Typical random measures Ξ belonging to our class are • occupation measures of stable subordinators with stability index 0 < α < 1, • states of a Dawson-Watanabe superprocesses in R, d ≥ 2, • intersection local times of two Brownian paths in R, d = 2, 3. Very roughly, with some modification in the critical cases d = 2, the following basic common properties of these examples can be identified: • ...

Integration of the Swift-Hohenberg (SH) structure factor (SF) provided analytic results for the total power P , the first moment k, and the variance σ. Comparison of σ = 1/ξ with the halfwidth 1/ξ shows that ξ ∼ √ ξ. This may explain previous experimental results for domain chaos in Rayleigh-Bénard convection with rotation that indicated ξ ∼ εeff (ε is the distance above threshold) with νeff ≃ ...

For a vector eld ξ on R we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the ow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a de nable set. This allows us to give two restatements of Dulac's Problem for ξ that is, the question whether ξ has nitely many limit cycles in model-theoretic terms, one involving ...

On the basis of the results of ξ(2230) → π+π−, pp̄ and KK̄, measured by the BES Collaboration in radiative J/ψ decays, combined with the upper limit of Br(ξ → pp̄)Br(ξ → KK̄), measured by PS185 experiment, we argue that the distinctive properties of ξ(2230), the flavor-symmetric decays and the narrow partial decay widths to ππ andKK̄ as well as its copious production in radiative J/ψ decay, would st...

Abstract In the conventional metric formulation of gravity, Higgs Inflation model violates unitarity in electroweak vacuum scattering at energy scale Λ ∼ M Pl /ξ, where ξ 10 4 is non-minimal coupling to Ricci scalar. Palatini it commonly believed that /√(ξ), 9 . Here we reconsider violation formulation. We argue there no non-minimally coupled Standard Model energies below Planck scale. this cas...

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 stochastic complex Gaussian limit. On the other hand, when the two-point correlation function decays sl...

(H) I := [t,∞), r,p ∈ C(I,R), r(t) > , and p(t)≥ ; (H) q ∈ C(I× [a,b], [,∞)) and q(t, ξ ) is not eventually zero on any [tμ,∞)× [a,b], tμ ∈ I; (H) g ∈ C(I× [a,b], [,∞)), lim inft→∞ g(t, ξ ) =∞, and g(t,a)≤ g(t, ξ ) for ξ ∈ [a,b]; (H) τ ∈ C(I,R), τ ′(t) > , limt→∞ τ (t) =∞, and g(τ (t), ξ ) = τ [g(t, ξ )]; (H) σ ∈ C([a,b],R) is nondecreasing and the integral of (.) is taken in the...

Based on 1.35 million polarized Ξ − events, we measure the parameter φ Ξ to be −1.61 • ±2.66 • ±0.37 • for the Ξ − → Λπ − decay. New results for the parameters β Ξ and γ Ξ are also presented. Assuming that the CP-violating phase-shift difference is negligible, we deduce the strong phase-shift difference between the P-wave and S-wave amplitudes of the Λπ final state to be 3.17 • ± 5.28 • ± 0.73 ...

i=1 hi(ai) (S1) cf. Eqs. (7) and (18). Note that, to lighten notations, we do not explicitly distinguish here between attractive and repulsive patterns. Attractive patterns simply correspond to real-valued patterns: ξ i (a) = ξ +,μ i (a). Repulsive patterns have purely imaginary components in the formula above: ξ i (a) = ı̂ ξ −,ν i (a), with ı̂ 2 = −1 and ξ i (a) real-valued. Our aim is to calcul...