Exponential Synchronization of Delayed Stochastic Complex Dynamical Networks via Hybrid Impulsive Control

Dear Editor,This letter addresses the synchronization problem of a class of delayed stochastic complex dynamical networks consisting of multiple drive and response nodes.The aim is to achieve mean square exponential synchronization for the drive-response nodes despite the simultaneous presence of time delays and stochastic noises in node dynamics.

关于两个两点Witten-Kontsevich关联子公式等价的一个注记

We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by Bertola-Dubrovin-Yang and by Zograf, respectively.

Experimental study of freak waves due to three-dimensional island terrain in random wave

An experimental study is carried out for waves passing an isolated reef terrain in a wave tank. A three-dimensional model of a representative and isolated reef terrain in the West Pacific is built. Random wave trains with various periods and wave heights are generated by a wave maker using the improved JONSWAP spectrum. It is observed that there are different kinds of generation processes and waveforms of freak waves. The freak wave factor Hm/Hs (where Hm is the maximum wave height of wave series, and Hs is significant wave height) is analyzed in detail, in terms of the skewness, kurtosis and water depth, as well as the relationship between freak wave height H& and skewness. The freak wave factor Hm/Hs is found to be in positive correlation with the kurtosis, while larger H[x tends to be related with bigger skewness. The rapid variation of water depth, such as slope and seamount, contributes to the occurrence probability of freak waves.

CYCLIC CODES OVER THE RING Z(_P^2) OF LENGTH p^e

The study of cyclic codes over rings has generated a lot of public interest.In this paper,we study cyclic codes and their dual codes over the ring Z P2 of length pe,and find a set of generators for these codes.The ranks and minimal generator sets of these codes are studied as well,which play an important role in decoding and determining the distance distribution of codes.

COMPLEXITY ANALYSIS OF TIME SERIES GENERATED BY ELEMENTARY CELLULAR AUTOMATA

Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the classification problem of all 256 elementary cellular automata is discussed from the point of view of time series generated by them,and examples in each class are provided to explain the methods used.

INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.

Unstable and exact periodic solutions of three-particles time-dependent FPU chains

For lower dimensional Fermi–Pasta–Ulam（FPU） chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α（t） and β（t） with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.

Impact of Long-range Desert Dust Transport on Hydrometeor Formation over Coastal East Asia

Model simulations and hydrological reanalysis data for 2007 are applied to investigate the impact of long-range desert dust transport on hydrometeor formation over coastal East Asia. Results are analyzed from Hong Kong and Shanghai, which are two representative coastal cities of East Asia. Long-range desert dust transport impacts mainly spring and summer clouds and precipitation over coastal East Asia. In spring, clouds and precipitation come mainly from large-scale condensation and are impacted mainly by dust from the Gobi, Sahara, and Thar deserts. These desert dusts can participate in the precipitation within and below the clouds. At lower latitudes, the dust particles act mainly as water nuclei. At higher latitudes, they act as both water nuclei and ice nuclei. The effect of Gobi, Sahara, and Thar dust on large-scale clouds and precipitation becomes stronger at higher latitudes. In summer, clouds and precipitation over coastal East Asia come mainly from convection and are impacted mainly by dust from the Taklamakan, Arabian, and Karakum-Kavir deserts. Most Taklamakan dust particles can participate in precipitation within convective clouds as ice nuclei, while Arabian and Karakum-Kavir dust particles participate only as water nuclei in precipitation below the clouds. The effect of Taklamakan dust on convective clouds and precipitation becomes stronger at lower latitudes. Of all the desert dusts, that from the Gobi and Taklamakan deserts has the relatively largest impact. Gobi dust impacts climate change in coastal East Asia by affecting spring water clouds at higher latitudes.

Dynamic analysis of stochastic delayed cellular neural networks

The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtained to check the almost sure exponential stability of the DCNNs.

Delay-dependent H-infinity control for continuous time-delay systems via state feedback

The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.

On Ha's Version of Set-valued Ekeland's Variational Principle

By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187-206 （2005）] established a new version of Ekeland＇s variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha＇s version of set-valued Ekeland＇s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha＇s version, we deduce a Caristi-Kirk＇s fixed point theorem and a Takahashi＇s nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other.

The Finite-time Ruin Probability of a Discrete-time Risk Model with Subexponential and Dependent Insurance and Financial Risks

Consider a discrete-time risk model with insurance and financial risks in a stochastic economic environment. Assume that the insurance and financial risks form a sequence of independent and identically distributed random vectors with a generic random vector following a wide type of dependence structure. An asymptotic formula for the finite-time ruin probability with subexponential insurance risks is derived. In doing so, the subexponentiality of the product of two dependent random variables is investigated simultaneously.

A Short Proof of Ramanujan＇s 1ψ1 Formula

In this paper,we give a short proof of the celebrated Ramanujan's 1ψ1 formula.

Probabilistic Model of Software Approximate Correctness

Correctness is a key attribute of software. Parameterized bisimulation provides a kind of abstract description to verify the correctness of software under environment. In real world situations, many softwares contain some probabilistic information. In this paper, we focus on the probabilistic construction of parameterized bisimulation. Firstly, we extend parameterized bisimulation to probabilistic parameterized bisimulation. Secondly, a quantitative model of approximate correctness of software is proposed. Finally, the subsititutivity laws of quantitative model with various combinators are proved.

Regularity for 3-D MHD Equations in Lorentz Space L^(3,∞)

.The regularity for 3-D MHD equations is considered in this paper,it is proved that the solutions(v,B,p)are Holder continuous if the velocity field v∈L^(∞)(0,T;L^(3,∞)_(x)(R^(3))with local small condition r^(-3)|{x∈B_(r)(x_(0):|v(x,t_(0))|>εr^(-1)}|≤ε and the magnetic field B∈L^(∞)(0,T;VMO^(-1)(R^(3)).

Two-Grid Discretization Scheme for Nonlinear Reaction Diffusion Equation by Mixed Finite Element Methods

In this paper,we study an efficient scheme for nonlinear reaction-diffusion equations discretized by mixed finite element methods.We mainly concern the case when pressure coefficients and source terms are nonlinear.To linearize the nonlinear mixed equations,we use the two-grid algorithm.We first solve the nonlinear equations on the coarse grid,then,on the fine mesh,we solve a linearized problem using Newton iteration once.It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h 1/2).As a result,solving such a large class of nonlinear equations will not be much more difficult than getting solutions of one linearized system.