Weighted estimates for commutators of singular integral operators with non-smooth kernels

In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise H¨ormander condition.     

Existence and Mann iterative approximations of nonoscillatory solutions of nth-order neutral delay differential equations

In this paper we consider the following nth-order neutral delay differential equation:

     

Stability results for convex vector-valued optimization problems

In this paper, we discuss the stability of the sets of efficient points of vector-valued optimization problems when the data of the approximate problems converges to the data of the original problem in the sense of Painlevé–Kuratowski. Our results improve the corresponding results obtained by Lucchetti and Miglierina (Optimization 53(5–6):517–528, 2004, Section 3).     

Asymptotic behaviors of higher order nonlinear dynamic equations on time scales

In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations $$y^{\triangle^n}(t)+\delta p(t)f(y(g(t)))=0$$ and $$y^{\triangle^n}(t)+\delta p(t)f(y(h(t)))=0$$ on an arbitrary time scale $\mathbb{T}$ with $\sup {\mathbb{T}}=\infty$ , where n is a positive integer and δ=1 or ?1. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.     

Extensions of linear systems to duals of countably Hilbertian spaces with graph topology

The state space for an infinite-dimensional system of the form = Ax + Bu can be extended to the dual of a countably Hilbertainspace with graph toplogy. The Study of countably Hilbertianspaces with graph topology and their duals is made. The structuresof the extensions of a C₀ semigroup and the stability theoryof the restrictions and extensions of the semigroup are illustrated.An existence and uniqueness theorem of the solution of the extendedsystem is given.     

Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay

Average synchronization and temporal order characterized by the rate of firing are studied in a spatially extended network system with the coupling time delay, which is locally modelled by a two-dimensional Rulkov map neuron. It is shown that there exists an optimal noise level, where average synchronization and temporal order are maximum irrespective of the coupling time delay. Furthermore, it is found that temporal order is weakened when the coupling time delay appears. However, the coupling time delay has a twofold effect on average synchronization, one associated with its increase, the other with its decrease. This clearly manifests that random perturbations and time delay play a complementary role in synchronization and temporal order.     

Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation arising in dusty plasma

The 2-D generalized variable-coefficient Kadomtsev-Petviashvili-Burgers equation representing many types of acoustic waves in cosmic and/or laboratory dusty plasmas is reduced by the modified classical direct similarity reduction method to nonlinear ordinary differential equation of fourth-order. Using the extended Riccati equation mapping method for solving the reduced equation, many new shock wave, solitary wave and periodic wave solutions are obtained with some constraints between the variable coefficients. Finally, some physical interpretations for the obtained solutions as, bright and dark solitons, periodic solitary wave, and shock wave in dust plasma and quantum plasma are achieved.