一类优美图

设u、ν是两个固定顶点.用b条内部互不相交且长度皆为a的道路连接u、ν所得的图用P_a,b表示.KM.Kathiresan证实P_2,2m-1(r,m皆为任意正整数)是优美的,且猜想:除了(a,b)=(2r+1,4s+2)外,所有的P_a,b都是优美的.杨元生已证实P_2r+1,2m-1是优美的,并且证实了当r=1,2,3,4时的P_2r,2m也是优美的.本文证实r=5,6,7时P_{2r,2m相似文献}   

n-极大子群为C-正规的有限群

首先,利用Hall子群的C－正规性,得到了有限群成为。可解群的一个充分条付,推广了Schur-Zassenhaus定理;其次,考查了 n－极大子群或其 2阶及 4阶循环子群为 C-正规对有限群结构的影响．     

Crystal Structure, Thermal Stability and Luminescence of Coordination Polymer [Cd（BBP）（p-PDOA）]n

Hydrothermal reaction of Cd（NO3）2·4H2O with bbp and p-PDOAH2 at 140 ℃ yielded a novel 1D cadmium（Ⅱ） coordination polymer, [Cd（bbp）（p-PDOA）]n （bbp=2,6-bis（benzimidazol-2-yl）pyridine, p-PDOA=p-phenylenedioxydiacetate dianion）, in which CdN3O4 pentagonal bipyramids were linked by p-PDOA ligands in a bis-bidentate mode to construct a zigzag chain with the adjacent Cd…Cd distance of 1.14（1） nm, There exists a 2D supramolecular network linked by π-π stacking with a face-to-face distance of 0.35（1） nm between the 2,6-bis（benzimidazol-2-yl） pyridine ligands and hydrogen-bonding interactions （0.27（4） nm）. A 3D supramolecular network was further constructed by these non-covalent interactions between the zippers. The TG/DTG showed that its chain skeleton was thermally stable up to 389 ℃ and the blue fluorescent emission of the complex was determined at 428 nm in a solid state with its long decay lifetime of 7.24 ns.     

Stochastic Resonance in Neural Systems with Small-World Connections

We study the stochastic resonance （SR） in Hodgkin-Huxley （HH） neural systems with small-world （SW） connections under the noise synaptic current and periodic stimulus, focusing on the dependence of properties of SR on coupling strength c. It is found that there exists a critical coupling strength c^＊ such that if c 〈 c^＊, then the SR can appear on the SW neural network. Especially, dependence of the critical coupling strength c^＊ on the number of neurons N shows the monotonic even almost linear increase of c^＊ as N increases and c^＊ on the SW network is smaller than that on the random network. For the effect of the SW network on the phenomenon of SR, we show that decreasing the connection-rewiring probability p of the network topology leads to an enhancement of SR. This indicates that the SR on the SW network is more prominent than that on the random network （p = 1.0）. In addition, it is noted that the effect becomes remarkable as coupling strength increases. Moreover, it is found that the SR weakens but resonance range becomes wider with the increase of c on the SW neural network.     

子群的半覆盖-远离性与有限群的可解性

有限群G的子群H称为在G中具有半覆盖-远离性质,若存在G的一个主群列1=G0相似文献   

A quantitative study on the stability of delay discrete singular systems

For quadratic delay discrete singular systems, an algebraic criterion on the stability is established, and the size of the uniform stability region and asymptotic stability region around zero is estimated. Hence, the criterion is both qualitative and quantitative. With the computer techniques, the criterion dependent of delay is easy test and applies to the application in the practice. An illustrative simulation is given to illustrate the application of the obtained result.     

A impulsive infective transmission SI model for pest control

In this paper, we propose a model with impulsive control of epidemics for pest management. By using Floquet's theorem, small‐amplitude perturbation skills and comparison theorem, we show that there exists a globally asymptotically stable susceptible pest‐eradication periodic solution when the release amount of infective pests is larger than some critical value. However, when the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial periodic susceptible pest‐eradication solution loses its stability. Further, the existence of a positive periodic endemic solution and other rich dynamics are also studied by numerical simulation. Therefore, we can use the amount of release of infective pests to control susceptible pests at desirable low levels. Copyright © 2007 John Wiley & Sons, Ltd.     

二次滞后离散奇异系统的吸引域

本文利用Lyapunov方法对二次滞后离散奇异系统进行定性、定量分析并给出了该类系统的零解一致稳定吸引域和渐近稳定吸引域的定量估计.当初始扰动是在渐近稳定吸引域时,二次时滞离散广义系统的初始值问题的解趋于零.发现这些判据与滞后无关,容易测试,便于工程上的应用.通过示例描述了该方法的应用.