scholarly journals Complete Heyting algebra-valued convergence semigroups

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 619-633
Author(s):  
T.M.G. Ahsanullah ◽  
Fawzi Al-Thukair
Keyword(s):  
Uniform Convergence ◽  
Heyting Algebra ◽  
Cancellative Semigroup ◽  
Convergence Space ◽  
Convergence Group ◽  
Convergence Structure ◽  
The Subject ◽  
Basic Facts

Considering a complete Heyting algebra H, we introduce a notion of stratified H-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified H-convergence semigroup is a stratified H-convergence group. We supply a variety of natural examples; and show that every stratified H-convergence semigroup with identity is a stratified H-quasiuniform convergence space. We also show that given a commutative cancellative semigroup equipped with a stratified H-quasi-unifom structure satisfying a certain property gives rise to a stratified H-convergence semigroup via a stratified H-quasi-uniform convergence structure.

Links between Probabilistic Convergence Groups Under Triangular Norms and Enriched Lattice-Valued Convergence Groups

2016 ◽  
Vol 12 (02) ◽  
pp. 53-76
Author(s):  
T. M. G. Ahsanullah ◽  
Fawzi Al-Thukair
Keyword(s):  
Uniform Convergence ◽  
Point Of View ◽  
Close Connection ◽  
Uniform Structure ◽  
Triangular Norms ◽  
Convergence Group ◽  
Convergence Structure ◽  
Basic Facts ◽  
New Perspective ◽  
Categorical Point

We propose here two types of probabilistic convergence groups under triangular norms; present some basic facts, and give some characterizations for both the cases. We look at the possible link from categorical point of view between each of the proposed type and enriched lattice-valued convergence group. We produce several natural examples on probabilistic convergence groups under triangular norms. We also present a notion of probabilistic uniform convergence structure in a new perspective, showing that every probabilistic convergence group is probabilistic uniformizable. Moreover, we prove that this probabilistic uniform structure maintains a close connection with a known enriched lattice-valued uniform convergence structure.

Probabilistic convergence transformation groups

2018 ◽  
Vol 68 (6) ◽  
pp. 1447-1464 ◽  
Author(s):  
T. M. G. Ahsanullah ◽  
Gunther Jäger
Keyword(s):  
Transformation Group ◽  
Convergence Space ◽  
Probabilistic Metric Space ◽  
Arbitrary Group ◽  
Convergence Group ◽  
Group Of Homeomorphisms ◽  
Convergence Structure ◽  
Probabilistic Metric ◽  
Probabilistic Convergence Space ◽  
Natural Way

Abstract We introduce a notion of a probabilistic convergence transformation group, and present various natural examples including quotient probabilistic convergence transformation group. In doing so, we construct a probabilistic convergence structure on the group of homeomorphisms and look into a probabilistic convergence group that arises from probabilistic uniform convergence structure on function spaces. Given a probabilistic convergence space, and an arbitrary group, we construct a probabilistic convergence transformation group. Introducing a notion of a probabilistic metric convergence transformation group on a probabilistic metric space, we obtain in a natural way a probabilistic convergence transformation group.

scholarly journals The order topology for function lattices and realcompactness

1981 ◽  
Vol 4 (2) ◽  
pp. 289-304 ◽  
Author(s):  
W. A. Feldman ◽  
J. F. Porter
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Order Topology ◽  
Convergence Space ◽  
Vector Lattices ◽  
Convergence Structure ◽  
Relative Uniform Convergence ◽  
Compact Convergence

A latticeK(X,Y)of continuous functions on spaceXis associated to each compactificationYofX. It is shown forK(X,Y)that the order topology is the topology of compact convergence onXif and only ifXis realcompact inY. This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes everyC(X)and all countably universally complete function lattices with 1. It is shown that a choice ofK(X,Y)endowed with a natural convergence structure serves as the convergence space completion ofVwith the relative uniform convergence.

scholarly journals Order compatibility for Cauchy spaces and convergence spaces

1987 ◽  
Vol 10 (2) ◽  
pp. 209-216
Author(s):  
D. C. Kent ◽  
Reino Vainio
Keyword(s):  
Uniform Convergence ◽  
Weak Order ◽  
Convergence Spaces ◽  
Convergence Structure ◽  
Cauchy Structure ◽  
Cauchy Spaces

A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi-uniform convergence structure onX. Howover, there are two natural ways to derive the former structures from the latter, leading to “strong” and “weak” notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence spaces.

scholarly journals The Clinical Physiology of the Lungs

PEDIATRICS ◽  
1955 ◽  
Vol 15 (2) ◽  
pp. 238-239
Keyword(s):  
Current Theory ◽  
Structural Components ◽  
Clinical Physiology ◽  
The Subject ◽  
Basic Facts

The author has brought together in this monograph material comprising originally a series of lectures, extended and amplified with the work of others. Discussion is organized around the basic structural components of the lung—arteries, veins, capillaries, bronchi and bronchioles, nerves, and lymphatics. The physiology of these is dealt with in broad outlines, allowing the author to lead the discussion smoothly from basic facts to current theory. His familiarity with the subject enables him to maintain the integration of the known facts, while disclosing the large questions which still remain, in an informal and provocative fashion.

scholarly journals A counterexample to the density of the space generated by the composition operators

1977 ◽  
Vol 16 (1) ◽  
pp. 79-81
Author(s):  
Ronald Beattie
Keyword(s):  
Vector Space ◽  
Dual Space ◽  
Composition Operators ◽  
Operator Space ◽  
Natural Analogue ◽  
Convergence Space ◽  
Continuous Convergence ◽  
Continuous Mappings ◽  
Convergence Structure

It is known that, for an arbitrary convergence space X, the vector space generated by X is dense in LcCc (X) where both C(X) and its dual space carry the continuous convergence structure. In this note, a natural analogue formulated for the operator space L(Cc(X), Cc(X)) is considered, namely: is the vector space generated by the composition operators associated to the continuous mappings in C(X, X) dense in Lc (Cc (X), Cc (X)) ? This question is answered in the negative by a counterexample.

Medical Malpractice Litigation

2019 ◽  
Author(s):  
David A. Hyman ◽  
Charles Silver
Keyword(s):  
Medical Malpractice ◽  
Healthcare Spending ◽  
Future Research ◽  
Real Problem ◽  
Damage Costs ◽  
The Subject ◽  
Basic Facts ◽  
Civil Justice System ◽  
The Impact ◽  
Noneconomic Damages

Medical malpractice is the best studied aspect of the civil justice system. But the subject is complicated, and there are heated disputes about basic facts. For example, are premium spikes driven by factors that are internal (i.e., number of claims, payout per claim, and damage costs) or external to the system? How large (or small) is the impact of a damages cap? Do caps have a bigger impact on the number of cases that are brought or the payment in the cases that remain? Do blockbuster verdicts cause defendants to settle cases for more than they are worth? Do caps attract physicians? Do caps reduce healthcare spending—and by how much? How much does it cost to resolve the high percentage of cases in which no damages are recovered? What is the comparative impact of a cap on noneconomic damages versus a cap on total damages? Other disputes involve normative questions. Is there too much med mal litigation or not enough? Are damage caps fair? Is the real problem bad doctors or predatory lawyers—or some combination of both? This article summarizes the empirical research on the performance of the med mal system, and highlights some areas for future research.

Geometry of Black Holes

2020 ◽  
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Einstein Equations ◽  
De Sitter ◽  
Black Hole Spacetimes ◽  
Local Coordinates ◽  
The Subject ◽  
Basic Facts ◽  
Kaluza Klein

There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

Resonances and chaos in the asteroid belt

1999 ◽  
Vol 173 ◽  
pp. 297-308
Author(s):  
M. Šidlichovský
Keyword(s):  
The Body ◽  
Asteroid Belt ◽  
Orbital Elements ◽  
Orbital Resonance ◽  
Chaotic Diffusion ◽  
Kirkwood Gaps ◽  
History Of ◽  
The Subject ◽  
Basic Facts ◽  
Three Body

AbstractThe present paper reviews the evolution of our understanding of the effect of resonances on the distribution of asteroids in the asteroid belt. The history of this problem goes back to the Kirkwood's discovery (1867) of the Kirkwood gaps located at resonances with Jupiter. We started to understand the mechanism of their origin only in last decades. It seems that only gravitational effects are sufficient for the depletion. It is now clear that the overlap of secular resonances inside the orbital resonance is the most effective mechanism leading to large chaos and variation of orbital elements. This results in the final removal of asteroids from the gaps by collisions with the inner planets. Chaos, however, does not always mean fast removal of the body. The question of the so called stable chaos will be discussed together with the offered explanations (the high order resonances and the so called three-body resonances). Recently it was shown that chaotic diffusion can play an important role for the 2/1 resonance where the aforementioned explanation for other gaps fails. Basic facts will be reviewed but we will not go into this problem as the importance of chaotic diffusion in dynamics of asteroids (and comets) will be the subject of invited lecture at this conference given by Morbidelli and Nesvorný.

Regular completions of uniform convergence spaces

1974 ◽  
Vol 11 (3) ◽  
pp. 413-424 ◽  
Author(s):  
R.J. Gazik ◽  
D.C. Kent ◽  
G.D. Richardson
Keyword(s):  
Uniform Convergence ◽  
Real Line ◽  
Dual Space ◽  
Function Algebra ◽  
Continuous Functions ◽  
Convergence Space ◽  
Uniform Spaces ◽  
Convergence Spaces ◽  
Uniform Convergence Space ◽  
Uniformly Continuous

A regular completion with universal property is obtained for each member of the class of u–embedded uniform convergence spaces, a class which includes the Hausdorff uniform spaces. This completion is obtained by embedding each u-embedded uniform convergence space (X, I) into the dual space of a complete function algebra composed of the uniformly continuous functions from (X, I) into the real line.

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