We examine the small ball asymptotics for the weak solution X of the stochastic wave equation ∂X ∂t (t, x)− ∂ X ∂x (t, x) = g(X(t, x)) + f(t, x)dW (t, x) on the real line with deterministic initial conditions.

We investigate the viability of a two-stage innationary scenario in the context of super-gravity, so as to resolve the problem of initial conditions for hybrid innation. We allow for non-renormalizable terms in the superpotential and consider the most general form of the KK ahler potential and the gauge kinetic function. We construct a model with two stages of innation, the rst driven by D-term...

In this paper we show that certain types of cosmological brane configurations may induce topological inflation. In generic models for topological inflation, there is a strict bound for the potential of the inflaton field. Naively, it seems that these constraints can be removed if inflation starts with a hybrid potential. However, it is difficult to combine topological inflation and hybrid infla...

Functional programs are merely equations; they may be manipulated by straightforward equational reasoning. In particular, one can use this style of reasoning to calculate programs, in the same way that one calculates numeric values in arithmetic. Many useful theorems for such reasoning derive from an algebraic view of programs, built around datatypes and their operations. Traditional algebraic ...

This is a correction to the proof of Theorem 2.1 of [1]. An error occurred in the " proof " of Lemma 2.2, which is false. The following should replace the proof of (c) (Sect. II, p. 821ff.), which will correct the proof of the theorem: The initial condition is satisfied by the summand in (2.3) coming from the identity permutation id. So what we have to show is σ =id C r

In the theory of deformation of Okamoto-Painlevé pair (S, Y ), a local cohomology group H D (ΘS(− logD)) plays an important role. In this paper, we estimate the local cohomology group of pair (S, Y ) for several types, and obtain the following results. For a pair (S, Y ) corresponding to the space of initial conditions of the Painlevé equations, we show that the local cohomology group H D (ΘS(−...

In a recent work (Covas et al., 1996), the behaviour and the robustness of truncated dynamos with a dynamic were studied with respect to a number of changes in the driving term of the dynamic equation, which was considered previously by Schmalz and Stix (1991) to be of the form A B . Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the ...

We solve the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.

and Applied Analysis 3 Using the initial conditions 2.3 , we can deduce from 2.2 for φ and ψ the following equations: φ t η ζ t − ξ1 ∫ t ξ1 ∫ τ ξ1 q s φ σ s ΔsΔτ, 2.5

In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution forms a “neck” which pinches in a finite time at a single point. We also obtain a detailed description of the neck pinching process.