scholarly journals On the difference property of families of measurable functions

2003 ◽  
Vol 97 (2) ◽  
pp. 169-180
Author(s):  
Rafał Filipów
Keyword(s):  
Difference Property ◽  
Measurable Functions ◽  
The Difference

scholarly journals On the difference property of Borel measurable functions

2010 ◽  
Vol 208 (1) ◽  
pp. 57-73
Author(s):  
Hiroshi Fujita ◽  
Tamás Mátrai
Keyword(s):  
Difference Property ◽  
Measurable Functions ◽  
The Difference ◽  
Borel Measurable

scholarly journals Some Applications of Supra Preopen Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
M. E. El-Shafei ◽  
A. H. Zakari ◽  
T. M. Al-shami
Keyword(s):  
Topological Spaces ◽  
Difference Property ◽  
Boundary Points ◽  
Separation Axioms ◽  
The Difference

The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

CHIRAL POTTS MODEL: CORNER TRANSFER MATRICES AND PARAMETRIZATIONS

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3489-3500 ◽  
Author(s):  
R.J. BAXTER
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Weight Functions ◽  
Chiral Potts Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Difference Property ◽  
The Difference

We consider the star-triangle relation and the form of its solutions. We present some simple parametrizations of the weight functions of the three-state chiral Potts model. This model does not have the “difference property”: we discuss the resulting difficulties in attempting to use the corner transfer matrix method for this model.

scholarly journals Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

2020 ◽  
Vol 13 (3) ◽  
pp. 427-443 ◽  
Author(s):  
Tareq M. AL-shami ◽  
E. A. Abo-Tabl ◽  
Baravan Assad ◽  
Mohamed Arahet
Keyword(s):  
Real Life ◽  
Research Area ◽  
Topological Spaces ◽  
Difference Property ◽  
Separation Axioms ◽  
Life Problems ◽  
New Concepts ◽  
Limit Points ◽  
The Difference

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

On the Difference Property of the Class of Pointwise Discontinuous Functions and of Some Related Classes

1984 ◽  
Vol 36 (4) ◽  
pp. 756-768 ◽  
Author(s):  
M. Laczkovich
Keyword(s):  
Additive Function ◽  
Continuous Functions ◽  
Real Numbers ◽  
Difference Property ◽  
Discontinuous Functions ◽  
Difference Function ◽  
De Bruijn ◽  
The Difference ◽  
Image Position

Let R denote the set of real numbers. For f:R → R and h ∈ R, the difference function Δhf is defined byThe function H:R → R is called additive if it satisfies Cauchy's equationLet ℱ be a class of real valued functions defined on R. ℱ is said to have the difference property if, for every function f:R → R satisfying Δhf ∈ ℱ for every h ∈ R, there exists an additive function H such that f — H ∈ ℱIt was conjectured by P. Erdos that the class of continuous functions has the difference property. This conjecture was proved by N. G. de Bruijn in [1], where the difference property of several other classes was verified as well. (For other references, see [6].)

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

Influence of Cell Wall Composition on the Fossilisation of Bacteria and the Implications for the Search for Early Life Forms

1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall
Keyword(s):  
Cell Wall ◽  
Life Forms ◽  
Cation Binding ◽  
Positive Bacterium ◽  
Gram Positive ◽  
Gram Positive Bacteria ◽  
Transmission Electron ◽  
Hydrothermal Sediments ◽  
Identification Of Bacteria ◽  
The Difference

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.

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