Ringel对偶代数的三角分解

本文证明了树型偏序集的扭双指标代数的Ringel对偶代数存在三角分解,并具体给出了一种三角分解的结构,     

一类具有非线性发生率和治疗函数的传染病模型研究

传染病动力学系统的数学建模中,合理的使用非线性发生率往往更能使模型与实际相吻合.并且在实际的疾病防治过程中,由于受到空间人力物力资源的影响一般存在最大治疗容量的限制.结合这两种情况建立了一类含非线性发生率和最大治疗容量限制的传染病模型.通过分析这个模型,得到无病平衡点和正平衡点的存在性、稳定性.进一步取发生率和治疗系统达到最大容量时的感染者人数作为分支参数,得到了Hopf分支和Bogdanov-Takens分支的存在条件,并进行了数值模拟.     

Dynamic behavior of a parasite-host model with general incidence

In this paper, we consider the global dynamics of a microparasite model with more general incidences. For the model with the bilinear incidence, Ebert et al. [D. Ebert, M. Lipsitch, K.L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist 156 (2000) 459-477] observed that parasites can reduce host density, but the extinction of both host population and parasite population occurs only under stochastic perturbations. Hwang and Kuang [T.W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol. 46 (2003) 17-30] studied the model with the standard incidence and found that the host population may be extinct in the absence of random disturbance. We consider more general incidences that characterize transitions from the bilinear incidence to the standard incidence to simulate behavior changes of populations from random mobility in a fixed area to the mobility with a fixed population density. Using the techniques of Xiao and Ruan [D. Xiao, S. Ruan, Global dynamics of a ratio-dependent predator-prey system, J. Math. Biol. 43 (2001) 268-290], it is shown that parasites can drive the host to extinction only by the standard incidence. The complete classifications of dynamical behaviors of the model are obtained by a qualitative analysis.     

Multiple-prism near-grazing-incidence grating solid-state dye-laser oscillator

Solid-state multiple-prism near grazing-incidence grating dye lasers have been configured in cavities as short as 73 mm using dye-doped modified PMMA gain media. Single-longitudinal-mode emission, in near-Gaussian temporal pulses of 6-7 ns (FWHM) duration, has been achieved. Measured laser linewidths are in the 375 MHz range, and beam divergence is 2.3 mrad, at 3%-4% conversion efficiencies.     

TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.     

用于倾斜入射的波分复用薄膜滤光片的特性及改进

对倾斜入射时窄带薄膜滤光片的特性作了描述 ,由于低折射率间隔层的滤光片 ,倾斜入射时 p偏振分量的通带比s分量更移向短波 ,而高折射率间隔层的滤光片则反之 ,因此可把间隔层同时设计成高、低折射率两种材料 ,或选用适当的中间折射率材料 ,使p分量和s分量两个通带的中心波长重合。设计了用于 2 0°入射角的密集波分复用 (DWDM )滤光片 ,并给出了实验结果。     

关于(0,1)的对称和规范矩阵

给出更多的对于给定行和向量存在（０，１）对称矩阵的等价条件，同时也讨论了（０，１）规范矩阵的情形．     

3‐Designs of PSL(2, 2n) With block sizes 4 and 5

We determine the distribution of 3‐designs among the orbits of 4‐ and 5‐element subsets under the action of PSL(2,2ⁿ) on the projective line. Thus we give complete information on all Kramer–Mesner matrices for the action of PSL(2,2ⁿ) on 3‐sets versus 4‐ and 5‐sets. As a consequence, all 3‐designs with block sizes 4 and 5 and automorphism group PSL(2,2ⁿ) can immediately be obtained. © 2003 Wiley Periodicals, Inc.     

图论中矩阵的可实现性

对图的关联矩阵,邻接矩阵,基本割集矩阵,基本圈矩阵的可实现性分别进行了论证,并将邻接矩阵的可实现性推广到一般形式.得到了同一个基本割集矩阵的奥凯达图形是不唯一的;以及这些奥凯达图形所对应的图是互相同构的结果;并且指出了基本圈矩阵的可实现性可以依靠基本割集矩阵的可实现性来解决.     

The Flag-Transitive C 3-Geometries of Finite Order

It is shown that a flag-transitive C ₃-geometry of finite order (x, y) with x2 is either a finite building of type C ₃ (and hence the classical polar space for a 6-dimensional symplectic space, a 6-dimensional orthogonal space of plus type, a 6- or 7-dimensional hermitian space, a 7-dimensional orthogonal space, or an 8-dimensional orthogonal space of minus type) or the sporadic A ₇-geometry with 7 points.