An extension of a result of ribe

It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p _n}, 1≦p _n<∞,p _n→p, the spaceX=(Σ⊕l _{p n}) _q (resp.U=(Σ⊕L _{p n}(0, 1)) _q ) is uniformly homeomorphic toX⊕l _p (resp.U⊕L _p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent.     

An extension of a result of Sierpiński

As an application of Roth's theorem concerning the rational approximation of algebraic numbers, two sufficiency conditions are derived for an alternating series of rational terms to converge to a transcendental number. The first of these conditions represents an extension of an earlier condition of Sierpiński for the convergence of alternating series to irrational values.     

An extension of a result of Burdzy and Lawler

Summary It is shown that for all mean zero, finite variance random walks, the critical non-intersection exponents are equal to those for Brownian motion. The method uses the local time of intersection.Research supported by grants from NSA and NSF     

An extension of a result of Hwang and Pyo

In this paper, we extend a majorization result of Hwang and Pyo [LAA 332-334 (2001) pp. 15-21] from the ordinary majorization ordering to the class of group induced cone orderings induced by non-effective groups. The case of effective groups is also investigated. A particular attention is paid to positive operators.     

An extension of a result of Zaharescu on irreducible polynomials

It is well known that if f(x) is a monic irreducible polynomial of degree d with coefficients in a complete valued field (K, ‖), then any monic polynomial of degree d over K which is sufficiently close to f(x) with respect to ‖ is also irreducible over K. In 2004, Zaharescu proved a similar result applicable to separable, irreducible polynomials over valued fields which are not necessarily complete. In this paper, the authors extend Zaharescu’s result to all irreducible polynomials without assuming separability.     

An extension of a result by Lonke to intersection bodies

In this paper we prove that intersection bodies cannot be direct sums using Fourier analytic techniques. This extends a result by Lonke. We also prove a necessary regularity condition and a convexity condition for a body of revolution to be an intersection body of a star body.     

An extension of Gander’s result for quadratic equations

In the study of iterative methods with high order of convergence, Gander provides a general expression for iterative methods with order of convergence at least three in the scalar case. Taking into account an extension of this result, we define a family of iterations in Banach spaces with R-order of convergence at least four for quadratic equations.     

An extension of Goldie's result and further results in infinite divisibility

Summary It is shown that gamma random variables satisfy a certain factorisation property. Using this property, Goldie's result on mixtures of the exponential distributions is extended. The note also establishes that the generalized inverse Gaussian distribution and the generalized hyperbolic distribution considered by Barndorff-Nielsen and Halgreen (1977) are indeed self-decomposable.     

An extension result for the Landau-Lifshitz equation with Neumann boundary condition

We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in thre...     

An extension of Cameron's result on block schematic Steiner systems

It is shown that if a Steiner system S(t, k, v) (t ? 3) is block schematic, then v is bounded above by a function of k.     

An extension result of the opposing mixed convection problem arising in boundary layer theory

We prove analytically the existence of solutions for the opposing mixed convection problem when the external temperature is descending. The obtained result extends some recent study.     

A Serrin-type symmetry result on model manifolds: An extension of the Weinberger argument

We consider the classical ‘‘Serrin's symmetry result” for the overdetermined boundary value problem related to the equation $\mathrm{\Delta }u=?1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable ‘‘compatibility” assumption between the solution and the geometry of the model.     

The index number of an -space: An extension of a result of M.Takeuchi's

M. Takeuchi proved the following nice result: The ``two-number' of a symmetric -space is equal to the sum of the Betti numbers of the space with coefficients in . In the present paper an extension of this result is given for general -spaces.