scholarly journals On the relationship between ordinary thin sets and full-thin sets

1980 ◽  
Vol 29 (3) ◽  
pp. 348-361
Author(s):  
J. S. Hwang ◽  
H. L. Jackson
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Boundary Point ◽  
Subject Classification ◽  
Thin Set ◽  
Thin Sets ◽  
The Relationship

AbstractIn this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.

Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone

2003 ◽  
Vol 46 (2) ◽  
pp. 252-264 ◽  
Author(s):  
Ikuko Miyamoto ◽  
Minoru Yanagishita ◽  
Hidenobu Yoshida
Keyword(s):  
Half Space ◽  
Corner Point ◽  
Smooth Boundary ◽  
Thin Set ◽  
Special Domain ◽  
Thin Sets ◽  
Minimally Thin Set

AbstractThis paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at ∞ of a cone.

scholarly journals Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone

2012 ◽  
Vol 2012 ◽  
pp. 1-29
Author(s):  
Pinhong Long ◽  
Zhiqiang Gao ◽  
Guantie Deng
Keyword(s):  
Schrödinger Operator ◽  
Boundary Point ◽  
Martin Boundary ◽  
Schrodinger Operator ◽  
Stationary Schrödinger Operator ◽  
Thin Set ◽  
Thin Sets ◽  
Wiener Type ◽  
Minimally Thin Set ◽  
Rarefied Set

We give some criteria fora-minimally thin sets anda-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside ana-rarefied set. Finally we illustrate the relation between thea-minimally thin set and thea-rarefied set in a cone.

scholarly journals Reflective subcategories

2000 ◽  
Vol 42 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Juan Rada ◽  
Manuel Saorín ◽  
Alberto del Valle
Keyword(s):  
Category Theory ◽  
Full Subcategory ◽  
Subject Classification ◽  
Adjoint Functor ◽  
Direct Limits ◽  
The Relationship ◽  
Good Behaviour

Given a full subcategory [Fscr ] of a category [Ascr ], the existence of left [Fscr ]-approximations (or [Fscr ]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that [Fscr ] is reflective in [Ascr ], in the classical terminology of category theory.In the first part of the paper we establish, for a rather general [Ascr ], the relationship between reflectivity and covariant finiteness of [Fscr ] in [Ascr ], and generalize Freyd's adjoint functor theorem (for inclusion functors) to not necessarily complete categories. Also, we study the good behaviour of reflections with respect to direct limits. Most results in this part are dualizable, thus providing corresponding versions for coreflective subcategories.In the second half of the paper we give several examples of reflective subcategories of abelian and module categories, mainly of subcategories of the form Copres (M) and Add (M). The second case covers the study of all covariantly finite, generalized Krull-Schmidt subcategories of {\rm Mod}_{R}, and has some connections with the “pure-semisimple conjecture”.1991 Mathematics Subject Classification 18A40, 16D90, 16E70.

scholarly journals Frequency-dependent impedance and surface waves on the boundary of a stratified dielectric medium

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190218
Author(s):  
Kirill Cherednichenko ◽  
William Graham
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Half Space ◽  
Dielectric Medium ◽  
Interface Condition ◽  
Theme Issue ◽  
Structured Media ◽  
Loss Parameter ◽  
The Relationship ◽  
Dynamic Phenomena

We analyse waves propagating along the interface between half-spaces filled with a perfect dielectric and a Lorentz material. We show that the corresponding interface condition leads to a generalization of the classical Leontovich condition on the boundary of a dielectric half-space. We study when this condition supports propagation of (dispersive) surface waves. We derive the related dispersion relation for waves along the boundary of a stratified half-space and determine the relationship between the loss parameter, frequency and wavenumber for which interfacial waves exist. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

scholarly journals Further properties of the Bergman spaces of slice regular functions

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Half Plane ◽  
Bergman Kernel ◽  
Bergman Spaces ◽  
Reflection Principle ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Complex Half Plane ◽  
Schwarz Reflection Principle

AbstractWe continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.

scholarly journals A uniqueness set for all Hp(Bn) with p>0

1978 ◽  
Vol 26 (1) ◽  
pp. 65-69 ◽  
Author(s):  
P. S. Chee
Keyword(s):  
Unit Ball ◽  
Subject Classification ◽  
Open Unit ◽  
Finite Area ◽  
Open Unit Ball ◽  
Uniqueness Set

AbstractFor n≥2, a hypersurface in the open unit ball Bn in is constructed which satisfies the generalized Blaschke condition and is a uniqueness set for all Hp(Bn) with p>0. If n≥3, the hypersurface can be chosen to have finite area.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 32 A 10.

scholarly journals On -Quasi Irresolute Functions

2017 ◽  
Vol 1 (2) ◽  
pp. 72-77
Author(s):  
C. Janaki ◽  
Ganes M. Pandya
Keyword(s):  
Subject Classification ◽  
New Class ◽  
2000 Mathematics Subject Classification ◽  
The Relationship ◽  
Class Of Functions

In this paper we introduce a new class of functions called -quasi irresolute functions. The notion of -quasi graphs are introduced and the relationship between -quasi irresolute functions and -quasi closed graphs is analysed. 2000 Mathematics Subject Classification : 54C08, 54C10.

On Measures of Affinity for Truncated Distributions

2007 ◽  
Vol 59 (3-4) ◽  
pp. 151-162
Author(s):  
S. Smitha ◽  
K. R. Muraleedharan Nair ◽  
P. G. Sankaran
Keyword(s):  
Functional Form ◽  
Hazard Model ◽  
Subject Classification ◽  
Proportional Hazard ◽  
Proportional Hazard Model ◽  
Characterization Result ◽  
Truncated Distributions ◽  
Relationship Of ◽  
The Relationship

Abstract: In the present paper we define affinity for truncated distributions and examine its properties. The relationship of this measure with other discrimination measures is examined. We also provide a characterization result for the proportional hazard model using the functional form of the truncated affinity. AMS (2000) Subject Classification: 62E10, 90B25

scholarly journals Local properties of maps of the ball

2003 ◽  
Vol 2003 (2) ◽  
pp. 75-81
Author(s):  
Yakar Kannai
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Interior Point ◽  
Closed Unit Ball ◽  
Game Theoretic ◽  
Local Properties ◽  
Constant Mapping ◽  
Quasianalytic Functions

Letfbe an essential map ofSn−1into itself (i.e.,fis not homotopic to a constant mapping) admitting an extension mapping the closed unit ballB¯nintoℝn. Then, for every interior pointyofBn, there exists a pointxinf−1(y)such that the image of no neighborhood ofxis contained in a coordinate half space withyon its boundary. Under additional conditions, the image of a neighborhood ofxcovers a neighborhood ofy. Differential versions are valid for quasianalytic functions. These results are motivated by game-theoretic considerations.

Sign in / Sign up

Export Citation Format

Share Document