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.     

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.     

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．     

Borel measures in consonant spaces

A topology on a set X is called consonant if the Scott topology of the lattice is compactly generated; equivalently, if the upper Kuratowski topology and the co-compact topology on closed sets of X coincide. It is proved that every completely regular consonant space is a Prohorov space, and that every first countable regular consonant space is hereditarily Baire. If X is metrizable separable and co-analytic, then X is consonant if and only if X is Polish. Finally, we prove that every pseudocompact topological group which is consonant is compact. Several problems of Dolecki, Greco and Lechicki, of Nogura and Shakmatov, are solved.     

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.     

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.     

油田注水系统拓扑布局优化的混合遗传算法

以投资最小为目标函数,建立了注水系统拓扑布局优化数学模型.根据模型特点,将优化问题分为两层,分别采用遗传算法和非线性优化方法进行求解.并对遗传算法的操作过程进行了改进,调整了适应函数,改进了交叉和变异操作,结合了模拟退火算法,在操作过程中使约束条件得到满足,减少了不可行解的产生,使遗传算法的优化性能得到了提高.优化算例说明了该方法的有效性.     

非线性泰勒规则的形成机理研究

从菲利普斯曲线非线性和央行损失函数非对称性两个视角论证了非线性泰勒规则的形成机理,数理证明结论显示:无论菲利普斯曲线是上凸还是下凹,都意味着通货膨胀对产出缺口的反应是非对称的,都会导致泰勒规则的非线性;央行损失函数的非对称性是导致泰勒规则非线性的另一个原因.当存在扩张谨慎需求时,利率曲线是下凹的;当存在价格平稳谨慎需求...     

Logic optimality for multi-objective optimization

Pareto dominance is one of the most basic concepts in multi-objective optimization. However, it is inefficient when the number of objectives is large because in this case it leads to an unmanageable number of Pareto solutions. In order to solve this problem, a new concept of logic dominance is defined by considering the number of improved objectives and the quantity of improvement simultaneously, where probabilistic logic is applied to measure the quantity of improvement. Based on logic dominance, the corresponding logic nondominated solution is defined as a feasible solution which is not dominated by other ones based on this new relationship, and it is proved that each logic nondominated solution is also a Pareto solution. Essentially, logic dominance is an extension of Pareto dominance. Since there are already several extensions for Pareto dominance, some comparisons are given in terms of numerical examples, which indicates that logic dominance is more efficient. As an application of logic dominance, a house choice problem with five objectives is considered.     

基于存档策略的多目标优化的遗传算法及其收敛性分析

设计了一种用遗传算法求解多目标优化问题的有效方法——基于存档策略的多目标优化的遗传算法,并讨论了此算法的收敛性.首先给出档案的定义,设计出基于支配关系下的带有存档策略遗传算法,并通过算例检验了算法的有效性;然后引入了两档案间的距离的概念,在此距离定义的基础上证明了算法在概率意义下是收敛的.     

基于决策者信任水平和组合赋权的不完全偏好复杂大群体应急决策方法

针对属性权重完全未知且专家偏好出现残缺值的复杂大群体应急决策问题,提出了一种新的决策方法。首先,设计了一套基于决策者信任水平的残缺值填充机制,对缺失的偏好信息进行补充。然后,将各方案的大群体偏好信息进行聚类,基于方案信息熵和群体偏好冲突水平构建组合赋权方法,对属性权重进行测算,进而得到各个方案的综合评价值。最后对该方法进行了实例验证,验证结果表明本文提出的方法具有良好的可行性和有效性。     

平坦的多项式剩余类环

本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

销售市场和回收市场同时扰动下的闭环供应链协调应对

考虑一个闭环供应链由单个制造商和单个零售商组成,产品的制造和再制造由制造商负责,产品的销售和废旧品的回收由零售商负责。在建立博弈模型的基础上,首先分析了闭环供应链在收益共享契约下的协调性,接着分析了收益共享契约对突发事件下闭环供应链的协调应对。分析结果表明:当突发事件导致销售市场规模和废旧品回收市场初始规模同时发生变化时,闭环供应链的协调将被打破,为此对收益共享契约进行了调整,调整后的收益共享契约使闭环供应链具有抗突发事件性;最后,通过数值计算实例对此进行了验证分析。     

加权和法在Vague集中的应用

针对应用广泛的加权和法的特征,研究在Vague集中应用加权和法,提出了在Vague集中应用加权和的方法,并通过实际算例验证了此方法的有效性.     

Primitive connected and additive theories of polygons

We study into monoids S the class of all S-polygons over which is primitive normal, primitive connected, or additive, that is, the monoids S the theory of any S-polygon over which is primitive normal, primitive connected, or additive. It is proved that the class of all S-polygons is primitive normal iff S is a linearly ordered monoid, and that it is primitive connected iff S is a group. It is pointed out that there exists no monoid S with an additive class of all S-polygons. __________ Translated from Algebra i Logika, Vol. 45, No. 3, pp. 300–313, May–June, 2006.     

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.     

POINTED REPRESENTATIONS OFINFINITE DIMENSIONAL LIE ALGEBRAS

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On stability of switched homogeneous nonlinear systems

In this paper, the problem of stability of switched homogeneous systems is addressed. First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case. Following the previous results, a sufficient condition is obtained for stability of switched nonlinear homogeneous systems, and a switching law is designed by partition of state space. In particular, a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule. Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented. Similar to the condition for linear systems, the LMI-type condition is easily verifiable. An example is given to illustrate that candidate common Lyapunov function is a key point for design of switching law.