一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.     

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.     

On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

Generalized P(N)-graded Lie superalgebras

We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction.     

Stabilization to a positive equilibrium for some reaction–diffusion systems

The aim of this paper is to study the asymptotic behavior of solutions for some reaction–diffusion systems in biology. First, we establish a Liouville type theorem for entire solutions of these reaction–diffusion systems. Based on this theorem, we derive the stabilization of the solutions of the reaction–diffusion system to the unique positive constant state, under the condition that this positive constant state is globally stable in the corresponding kinetic systems. Two specific examples about spreading phenomena from ecology and epidemiology are given to illustrate the application of this theory.     

多级孔芳香骨架材料的合成及固载硫脲催化剂的研究

合成了一种多级孔芳香骨架材料(PAF-70); 使用由氨基修饰过的单体, 应用该合成策略得到了同样具有窄分布介孔的含有氨基活性位点的PAF材料, 并通过硫脲单体与其氨基活性位点的反应, 将硫脲基团引入PAF-70材料中, 获得了含有硫脲催化位点的材料(PAF-70-thiourea). 氮气吸附-脱附测试结果显示, PAF-70存在孔径分布较窄的介孔, 介孔孔径为3.8 nm, 与模拟计算值(约3.7 nm)吻合. 热重分析结果表明, PAF-70具有很高的热稳定性. PAF-70在大多数溶剂中可以稳定存在, 具有良好的化学稳定性. 将PAF-70-thiourea作为催化剂, 应用在N-溴代琥珀酰亚胺(NBS)氧化醇类的反应中, 其表现出较高的催化活性、 较高的稳定性和广泛的底物适用性. 与含有相同硫脲催化位点的金属有机框架(MOF)材料(IRMOF-3-thiourea)作为催化剂对比, 进一步证实PAFs材料非常适合作为催化有机反应的固载平台.