Large deviations for the stochastic shell model of turbulence

In this work, we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for solutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell–Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.      

Weighted norm inequalities for geometric fractional maximal operators

For 0 < let Tf denote one of the operators

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Clifford martingale Φ-Equivalence betweenS(f) andf*

TheL ²-norm equivalence between a Clifford martingalef and its square functionS(f) plays an important role in the proof of theL ²-boundedness of Cauchy integral operators on Lipschitz graphs and the CliffordT(b) Theorem [2, 4]. This note generalises the result to the Φ-equivalence between the maximal functionf* andS(f), where Φ is a nondecreasing and continuous function fromIR ⁺ toIR ⁺, of the moderate growth Φ(2u)≤C ₁Φ(u) and satisfies Φ(0)=0.     

Asymptotic expansion of norm associated with conjugate trigonometric polynomial

LetT _n (x) be trigonometric polynomial of degreen, and be conjugation ofT _n (x). In this paper we obtain the complete asymptotic expansion for

Lower bounds of some singular integrals and their applications

Let and . We are interested in the lower bounds of the integral:

A vector valued transference of Fourier-Bessel multipliers onto Hankel multipliers with applications

In this note we prove a vector valued transference theorem relating Fourier-Bessel multipliers and Hankel multipliers. An application of such a transference theorem allows to show that results of Córdoba [3] and Romera [4] can be deduced from a recent result of Balodis and Córdoba [1, Theorem 3]. Partially supported by DGICYT Grant PB 97-1489 (Spain). Partially supported by KBN grant # 2 PO3A 034 20.     

Limit theorems for random walks with dynamical random transitions

Let be an ergodic and conservative non-singular transformation of (, ,m) (thedynamic environment), let _w be a random probability on a locally compact second countable groupG, and define

On some properties of cohomotopy-type functors

It is shown that if II ⁿ ,n\s>2, are Chogoshvili's cohomotopy functors [1, 2, 3], then

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at if

Une classe d'algèbres de Fréchet à caractères continus

We prove in a simpler and direct manner using the spectral theory that every Fréchet algebra which is rationnally generated by a real or orthogonal subset is functionally continuous. These results include as a special case the results of R. Arens, H. Goldmann, E. A. Michael and W. Zelazko.

     

On the almost sure central limit theorem and domains of attraction

We give necessary and sufficient criteria for a sequence (X _n) of i.i.d. r.v.'s to satisfy the a.s. central limit theorem, i.e.,

On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations

Generalized solution to a semilinear hyperbolic system with a non-Lipshitz nonlinearity

Let

An oscillation criterion for functional differential equations with deviating arguments

An oscillation criterion is given for the differential equation

On the reducibility of the postulation Hilbert scheme

We give a condition in terms of the possible graded Betti numbers compatible with a given Hilbert functionH of 0-dimensional subschemes of ℙ ⁿ which implies the reducibility of the postulation Hilbert scheme and of its subscheme which parametrizes reduced subschemes with Hilbert functionH.     

A useful fixpoint theorem

A sufficient condition for each extensive mapping of an ordered set to have a fixpoint is presented. Financial support of the Grant Agency of the Czech Republic under the grant no. 201/93/0950 is gratefully acknowledged.     

Stochastic invariant imbedding

We study stochastic differential equations of the type:

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

We study the limit behaviour of solutions of with initial data k δ ₀ when k → ∞, where h is a positive nondecreasing function and p > 1. If h(r) = r ^β , β > N(p − 1) − 2, we prove that the limit function u _∞ is an explicit very singular solution, while such a solution does not exist if β ≤  N(p − 1) − 2. If lim inf _{r→ 0} r ² ln (1/h(r))  >  0, u _∞ has a persistent singularity at (0, t) (t ≥  0). If , u _∞ has a pointwise singularity localized at (0, 0).     

The critical value for some non-attractive long range nearest particle systems

We consider the nearest particle system which gives birth rate to each vacant interval, concentrated on the interval's midpoint(s). We prove that a critical value for exists and equals one. The proof extends to a large class of nearest particle systems. This paper solves a problem suggested by Liggett (1985).In the following we deal with nearest particle systems { _t :t0}. These can be described as particle systems with the following flip rates: