and Applied Analysis 3 H4 f ∈ C R,R ; there exist two constants s2 < 0 < s1 such that f s2 f 0 f s1 0, f s > 0 for s ∈ 0, s1 ∪ s1,∞ , and f s < 0 for s ∈ −∞, s2 ∪ s2, 0 . The rest of this paper is organized as follows. In Section 2, we give some notations and the main results. Section 3 is devoted to proving the main results. 2. Statement of the Main Results Let Y {u ∈ C R,R : u t u t ω }with t...

Norm, one of the NLM Lexical tools, is a commonly used retrieval tool for natural language processing applications with the Unified Medical Language System® (UMLS). One of the core normalization techniques is to find the uninflected form of terms. Terms in UMLS Metathesaurus® have (s), (es), or (ies) attached to them as a shorthand way of representing either singular or plural nouns. An ideal n...

Let Cn be the origin-containing cluster in subcritical percolation on the lattice 1 nZ , viewed as a random variable in the space Ω of compact, connected, origin-containing subsets of R, endowed with the Hausdorff metric δ. When d ≥ 2, and Γ is any open subset of Ω, we prove that lim n→∞ 1 n logP (Cn ∈ Γ) = − inf S∈Γ λ(S) where λ(S) is the one-dimensional Hausdorff measure of S defined using th...

In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired A. B?ttcher?s result [3], prove that S-resolvent norm bounded is not constant any open set set. Beside, find characterization S-pseudospectrum operator means S-spectra all perturbed with perturbations have norms strictly less than ?.

Assuming the Generalized Riemann Hypothesis (GRH), we show that the norm-Euclidean Galois cubic fields are exactly those with discriminant ∆ = 7, 9, 13, 19, 31, 37, 43, 61, 67, 103, 109, 127, 157 . A large part of the proof is in establishing the following more general result: Let K be a Galois number field of odd prime degree ` and conductor f . Assume the GRH for ζK(s). If 38(`− 1)(log f) log...

We show that Sobolev norm convergence of a stationary subdivision scheme is equivalent to standard norm convergence of the stationary subdivision scheme to a limit function in the Sobolev space. Stationary subdivision is an iterative method for the generation of reenable functions which are the main building blocks for the construction of wavelets. For this reason and also because of its use in...

We prove that the weak Riemannian metric induced by the fractional Sobolev norm H on the diffeomorphisms group of the circle is geodesically complete, provided s > 3/2.

the object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces H, for s negative but close to 0. For smooth solutions there is an a priori upper bound for the H norm of the solution, in terms of the H norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrar...