We consider ”nonconventional” averaging setup in the form dX(t) dt = ǫB ` X(t), ξ(q1(t)), ξ(q2(t)), ..., ξ(ql(t)) ́ where ξ(t), t ≥ 0 is either a stochastic process or a dynamical system (i.e. then ξ(t) = F x) with sufficiently fast mixing while qj(t) = αjt, α1 < α2 < ... < αk and qj , j = k+1, ..., l grow faster than linearly. We show that the properly normalized error term in the ”nonconventio...

T̂ [θ](ξ) = m(ξ)θ̂(ξ), ξ ∈ Z. We make the following assumptions about m. We assume that m : R\{0} → R is even, 0-homogeneous, and m(ξ) · ξ = 0 a.e. Note that m is not necessarily smooth or even bounded, so the operator T is not assumed to be of Calderón-Zygmund type. We say that the pair (θ, u) ∈ Lloc(R × T) is a weak solution of the system (1)–(4) on R if for every φ ∈ C∞ 0 (R× T) the following ...

In the context of paracontact geometry, η-Ricci solitons are considered on manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0, S · R(ξ,X) = 0, W2(ξ,X) · S = 0 and S · W2(ξ,X) = 0. We prove that on a para-Kenmotsu manifold (M,φ, ξ, η, g), the existence of an η-Ricci soliton implies that (M, g) is quasi-Einstein and if the Ricci curvature satisfies R(ξ,X) · S = 0, then (M, g) is Ei...

We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying then the Fourier transform ζ̂ε(t, ξ) of the appropriately scaled solution converges point-wise in ξ to a deterministic limit, exponentially decaying in time. On the other hand, when the two-point correlation f...

In this paper author has obtained the neutrix product of x+ −r and δ (α) (x), where α is a positive fractional number. Key Words: Neutrix limit, fractional-differentiation, sequence, function. Ams Subject Classification- 46F 1. INTRODUCTION N defined by J.G. vander Corput [2] as commutative additive group functions ν(ξ) on domain N' with values in N", further if for some ν N, = γ all ξ N', then...

We show that, for any transcendental real number ξ, the uniform exponent of simultaneous approximation of the triple (ξ, ξ, ξ) by rational numbers with the same denominator is at most (1 + 2γ − √ 1 + 4γ)/2 ∼= 0.4245 where γ = (1 + √ 5)/2 stands for the golden ratio. As a consequence, we get a lower bound on the exponent of approximation of such a number ξ by algebraic integers of degree at most 4.

Résumé – Étant donné un nombre réel ξ et un entier n ≥ 1, nous définissons quatre exposants d’approximation diophantienne, qui viennent s’ajouter aux exposants wn(ξ) et w∗ n(ξ) introduits par Mahler et Koksma. Nous calculons leurs six valeurs lorsque n = 2 et ξ est un nombre réel dont le développement en fraction continue cöıncide à partir d’un certain rang avec une suite sturmienne d’entiers p...

A new precision measurement of the Ξ mass has been performed at the NA48 experiment at the CERN SPS. The value obtained is [1314.82±0.06 (stat.) ±0.2 (syst.)]MeV/c. The branching ratios of Ξ radiative decays have been measured as: Br(Ξ → Λγ) = [1.90 ± 0.34(stat.) ± 0.19(syst.)] · 10−3 and Br(Ξ → Σγ) = [3.14 ± 0.76(stat.) ± 0.32(syst.)] · 10−3. 70 The NA48 Collaboration: Precision measurement of...

Let ξ ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made Πξ by refining the Polish topology on the real line. These sets are called potentially Πξ . We give a Hurewicz-like test to recognize potentially Πξ sets. 1. Preliminaries in dimension one Let us recall some results in dimension one before studying Borel subsets of the plane. In descriptive set theory, a ...

It is shown that the signature of a manifold with a symplectic circle action, having only isolated fixed points, equals the alternating sum of the Novikov numbers corresponding to the cohomology class of the generalized moment map. The same is true for more general fixed point sets 1. Theorem. Let M be a symplectic manifold with a symplectic circle action having only isolated fixed points. Then...