Gamma-convergence of Gaussian fractional perimeter

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alessandro Carbotti ◽  
Simone Cito ◽  
Domenico Angelo La Manna ◽  
Diego Pallara
Keyword(s):  
Typical Feature ◽  
Gamma Convergence ◽  
Fractional Powers ◽  
Γ Convergence ◽  
Definition Of

Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 - {s\to 1^{-}} . Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.

scholarly journals FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE

2007 ◽  
Vol 18 (03) ◽  
pp. 281-299 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Fourier Series ◽  
Fractional Derivative ◽  
Taylor Series ◽  
Fractional Derivatives ◽  
Fractional Power ◽  
Weyl Quantization ◽  
Fractional Powers ◽  
Derivative Operator ◽  
Quantization Procedure ◽  
Definition Of

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

scholarly journals Multi-parameter homogenization by localization and blow-up

2004 ◽  
Vol 134 (5) ◽  
pp. 801-814 ◽  
Author(s):  
Felipe Alvarez ◽  
Jean-Philippe Mandallena
Keyword(s):  
Blow Up ◽  
Extension Theorem ◽  
Direct Verification ◽  
Compactness Method ◽  
Connected Sets ◽  
Slicing Method ◽  
Γ Convergence ◽  
The One ◽  
Definition Of

We give an alternative self-contained proof of the homogenization theorem for periodic multi-parameter integrals that was established by the authors. The proof in that paper relies on the so-called compactness method for Γ-convergence, while the one presented here is by direct verification: the candidate to be the limit homogenized functional is first exhibited and the definition of Γ-convergence is then verified. This is done by an extension of bounded gradient sequences using the Acerbi et al. extension theorem from connected sets, and by the adaptation of some localization and blow-up techniques developed by Fonseca and Müller, together with De Giorgi's slicing method.

MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE

2006 ◽  
Vol 04 (01) ◽  
pp. 31-60 ◽  
Author(s):  
KARIM TRABELSI
Keyword(s):  
Integral Representation ◽  
Internal Energy ◽  
Elastic Membrane ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Incompressible Materials ◽  
Plate Models ◽  
Γ Convergence ◽  
Nonlinearly Elastic

In this paper, we derive nonlinearly elastic membrane plate models for hyperelastic incompressible materials using Γ-convergence arguments. We obtain an integral representation of the limit two-dimensional internal energy owing to a result of singular functionals relaxation due to Ben Belgacem [6].

Context Aware Service System Supported the Collaborative Management of Distribution Task

2010 ◽  
Vol 143-144 ◽  
pp. 201-206
Author(s):  
Liang Xiao ◽  
Fan Wang
Keyword(s):  
Service System ◽  
Information Service ◽  
Dynamic Environment ◽  
Typical Feature ◽  
Collaborative Management ◽  
Context Aware ◽  
Task Context ◽  
Context Management ◽  
Effective Implementation ◽  
Definition Of

Distribution tasks have typical feature of context dependence. Attaining the mission-related dynamic context information service timely and accurately has a significant effect to the execution efficiency of the distribution task. On the basis of the definition of four distribution contexts systematically: network context , product context, customer context, resource context, this paper proposes the model of context management of distribution task, and the collaborative service and process mechanism of distribution tasks base on task context, it is of great value and significance to support the effective implementation of collaborative management of the distribution task in dynamic environment.

scholarly journals A high-dimensionality-trait-driven learning paradigm for high dimensional credit classification

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Lean Yu ◽  
Lihang Yu ◽  
Kaitao Yu
Keyword(s):  
Feature Extraction ◽  
Credit Risk ◽  
Sample Size ◽  
Extraction Methods ◽  
Typical Feature ◽  
High Dimensionality ◽  
High Dimensional ◽  
Learning Paradigm ◽  
Classifier Selection ◽  
Definition Of

AbstractTo solve the high-dimensionality issue and improve its accuracy in credit risk assessment, a high-dimensionality-trait-driven learning paradigm is proposed for feature extraction and classifier selection. The proposed paradigm consists of three main stages: categorization of high dimensional data, high-dimensionality-trait-driven feature extraction, and high-dimensionality-trait-driven classifier selection. In the first stage, according to the definition of high-dimensionality and the relationship between sample size and feature dimensions, the high-dimensionality traits of credit dataset are further categorized into two types: 100 < feature dimensions < sample size, and feature dimensions ≥ sample size. In the second stage, some typical feature extraction methods are tested regarding the two categories of high dimensionality. In the final stage, four types of classifiers are performed to evaluate credit risk considering different high-dimensionality traits. For the purpose of illustration and verification, credit classification experiments are performed on two publicly available credit risk datasets, and the results show that the proposed high-dimensionality-trait-driven learning paradigm for feature extraction and classifier selection is effective in handling high-dimensional credit classification issues and improving credit classification accuracy relative to the benchmark models listed in this study.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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