LetX be a standard probability space and Tt a measure-preserving semiflow on X. We show that there exists a set X0 of full measure in X such that for any x ∈ X0 and t ≥ 0 there are measures μx,t and μ − x,t which for all but a countable number of t give a distribution on the set of points y such that Tt(y) = Tt(x). These measures arise by taking weak∗−limits of suitable conditional expectations...

We study the qualitative properties of functions belonging to corresponding De Giorgi classes ?Br(1??)(x0)?(x,|?(u?k)±|)dx???Br(x0)?(x,(u?k)±?r)dx,where ?, r?(0,1), k?R and function ? satisfies non-logarithmic condition (r?n?Br(x0)[?(x,vr)]sdx)1s(r?n?Br(x0)[?(x,vr)]?tdx)1t?c(K)?(x0,r),r?v?K?(r), under some assumptions on ?(r) ?(x0,r) numbers s, t>1. These conditions generalize known logarithmic...

We consider a family of skew tent maps fa on the unit interval, determined by parameter a, with 0<a<1. give decision procedure, that input and point x0 in determines whether or not sequence x0,fa(x0),fa2(x0),... iterates reaches one two fixed points after finite number iterations.

Let Γ(x0) be a finite rooted tree, for which Γ is the underlying tree and x0 root. T Terwilliger algebra of with respect to x0. We study structure principal T-module. As result, it shown that recognizes isomorphism class Γ(x0).

I. Introduction 575 1. The decay K° — • TT + W~. Basic experimental results 575 2. Attempts to explain the decay Kjj —-K*W~ without violation of CP invariance 576 3. The purpose of this article 577 4. The hypothesis of CPT invariance 577 5. A new interaction 578 6. The a particles 579 7. Summary of processes 579 n. Neutral K mesons 581 8. Description of K° mesons 581 9. The decays K^ — w*ir~ an...

This paper characterizes the possible blow-up of solutions for 3D magneto-hydrodynamics (MHD short) equations. We first establish some ϵ-regularity criteria in Lq,∞ spaces suitable weak solutions, and then together with an embedding theorem from Lp,∞ space into a Morrey type we characterize local behaviors near potential singular point. More precisely, show that if z0=(t0,x0) is point, any r>0 ...

In this work, we introduce DIRECTGO , a new MATLAB toolbox for derivative-free global optimization. collects various deterministic DIRECT -type algorithms box-constrained, generally constrained, and problems with hidden constraints. Each sequential algorithm is implemented in two ways: using static dynamic data structures more efficient information storage organization. Furthermore, parallel sc...