In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.

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...

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.

We study the regularity problem for sub-Riemannian geodesics, i.e., for those curves that minimize length among all curves joining two fixed endpoints and whose derivatives are tangent to a given, smooth distribution of planes with constant rank. We review necessary conditions for optimality and we introduce extremals and the Goh condition. The regularity problem is nontrivial due to the presen...

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.