The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik

2008 ◽  
pp. 45-50
Keyword(s):  
Scalar Case

Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities

2020 ◽  
Vol 23 (3) ◽  
pp. 723-752 ◽  
Author(s):  
Alessio Fiscella ◽  
Patrizia Pucci
Keyword(s):  
Scalar Case ◽  
Fractional Operator ◽  
Nontrivial Solutions ◽  
Fractional Systems ◽  
Lack Of Compactness ◽  
Critical Nonlinearities ◽  
Kirchhoff Model

AbstractThis paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non–degenerate.

scholarly journals Matrix and vector sequence transformations revisited

1995 ◽  
Vol 38 (3) ◽  
pp. 495-510 ◽  
Author(s):  
C. Brezinski ◽  
A. Salam
Keyword(s):  
Linear Equations ◽  
Convergence Acceleration ◽  
Difference Operators ◽  
Scalar Case ◽  
Extrapolation Methods ◽  
System Of Linear Equations ◽  
Vector Sequence ◽  
The Matrix ◽  
Sequence Transformations

Sequence transformations are extrapolation methods. They are used for the purpose of convergence acceleration. In the scalar case, such algorithms can be obtained by two different approaches which are equivalent. The first one is an elimination approach based on the solution of a system of linear equations and it makes use of determinants. The second approach is based on the notion of annihilation difference operators. In this paper, these two approaches are generalized to the matrix and the vector cases.

scholarly journals Schéma SRNHS Analyse et Application d'un schéma aux volumes finis dédié aux systèmes non homogènes

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Slah SAHMIM ◽  
Fayssal Benkhaldoun
Keyword(s):  
Shallow Water ◽  
Scalar Case ◽  
Finite Volume Scheme ◽  
Two Phase ◽  
Homogeneous Systems ◽  
Selfsimilar Solution ◽  
International Audience ◽  
The Stability ◽  
New Formulation ◽  
Water Problems

International audience This article is devoted to the analysis, and improvement of a finite volume scheme proposed recently for a class of non homogeneous systems. We consider those for which the corressponding Riemann problem admits a selfsimilar solution. Some important examples of such problems are Shallow Water problems with irregular topography and two phase flows. The stability analysis of the considered scheme, in the homogeneous scalar case, leads to a new formulation which has a naturel extension to non homogeneous systems. Comparative numerical experiments for Shallow Water equations with sourec term, and a two phase problem (Ransom faucet) are presented to validate the scheme. Cet article concerne l'analyse et l'application, d'un schéma proposé récemment por une classe de systèmes non homogènes. Nous considérons ceux pour lesquels le problème de Riemann correpondant admet une solution autosimilaire. Deux exemples importants de tels problèmes sont l'écoulement d'eau peu profonde au-dessus d'un fond non plat et les problèmes diphasiques. l'analyse de stabilité du schéma, dans le cas scalaire homogène, amène à une nouvelle écriture qui a une extension naturelle pour le cas non homogène. Des expériences numériques comparatives pour des équations de saint-Venant avec topographie variable, et un problème diphasique (Robinet de Ransom) sont présentés pour évaluer l'efficacité du schéma.

THE BETHE–SALPETER EQUATION APPROACH TO BOUND STATE: SCALAR–FERMION CASE AND SCALAR–SCALAR CASE

2007 ◽  
Vol 22 (39) ◽  
pp. 2979-2992 ◽  
Author(s):  
JIAO-KAI CHEN ◽  
ZHENG-XIN TANG ◽  
QING-DONG CHEN
Keyword(s):  
Bound States ◽  
Bound State ◽  
Wave Functions ◽  
Scalar Case ◽  
Equation Approach

The general form of the Bethe–Salpeter wave functions for bound states comprising one scalar constituent and one fermion, or two scalars is presented. Using the reduced Salpeter equation obtained, we can work out the effective nonrelativistic potentials. And one new version of reduced Bethe–Salpeter equation is proposed by extending Gross approximation.

Three-Dimensional Field Intensity Shaping: The Scalar Case

2018 ◽  
Vol 17 (3) ◽  
pp. 360-363 ◽  
Author(s):  
Gennaro G. Bellizzi ◽  
Domenica A. M. Iero ◽  
Lorenzo Crocco ◽  
Tommaso Isernia
Keyword(s):  
Field Intensity ◽  
Three Dimensional ◽  
Scalar Case

CAPITAL ALLOCATION FOR SET-VALUED RISK MEASURES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050009
Author(s):  
FRANCESCA CENTRONE ◽  
EMANUELA ROSAZZA GIANIN
Keyword(s):  
Convex Set ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Allocation ◽  
Allocation Rule ◽  
Scalar Case ◽  
Representation Theorems ◽  
Allocation Rules ◽  
The One ◽  
Definition Of

We introduce the definition of set-valued capital allocation rule, in the context of set-valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under some reasonable assumptions, we define some set-valued capital allocation rules relying on the representation theorems for coherent and convex set-valued risk measures and investigate their link with the notion of sub-differential for set-valued functions. We also introduce and study the set-valued analogous of some properties of classical capital allocation rules, such as the one of no undercut. Furthermore, we compare these rules with some of those mostly used for univariate (single-valued) risk measures. Examples and comparisons with the scalar case are provided at the end.

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