Best constants of Banach-Stone type theorems in subgroups of 𝐶(𝐾)

2021 ◽  
Author(s):  
Yunbai Dong ◽  
Denny Leung ◽  
Lei Li ◽  
Liguang Wang
Keyword(s):  
Best Constants ◽  
Stone Type

scholarly journals Two semigroups of continuous relations

1977 ◽  
Vol 23 (1) ◽  
pp. 46-58 ◽  
Author(s):  
A. R. Bednarek ◽  
Eugene M. Norris
Keyword(s):  
Large Class ◽  
Algebraic Structure ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Completely Regular ◽  
Topological Semigroups ◽  
Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

scholarly journals Dual-energy computed tomography for stone type assessment: A pilot study of DECT with five indices

2020 ◽  
Vol 21 ◽  
pp. S85
Author(s):  
V. Rudenko ◽  
N. Serova ◽  
L. Kapanadze ◽  
M. Taratkin ◽  
Z. Okhunov ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Pilot Study ◽  
Dual Energy ◽  
Dual Energy Computed Tomography ◽  
Stone Type

Maximal linked systems on families of measurable rectangles

2021 ◽  
pp. 77-104
Author(s):  
Aleksandr G. Chentsov
Keyword(s):  
Probability Theory ◽  
Measure Theory ◽  
Cartesian Product ◽  
Wide Sense ◽  
The Family ◽  
Principal Property ◽  
Measurable Structure ◽  
Stone Type ◽  
By Products ◽  
Algebra Of Sets

Linked and maximal linked systems (MLS) on π -systems of measurable (in the wide sense) rectangles are considered (π-system is a family of sets closed with respect to finite intersections). Structures in the form of measurable rectangles are used in measure theory and probability theory and usually lead to semi-algebra of subsets of cartesian product. In the present article, sets-factors are supposed to be equipped with π-systems with “zero” and “unit”. This, in particular, can correspond to a standard measurable structure in the form of semialgebra, algebra, or σ-algebra of sets. In the general case, the family of measurable rectangles itself forms a π -system of set-product (the measurability is identified with belonging to a π - system) which allows to consider MLS on a given π -system (of measurable rectangles). The following principal property is established: for all considered variants of π -system of measurable rectangles, MLS on a product are exhausted by products of MLS on sets-factors. In addition, in the case of infinity product, along with traditional, the “box” variant allowing a natural analogy with the base of box topology is considered. For the case of product of two widely understood measurable spaces, one homeomorphism property concerning equipments by the Stone type topologies is established.

scholarly journals Quantum weakest preconditions

2006 ◽  
Vol 16 (3) ◽  
pp. 429-451 ◽  
Author(s):  
ELLIE D'HONDT ◽  
PRAKASH PANANGADEN
Keyword(s):  
Quantum Computation ◽  
Representation Theorem ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Weakest Precondition ◽  
Positive Maps ◽  
Weakest Preconditions ◽  
Predicate Transformer ◽  
Usual State ◽  
Stone Type

We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming, we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example, we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilisers.

scholarly journals On Certain Extension of Hilbert's Integral Inequality with Best Constants

2008 ◽  
Vol 48 (3) ◽  
pp. 457-463
Author(s):  
Yongjin Li ◽  
Yu Lin ◽  
Bing He
Keyword(s):  
Integral Inequality ◽  
Best Constants
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