LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the err...     

Dynamics of n+1-dimensional impulsive reaction-diffusion predator-prey system with Holling type III functional response

An n+1-dimensional impulsive reaction-diffusion periodic predator-prey system with Holling type III functional response is investigated in the present paper. Sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established based on the comparison theory of differential equation and upper and lower solution method. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given in the end of the paper.     

Generalized Leibniz functional matrices and divided difference form of the Lagrange–Bürmann formula

In this paper, we derive two versions of divided difference form of the Lagrange–Bürmann expansion formula. The first version expresses all coefficients by a form of a determinant. By means of the factorizations of the generalized Leibniz functional matrices with respect to a sequence, we obtain the second version with coefficients represented by a finite sum. Some new matrix inversions are also investigated.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

Nonparametric estimation of quantiles for a class of stationary processes

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.     

A hyperbranched,rotaxane‐type mechanically interlocked polymer

Based on the dibenzo‐24‐crown‐8/1,2‐bis(pyridinium)ethane recognition motif, a hyperbranched mechanically interlocked polymer was prepared by polyesterification of an easily available dynamic trifunctional AB₂ pseudorotaxane monomer. It was characterized by various techniques including ¹H NMR, COSY, NOESY, GPC, viscosity, TGA, dynamic laser light scattering, AFM, and SEM. Its GPC M_n was determined to be 191 kDa with polydispersity 1.7 and its hydrodynamic diameter in a dilute solution in acetone was about 70 nm. This measured M_n value corresponds to about 93 repeating units. The study reported here presents not only a new polymer topology but also a novel and convenient way to prepare mechanically interlocked polymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4067–4073, 2010