Search results for "domain"
showing 10 items of 2485 documents
An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields
2004
[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…
Solvability of the divergence equation implies John via Poincaré inequality
2014
Abstract Let Ω ⊂ R 2 be a bounded simply connected domain. We show that, for a fixed (every) p ∈ ( 1 , ∞ ) , the divergence equation div v = f is solvable in W 0 1 , p ( Ω ) 2 for every f ∈ L 0 p ( Ω ) , if and only if Ω is a John domain, if and only if the weighted Poincare inequality ∫ Ω | u ( x ) − u Ω | q d x ≤ C ∫ Ω | ∇ u ( x ) | q dist ( x , ∂ Ω ) q d x holds for some (every) q ∈ [ 1 , ∞ ) . This gives a positive answer to a question raised by Russ (2013) in the case of bounded simply connected domains. In higher dimensions similar results are proved under some additional assumptions on the domain in question.
Riesz-Fischer Maps, Semi-frames and Frames in Rigged Hilbert Spaces
2021
In this note we present a review, some considerations and new results about maps with values in a distribution space and domain in a σ-finite measure space X. Namely, this is a survey about Bessel maps, frames and bases (in particular Riesz and Gel’fand bases) in a distribution space. In this setting, the Riesz-Fischer maps and semi-frames are defined and new results about them are obtained. Some examples in tempered distributions space are examined.
Commutative Partial O*-Algebras
2002
This chapter is devoted to the integrability of commutative partial O*-algebras. Three notions of weak commutativity, commutativity and strong commutativity of an O*-vector space are defined and investigated. In Section 3.1, we analyze the relation between the integrability of weakly commutative O*-vector space M and the commutativity of the von Neumann algebra (M w ′ )′. In Section 3.2, we study the integrable extensions of partial O*-algebras. In Section 3.3, we describe another explicit example, namely, the partial O*-algebra M[S, T] generated by two weakly commuting symmetric operators S and T defined on a common dense domain in a Hilbert space. In particular, we investigate in detail t…
Computing Difficulties for Deriving Poverty Indices from Some Functional Forms of Lorenz Curves
2014
We examine three families of classical one-parameter functional forms for estimating a Lorenz curve: the power form (Pareto, elementary form), the exponential form (Gupta, elementary form) and fractional form (Rohde). For the first time, we systematically study these functions not for their ability to be estimated but on the point of view of the possibility of deriving poverty indices, which implies first determining the headcount ratio (i.e., the percentage of poor). We show that computing difficulties have been largely underestimated. Two forms, the most simple ones, pose no problem: the elementary power and exponential forms. However, the Pareto functional form poses problem with a restr…
Caractérisation et diagenèse thermique des roches mères pétrolières de la série des Schistes d'âge néocomien moyen-barrémien dans le bassin intérieur…
2006
8 pages; International audience
Cross-Domain Recommendations with Overlapping Items
2016
In recent years, there has been an increasing interest in cross-domain recommender systems. However, most existing works focus on the situation when only users or users and items overlap in different domains. In this paper, we investigate whether the source domain can boost the recommendation performance in the target domain when only items overlap. Due to the lack of publicly available datasets, we collect a dataset from two domains related to music, involving both the users’ rating scores and the description of the items. We then conduct experiments using collaborative filtering and content-based filtering approaches for validation purpose. According to our experimental results, the sourc…
Ontology-based standardization on knowledge exchange in social knowledge management environments
2012
After the hype around Web 2.0, organizations have revisited their efforts on knowledge management in order to create beneficial effects from their employees' activities in social environments. While there is not much doubt about the positive effects on creativity and flexibility, handling the variety of knowledge work environments that are in use at different organizational units or business partners can negatively affect productivity. While standards have generally mushroomed in the IT domain, there is a lack of standards in knowledge management. This paper argues for a standard on exchanging knowledge between social environments. We revisit related work, particularly standards which can b…
Exploiting ongoing EEG with multilinear partial least squares during free-listening to music
2016
During real-world experiences, determining the stimulus-relevant brain activity is excitingly attractive and is very challenging, particularly in electroencephalography. Here, spectrograms of ongoing electroencephalogram (EEG) of one participant constructed a third-order tensor with three factors of time, frequency and space; and the stimulus data consisting of acoustical features derived from the naturalistic and continuous music formulated a matrix with two factors of time and the number of features. Thus, the multilinear partial least squares (PLS) conforming to the canonical polyadic (CP) model was performed on the tensor and the matrix for decomposing the ongoing EEG. Consequently, we …
Icons: Visual representation to enrich requirements engineering work
2013
Adapting icons in requirements engineering can support the multifaceted needs of stakeholders. Conventional ap- proaches to RE are mainly highlighted in diagrams. This paper introduces icon-based information as a way to represent ideas and concepts in the requirements engineering domain. We report on icon artifacts that support requirements engi- neering work such as priority types, status states and stakeholder kinds. We evaluate how users interpret meanings of icons and the efficacy of icon prototypes shaped to represent those requirements attributes. Our hypothesis is whether practitioners can recognize the icons’ meaning in terms of their functional representation. According to the empi…