An explicit form for extremal functions in the embedding constant problem for Sobolev spaces

2020 ◽  
Vol 80 ◽  
pp. 189-210
Author(s):  
I. A. Sheipak ◽  
T. A. Garmanova
Keyword(s):  
Explicit Form ◽  
Sobolev Spaces ◽  
Extremal Functions ◽  
Embedding Constant

Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives

1990 ◽  
pp. 246-271
Author(s):  
V. M. Gol’dshtein ◽  
Yu. G. Reshetnyak
Keyword(s):  
Sobolev Spaces ◽  
Generalized Derivatives ◽  
Extremal Functions

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

Solutions to a nonlocal elliptic problem in Orlicz-Sobolev spaces

2017 ◽  
Vol 2 (1) ◽  
pp. 1-8
Author(s):  
Mustafa Avci ◽  
◽  
Zehra Yucedag ◽  
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Nonlocal Elliptic Problem

ENDOGENOUS GROWTH MODEL WITH HUMAN CAPITAL ON THE CIRCLE

2020 ◽  
pp. 4-9
Author(s):  
А.В. Королев
Keyword(s):  
Human Capital ◽  
Spatial Structure ◽  
Endogenous Growth ◽  
Explicit Form ◽  
Growth Model ◽  
Main Attention ◽  
Endogenous Growth Model ◽  
Central Plan ◽  
Special Case

В статье рассматривается модель эндогенного роста с человеческим капи-талом на простой пространственной структуре (окружности). Особое вни-мание уделено специальному случаю - комбинации параметров, при кото-рой удаётся получить решение задачи центрального планировщика на окружности в явном виде, что другим авторам не удавалось. In this article the endogenous growth model with human capital on the simple spatial structure (the circle) is considered. We pay main attention to a special case of a combination of parameters for which we were able to solve the central plan-ner problem on the circle in an explicit form, which other authors did not suc-ceed to do.

Modeling Small-scale Patterns in Natural Images by Sequential Eigenvalue Problems in Sobolev Spaces

2010 ◽  
Vol 35 (12) ◽  
pp. 1568-1572
Author(s):  
Peng HE ◽  
Jian-Hua TAO
Keyword(s):  
Sobolev Spaces ◽  
Eigenvalue Problems ◽  
Natural Images ◽  
Small Scale

Determination of rate constants of redox reactions of second order from current-less potential-time curves by a simplified graphical-numerical method

1983 ◽  
Vol 48 (5) ◽  
pp. 1358-1367 ◽  
Author(s):  
Antonín Tockstein ◽  
František Skopal
Keyword(s):  
Numerical Method ◽  
Explicit Form ◽  
Rate Constant ◽  
Optimization Algorithm ◽  
Rate Constants ◽  
Redox Reactions ◽  
Second Order ◽  
Wide Region ◽  
Recurrent Formula

A method for constructing curves is proposed that are linear in a wide region and from whose slopes it is possible to determine the rate constant, if a parameter, θ, is calculated numerically from a rapidly converging recurrent formula or from its explicit form. The values of rate constants and parameter θ thus simply found are compared with those found by an optimization algorithm on a computer; the deviations do not exceed ±10%.

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

scholarly journals Bayesian credibility premium with GB2 copulas

2020 ◽  
Vol 8 (1) ◽  
pp. 157-171 ◽  
Author(s):  
Himchan Jeong ◽  
Emiliano A. Valdez
Keyword(s):  
Probability Measure ◽  
Explicit Form ◽  
Insurance Premium ◽  
Response Variable ◽  
Generalized Pareto ◽  
Special Case ◽  
Change Of Probability Measure

AbstractFor observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

scholarly journals On the Boundary Dieudonné–Pick Lemma

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov
Keyword(s):  
Fixed Point ◽  
Interior Point ◽  
Sharp Estimate ◽  
General Boundary ◽  
Extremal Functions ◽  
Angular Derivative ◽  
Additional Information ◽  
Carathéodory Theorem ◽  
Class Of Functions ◽  
Boundary Fixed Point

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.

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