Periodic,breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude $\eta \to 0$.     

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.     

The regularity of the multiple higher-order poles solitons of the NLS equation

Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations.     

Painlev′e Prop erty and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has P...     

C_(2~6)烯烃在H-ZSM-5分子筛周期性模型上吸附的理论研究

采用密度泛函理论中的PBE-D方法研究了C2~6直链烯烃以及丁烯异构体在H-ZSM-5分子筛周期性模型上的吸附行为。结果表明,对于C2~6直链烯烃,随着碳数的增加,烯烃的吸附能以-12 kJ/mol的常数线性增大,体系中色散校正能ED以-13 kJ/mol的常数线性增大,而不考虑范德华力的能量E*随碳数增加变化不大,只在C5和C6时由于空间阻力凸显而减小。ED显著大于E*,说明烯烃在分子筛孔道中吸附时范德华力起主要作用,且碳数增加其影响增大。丁烯异构体吸附能大小顺序为:反式-2-丁烯顺式-2-丁烯正丁烯异丁烯。正丁烯的3种异构体ED相近且都比正丁烯的大,3种异构体的吸附能差异由E*不同引起。差分电荷密度分析表明,烯烃双键与酸性中心之间有电子聚集,且聚集程度与π配位作用相一致,而且酸性中心H原子有质子化趋向,O原子及其周围电子增加。