We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments, we present a functional central limit theorem. We also explain connections with other work and state open problems of interest.

The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for fi...

At the center of the theory of abelian p-groups are the classical theorems of Ulm, Zippin and Kaplansky, going back to the thirties, that classify countable p-groups by their Ulm invariants: the uniqueness theorem is referred to as Ulm's theorem, the existence theorem as Zippin's theorem. For each ordinal , the -th Ulm invariant of G can be de ned as the dimension fG( ) of the vector space (ove...

We prove an existence and uniqueness theorem for solving the operator equation F(x) + G(x)= 0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. We further obtain ...

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes: neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: 1. the singularity theorem, 2. the area theorem, 3. the uniqueness the...

We reexamine the Israel-type proof of uniqueness theorem static spacetime outside photon surface in Einstein-conformal scalar system. derive a systematic fashion new divergence identity which plays key role proof. Our includes three parameters, allowing us to give uniqueness.

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especial...

We shall prove the existence and uniqueness theorem of a solution to the nonlocal fuzzy differential equation using the contraction mapping principle. Ams Mathematics Subject Classification : 94D05, 34C27

We establish an existence and uniqueness theorem for prime decompositions of theta-curves in 3-manifolds. 2000 Math. Subj. Class. Primary: 57M25; Secondary: 57M15.

This article establishes the Baouendi-Treves approximation theorem for locally integrable structures whose vector fields have continuous coefficients. As a consequence, some uniqueness results are derived.