Let (X,W) be a balayage space, 1 ∈ W, or – equivalently – let W be the set of excessive functions of a Hunt process on a locally compact space X with countable base such that W separates points, every function in W is the supremum of its continuous minorants and there exist strictly positive continuous u, v ∈ W such that u/v → 0 at infinity. We suppose that there is a Green function G > 0 for X...

Let  R be bounded, open and convex. Let F W R ! R be convex, coercive of order p > 1 and such that the diameters of the projections of the faces of the epigraph of F are uniformly bounded. Then every minimizer of Z  F.rv.x// dx; v 2 CW 1;1 0 .;R/; is Hölder continuous in of order p 1 nCp 1 whenever is Lipschitz on @. A similar result for non convex Lagrangians that admit a minimizer follows.

The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a " reference " subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this criteria in mathematical physics and quantum probability. 1. Introduction A quantum dynamical semigroup (q.d.s.) T = (T t) t≥0 on B(h), the Banach space of bound...

1. Introduction. Let A be a topological space, F be a metrizable space, and C be the collection of continuous functions on X into Y. We shall be interested in two topologies on C. The compact-open or k-topology. Given compact subset K of X and open subset W of F, denote by (K, W) the collection of functions fEC such that fiK)E W. The assembly of finite intersections of sets iK, W) forms a base ...

This paper provides necessary as well sufficient conditions on the Hurst parameters so that continuous time parabolic Anderson model $$\frac{\partial u}{\partial t}=\frac{1}{2}\Delta +u{\dot{W}}$$ $$[0, \infty )\times {{\mathbb {R}}}^d $$ with $$d\ge 1$$ has a unique random field solution, where W(t, x) is fractional Brownian sheet {R}}}^d$$ and formally $$\dot{W} =\frac{\partial ^{d+1}}{\parti...

We give, first, two new applications related to the range characterization of trace operator in H 2 (Ω). After this, we characterize Sobolev spaces W 3,p (Ω) when Ω is a connected bounded domain ℝ with Lipschitz-continuous boundary.

purpose to date, little is known about the effects of a reduced level of jumping exercise regimens on bone turnover markers and mass. this study investigates the effects of different jumping exercise regimens with varying exercise loads on serum bone turnover markers and bone mass in female rats. methods a total of 144 female rats aged 12 weeks, were divided into 12 groups as follows: no exerci...

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

The filling radius function R of Gromov measures the minimal radii of van Kampen diagrams filling edge-circuits w in the Cayley 2complex of a finite presentation P. It is known that the Dehn function can be bounded above by a double exponential in R and the length of the loop, and it is an open question whether a single exponential bound suffices. We define the upper filling radius R(w) of w to...

Classical W-gravities and the corresponding quantum theories are reviewed. W-gravities are higher-spin gauge theories in two dimensions whose gauge algebras are W-algebras. The geometrical structure of classical W-gravity is investigated, leading to surprising connections with self-dual and special geometry. The anomalies that arise in quantum W-gravity are discussed, with particular attention ...