Abstract We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive master equations for the dynamics of the expected power in the discrete modes. In the case where the unperturbed dynamics has only discrete frequencies (finitely or infinitely many) the mode-power distribution is governed by an equation ...

Evidence from multiple studies suggests that Clostridium perfringens ε-toxin is a pore-forming toxin, assembling into oligomeric complexes in the plasma membrane of sensitive cells. In a previous study, we used gene-trap mutagenesis to identify mammalian factors contributing to toxin activity, including caveolin-2 (CAV2). In this study, we demonstrate the importance of caveolin-2 and its intera...

In this thesis, we present algorithmic solutions to shortest path queries on polyhedral surfaces and in polygonal domains. The research problems addressed in this thesis and shortest path problems in general are fundamental problems in geographic information systems (GIS) and computational geometry. We present novel algorithms that answer approximate shortest path queries between any pair of po...

We give a pedagogical review of the theory of CP violation with emphasis on the implications of recent experimental results. The review includes: (i) A detailed description of how CP violation arises in the Standard Model and in its extension that allows for neutrino masses; (ii) The formalism of CP violation in meson decays and its application to various K decays (ε K , ε ′ /ε and K → πνν), D ...

Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index ᾱX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of the classical theorem of Lorentz and ...

We consider a general second order self-adjoint elliptic operator on an arbitrary metric graph, to which small graph is glued. This obtained via rescaling given fixed γ by positive parameter ε. The coefficients in the differential expression are varying, and they, as well matrices boundary conditions, can also depend ε we assume that this dependence analytic. introduce special certain extension...

We consider the non-local Liouville equation $${\left( { - \Delta } \right)^{{1 \over 2}}}u = {h_\varepsilon }{e^u} 1\,\,\,\,\,{\rm{in}}\,\,{\mathbb{S}^1},$$ corresponding to prescription of geodesic curvature on circle. build a family solutions which blow up, when hε approaches function h as ε → 0, at critical point harmonic extension provided some generic assumptions are satisfied.

The motivation of this work is the study of the error term et (x,ω) in the averaging method for differential equations perturbed by a dynamical system. Results of convergence in distribution for ( e t (x,·) √ ε )ε>0 have been established in Khas’minskii [Theory Probab. Appl. 11 (1966) 211–228], Kifer [Ergodic Theory Dynamical Systems 15 (1995) 1143– 1172] and Pène [ESAIM Probab. Statist. 6 (200...

I shortly review the present status of the theoretical estimates of ε/ε . I consider a few aspects of the theoretical calculations which may be relevant in understanding the present experimental results. I discuss the role of higher order chiral corrections and in general of non-factorizable contributions for the explanation of the ∆I = 1/2 selection rule in kaon decays and ε/ε . Lacking reliab...