Search results for "DOMAIN"

Old and New on the Quasihyperbolic Metric

1998

Let D be a proper subdomain of \( {\mathbb{R}^d}\). Following Gehring and Palka [GP] we define the quasihyperbolic distance between a pair x 1, x 2 of points in D as the infimum of \( {\smallint _\gamma }\frac{{ds}}{{D\left( {x,\partial D} \right)}}\) over all rectifiable curves γ joining x 1, x 2 in D. We denote the quasihyperbolic distance between x 1, x 2 by k D (x 1, x 2). As pointed out by Gehring and Osgood [GO], x 1 and x 2 can be joined by a quasihyperbolic geodesic; also see [Mr]. The quasihyperbolic metric is comparable to the usual hyperbolic metric in a simply connected plane domain by the Koebe distortion theorem. For a multiply connected plane domain D these two metrics are co…

Quasi-Modes in Higher Dimension

2019

Recall that if a(x, ξ) and b(x, ξ) are two C1-functions defined on some domain in \({\mathbf {R}}^{2n}_{x,\xi }\), then we can define the Poisson bracket to be the C0-function on the same domain given by $$\displaystyle \{ a,b\} =a^{\prime }_\xi \cdot b^{\prime }_x-a^{\prime }_x \cdot b^{\prime }_\xi =H_a(b). $$ Here \(H_a=a^{\prime }_\xi \cdot \partial _x-a^{\prime }_x\cdot \partial _\xi \) denotes the Hamilton vector field of a. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hormander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.

Product Integration for Weakly Singular Integral Equations In ℝm

1985

In this note we discuss the numerical solution of the second kind Fredholm integral equation: $$ y(t) = f(t) + \lambda \int\limits_{\Omega } {{{\psi }_{\alpha }}(|t - s|)g(t,s)y(s)ds,\;t \in \bar{\Omega },} $$ (1) Where \( \lambda \in ;\not{ \subset }\backslash \{ 0\} \) , the functions f,g are given and continuous, |.| denotes the Euclidean norm, and φα, 0 \alpha > 0} \\ {\left\{ {\begin{array}{*{20}{c}} {\ln (r),} & {j = 0} \\ {{{r}^{{ - j}}}} & {j > 0} \\ \end{array} } \right\},\alpha = m} \\ \end{array} ,} \right. $$ with Cj not depending on r. Here Ω _ is the closure of a bounded domain Ω⊂ℝm.

Absolute continuity of mappings with finite geometric distortion

2015

Suppose that ⊂ R n is a domain with n ≥ 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with KO(·,f) ∈ L 1/(n 1) loc () is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U ⊂ is an open set with N(f,U) 0 depends only on n and on the maximum multiplicity N(f,U).

La Communication des Institutions Culturelles dans le Domaine des Arts du Spectacle Vivant en France

2001

Comparative genomics and protein domain graph analyses link ubiquitination and RNA metabolism.

2006

The human gene parkin, known to cause familial Parkinson disease, as well as several other genes, likely involved in other neurodegenerative diseases or in cancer, encode proteins of the RBR family of ubiquitin ligases. Here, we describe the structural diversity of the RBR family in order to infer their functional roles. Of particular interest is a relationship detected between RBR-mediated ubiquitination and RNA metabolism: a few RBR proteins contain RNA binding domains and DEAH-box RNA helicase domains. Global protein domain graph analyses demonstrate that this connection is not RBR-specific, but instead many other proteins contain both ubiquitination and RNA-related domains. These protei…

An Innovative Ambient Identification Method

2020

Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…

S1/4 Domain compliance and elastic power transmission in FOF1F0F1-ATPase

2008

Influence of Background Knowledge and Language Proficiency on Comprehension of Domain-Specific Texts by University Students

2019

This paper presents the results of a quantitative study that explores two factors contributing to reading comprehension of domain specific texts, namely level of language proficiency and background knowledge. Overall, 32 students participated in the study by taking two custom-designed reading comprehension tests. The test scores were further  analyzed using SPSS statistical software. The results of statistical tests revealed the differences between study groups as well as the effects of compensation. More precisely, the most proficient group scored higher on almost all tests and completed the tests more quickly than the remaining groups. The statistical tools used to test the data showed th…

Structure‐Activity Relationships of Benzamides and Isoindolines Designed as SARS‐CoV Protease Inhibitors Effective against SARS‐CoV‐2

2020

Abstract Inhibition of coronavirus (CoV)‐encoded papain‐like cysteine proteases (PLpro) represents an attractive strategy to treat infections by these important human pathogens. Herein we report on structure‐activity relationships (SAR) of the noncovalent active‐site directed inhibitor (R)‐5‐amino‐2‐methyl‐N‐(1‐(naphthalen‐1‐yl)ethyl) benzamide (2 b), which is known to bind into the S3 and S4 pockets of the SARS‐CoV PLpro. Moreover, we report the discovery of isoindolines as a new class of potent PLpro inhibitors. The studies also provide a deeper understanding of the binding modes of this inhibitor class. Importantly, the inhibitors were also confirmed to inhibit SARS‐CoV‐2 replication in …