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.

with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(£) need not be diagonal. However, he required that |Q(£)| ^ 1We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of Q(£) and smoothness of an associated positive-definite symmetric matri...

The detection of insu ciently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the pro le of the integrand at the quadrature knots which allows inferences approaching the theoretical 100% rate of success, under error estimate sharpening. The proposed procedure is of the highest interest...

We study the Q evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalontype) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA.

The Ulam sequence is defined as a1 = 1, a2 = 2 and an being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, . . . Ulam remarked that understanding the sequence, which has been described as ’quite erratic’, seems difficult and indeed nothing is known. We report the empirical dis...