The initial value problem for the KdV equation @tu+ u@xu + @ 3 xu = 0; u(x; 0) = (x) establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). It has been known for many years that this map K is continuous [2] , [17] and is proved recently being Lipschitz continuous [23]. In this paper it is shown that the nonlinear map K is in nitely many times Frechet di erentiable from H(R) to C([ T; T ];...

Let K be a closed subset of a smooth manifold M, and let f : K ! K be a continuous self-map of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M. We give a necessary condition for the smoothability of the faithfully innnitely interval-renormalizable homeomorphisms of Cantor sets in the unit interval. This class contain...

The well-known “splitting necklace theorem” of Alon [1] says that each necklace with k · ai beads of color i = 1, . . . , n can be fairly divided between k “thieves” by at most n(k − 1) cuts. Alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace [0, 1] where beads of given color are interpreted as measurable sets Ai ⊂ [0, 1] (or more g...

Inspired by an open problem of Alsina, Frank and Schweizer, k-Lipschitz t-norms are studied. The k-convexity of continuous monotone functions is introduced. Additive generators of k-Lipschitz tnorms are completely characterized by means of k-convexity. For a given k ∈ [1,∞[ the pointwise infimum A∗k of the class of all k-Lipschitz t-norms is introduced.

For any countable CW -complex K and a cardinal number τ ≥ ω we construct a completely metrizable space X(K, τ) of weight τ with the following properties: e-dimX(K, τ) ≤ K, X(K, τ) is an absolute extensor for all normal spaces Y with e-dimY ≤ K, and for any completely metrizable space Z of weight ≤ τ and e-dimZ ≤ K the set of closed embeddings Z → X(K, τ) is dense in the space C(Z,X(K, τ)) of al...

A mapping T from a topological space X to a topological space Y is said to be compact if T (X) is contained in a compact subset of Y. The aim of the paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends ...

Non-archimedean seminorms on rings and modules provide in general a structure which is richer than the associated linear topology [3], [2]. We want to characterize Banach spaces and commutative algebras over a complete non-trivially valued nonarchimedean field K, as linearly topologized modules over the ring of integers K◦ of K, with no reference to any specific norm. This is analog to the clas...

Let M be a smooth compact oriented Riemannian manifold, and let ∆ be the Laplace-Beltrami operator on M. Say 0 6= f ∈ S(R), and that f(0) = 0. For t > 0, let Kt(x, y) denote the kernel of f(t∆). Suppose f satisfies Daubechies’ criterion, and b > 0. For each j, write M as a disjoint union of measurable sets Ej,k with diameter at most ba j , and comparable to ba if ba is sufficiently small. Take ...

a field experiment was carried out during 2001 in the experimental fields of sugar beet seed institute in karaj. the objective of this study was to determine the response of some quantitative and qualitative traits of three sugar beet lines subjected to continuous water stress and normal conditions. three sugar beet lines 7219-p.69, bp-karaj and 7112 as tolerant, semi tolerant and sensitive to ...

Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...