Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on the square lattice

In this work we study the correlation function of the ground state of two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as correlation function. We estimate the exponent of spin correlation function for fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Critical behavior of a dynamical percolation model

The critical behavior of the dynamical percolation model, which realizes the molecular-aggregation conception and describes the crossover between the hadronic phase and the partonic phase, is studied in detail. The critical percolation distance for this model is obtained by using the probability P∞ of the appearance of an infinite cluster. Utilizing the finite-size scaling method the critical exponents γ/v and T are extracted from the distribution of the average cluster size and cluster number density. The influences of two model related factors, I.e. The maximum bond number and the definition of the infinite cluster, on the critical behavior are found to be small.     

On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.     

Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

Stable Exponents in Discrete Groups

It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to .     

The independence of initial vectors in the subdivision schemes

Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.     

On a semilinear Schrödinger equation with critical Sobolev exponent

We consider the semilinear Schrödinger equation , , where , are periodic in for , 0$">, is of subcritical growth and 0 is in a gap of the spectrum of . We show that under suitable hypotheses this equation has a solution . In particular, such a solution exists if and .

     

CHARACTERISTIC EXPONENTS FOR SECONDORDER PERIODIC LINEAR DIFFERENTIAL EQUATION

1IntroductionandMainResultsItiswellknownthatwhenp'--4q>0,secondorderautonomoussystemhastwocharacteristicexponentsfsothefollowingpropositionsareobvious.Proposition1Assumeq<0,then(1.1)hastwocharacteristicexponentswithoppositesigns.Proposition2Assumeq>0andp'…     

On computing the entropy of the Henon attractor

In a recent article D. Ruelle [inLecture Notes in Physics, No. 80 (Springer, Berlin, 1978)] has conjectured that for the Hénon attractor its measure theoretic entropy should be equal to its characteristic exponent. This result is known to be true for systems which satisfy Smale's Axiom A. In this article we report the results of our computations which suggest that Ruelle's conjecture may be true for the Hénon attractor. Further, in our study we are confronted with fundamental questions which suggest that certain existence theorems from ergodic theory are not sufficient from a computational point of view.     

Limit distributions and one-parameter groups of linear operators on Banach spaces

Let = {U_t: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {U_tn(μ₁ * μ₂*…*μ_n)*δ_xn}, where {μ_n}Q, {x_n}X and measures U_tnμ_j (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes L_m( ) as follows: L₀( )= ( (X); ), L_m( )= (L_m−1( ); ) for m=1, 2,… and L_∞( )=_m=0^∞L_m( ). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from L_m( ), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators.