $k\in \{3,4,5,6\}$, every signed planar graph without $C_k$ is signed 4-choosable. In this paper, we show that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-DP-colorable, which is an extension of the above results.     

Minima of sequences of Gaussian random variables

For a given sequence of real numbers $a_1,\dots ,a_n$ we denote the k-th smallest one by $k\text{-}{\min }_{1?i?n}{a}_i$. We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers $x_1,\dots ,x_n$ and every $k?n$ one has

$c\underset{1?j?k}{\max }\frac{k+1?j}{{\sum }_{i=j}^{n}1/x_i}?\mathbb{E}k\text{-}\underset{1?i?n}{\min }|x_i{g}_i|?C\ln (k+1)\underset{1?j?k}{\max }\frac{k+1?j}{{\sum }_{i=j}^{n}1/x_i},$

where $g_i\in N(0,1)$, $i=1,\dots ,n$, are independent Gaussian random variables. Moreover, if $k=1$ then the left hand side estimate does not require independence of the $g_i$s. Similar estimates hold for $\mathbb{E}k\text{-}{\min }_{1?i?n}{|x_i{g}_i|}^p$ as well. To cite this article: Y. Gordon et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Bifurcation of peakons and periodic cusp waves for the generalization of the Camassa–Holm equation

In this paper, we investigate the generalization of the Camassa–Holm equation $u_t+K{\left(u^m\right)}_x?{\left(u^n\right)}_{xxt}={[\frac{{\left({\left(u^n\right)}_x\right)}^2}{2}+u^n{\left(u^n\right)}_{xx}]}_x\text{,}$ where $K$ is a positive constant and $m,n\in \mathbb{N}$. The bifurcation and some explicit expressions of peakons and periodic cusp wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. Further, in the process of obtaining the bifurcation of phase portraits, we show that $K=\frac{m+n}{1+n}{c}^{\frac{n?m+1}{n}}$ is the peakon bifurcation parameter value for the equation. From the bifurcation theory, in general, the peakons can be obtained by taking the limit of the corresponding periodic cusp waves. However, we find that in the cases of $n\ge 2,m=n+1$, when $K$ tends to the corresponding bifurcation parameter value, the periodic cusp waves will no longer converge to the peakons, instead, they will still be the periodic cusp waves. To the best of our knowledge, up until now, this phenomenon has not appeared in any other literature. By further studying the cause of this phenomenon, we show that this planar system has some different characters from the previous Camassa–Holm systems. What is more, we obtain some periodic cusp wave solutions in the form of polynomial functions, which are different from those in the form of exponential functions. Some previous results are extended.     

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.     

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.     

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.     

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.     

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).     

On the longest common increasing binary subsequence

Let $X_1,X_2,\dots$ and $Y_1,Y_2,\dots$ be two independent sequences of iid Bernoulli random variables with parameter 1/2. Let ${\mathit{LCI}}_n$ be the length of the longest increasing sequence which is a subsequence of both finite sequences $X_1,\dots ,X_n$ and $Y_1,\dots ,Y_n$. We prove that, as n goes to infinity, $n^{?1/2}({\mathit{LCI}}_n?n/2)$ converges in law to a Brownian functional that we identify. To cite this article: C. Houdré et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Invariant measures of stochastic partial differential equations and conditioned diffusions

This work establishes and exploits a connection between the invariant measure of stochastic partial differential equations (SPDEs) and the law of bridge processes. Namely, it is shown that the invariant measure of $u_t=u_{xx}+f(u)+\sqrt{2?}\eta (x\text{,}t)$, where $\eta (x\text{,}t)$ is a space–time white-noise, is identical to the law of the bridge process associated to $\mathrm{d}U=a(U)\mathrm{d}x+\sqrt{?}\mathrm{d}W(x)$, provided that a and f are related by $?a^{″}(u)+2a^{\prime }(u)a(u)=?2f(u)$, $u\in \mathbb{R}$. Some consequences of this connection are investigated, including the existence and properties of the invariant measure for the SPDE on the line, $x\in \mathbb{R}$. To cite this article: M.G. Reznikoff, E. Vanden-Eijnden, C. R. Acad. Sci. Paris, Ser. I 340 (2005).