Search results for "DOMAINS"

The relationship of symptom dimensions with premorbid adjustment and cognitive characteristics at first episode psychosis: Findings from the EU-GEI s…

2021

Premorbid functioning and cognitive measures may reflect gradients of developmental impairment across diagnostic categories in psychosis. In this study, we sought to examine the associations of current cognition and premorbid adjustment with symptom dimensions in a large first episode psychosis (FEP) sample. We used data from the international EU-GEI study. Bifactor modelling of the Operational Criteria in Studies of Psychotic Illness (OPCRIT) ratings provided general and specific symptom dimension scores. Premorbid Adjustment Scale estimated premorbid social (PSF) and academic adjustment (PAF), and WAIS-brief version measured IQ. A MANCOVA model examined the relationship between symptom di…

Sharp Poincaré inequalities in a class of non-convex sets

2018

Let $gamma$ be a smooth, non-closed, simple curve whose image is symmetric with respect to the $y$-axis, and let $D$ be a planar domain consisting of the points on one side of $gamma$, within a suitable distance $delta$ of $gamma$. Denote by $mu_1^{odd}(D)$ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the $y$-axis. If $gamma$ satisfies some simple geometric conditions, then $mu_1^{odd}(D)$ can be sharply estimated from below in terms of the length of $gamma$ , its curvature, and $delta$. Moreover, we give explicit conditions on $delta$ that ensure $mu_1^{odd}(D)=mu_1(D)$. Finally, we can extend our bound on $mu_1^{odd}(D)$ to a …

Spaces of holomorphic functions in regular domains

2009

AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.

Sobolev-type spaces from generalized Poincaré inequalities

2007

We de ne a Sobolev space by means of a generalized Poincare inequality and relate it to a corresponding space based on upper gradients. 2000 Mathematics Subject Classi cation: Primary 46E35, Secondary 46E30, 26D10

Hitchhiker's guide to the fractional Sobolev spaces

2012

AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results.Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

Sobolev Extension on Lp-quasidisks

2021

AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.

Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

Zebrafish as a Model to Evaluate a CRISPR/Cas9-Based Exon Excision Approach as a Future Treatment Option for EYS-Associated Retinitis Pigmentosa

2021

Retinitis pigmentosa (RP) is an inherited retinal disease (IRD) with an overall prevalence of 1 in 4000 individuals. Mutations in EYS (Eyes shut homolog) are among the most frequent causes of non-syndromic autosomal recessively inherited RP and act via a loss-of-function mechanism. In light of the recent successes for other IRDs, we investigated the therapeutic potential of exon skipping for EYS-associated RP. CRISPR/Cas9 was employed to generate zebrafish from which the region encompassing the orthologous exons 37-41 of human EYS (eys exons 40-44) was excised from the genome. The excision of these exons was predicted to maintain the open reading frame and to result in the removal of exactl…

A Comparative Study on Nickel Binding to Hpn-like Polypeptides from Two Helicobacter pylori Strains

2021

Combined potentiometric titration and isothermal titration calorimetry (ITC) methods were used to study the interactions of nickel(II) ions with the N-terminal fragments and histidine-rich fragments of Hpn-like protein from two Helicobacter pylori strains (11637 and 26695). The ITC measurements were performed at various temperatures and buffers in order to extract proton-independent reaction enthalpies of nickel binding to each of the studied protein fragments. We bring up the problem of ITC results of nickel binding to the Hpn-like protein being not always compatible with those from potentiometry and MS regarding the stoichiometry and affinity. The roles of the ATCUN motif and multiple His…

Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects

2007

The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the pa…