scholarly journals On the structure of the pointwise density sets on the real line

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 2893-2899
Author(s):  
Magdalena Górajska ◽  
Jacek Hejduk
Keyword(s):  
Real Line ◽  
Baire Property ◽  
Density Point ◽  
The Real ◽  
Local Properties

The paper concerns some local properties of the sets with pointwise density points in terms of measure and category on the real line. We also construct nonmeasurable and not having the Baire property sets with pointwise density point.

scholarly journals Pointwise density topology

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Magdalena Górajska
Keyword(s):  
Real Line ◽  
Pointwise Convergence ◽  
Baire Property ◽  
Density Topology ◽  
Borel Set ◽  
Convergence In Measure ◽  
The Real ◽  
Measurable Set ◽  
New Type ◽  
Lebesgue Measurable Set

AbstractThe paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable.

scholarly journals A category analogue of the generalization of Lebesgue density topology

2009 ◽  
Vol 42 (1) ◽  
pp. 11-25
Author(s):  
Wojciech Wojdowski
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Density Point ◽  
Density Topology ◽  
The Real ◽  
Lebesgue Density ◽  
Real Anal

Abstract . A notion of AI -topology, a generalization of Wilczy´nski’s I-density topology (see [Wilczy´nski, W.: A generalization of the density topology, Real. Anal. Exchange 8 (1982-1983), 16-20] is introduced. The notion is based on his reformulation of the definition od Lebesgue density point. We consider a category version of the topology, which is a category analogue of the notion of an Ad- -density topology on the real line given in [Wojdowski, W.: A generalization ofdensity topology, Real. Anal. Exchange 32 (2006/2007), 1-10]. We also discuss the properties of continuous functions with respect to the topology.

scholarly journals On Semiregularization of Some Abstract Density Topologies Involving Sets Having The Baire Property

2016 ◽  
Vol 65 (1) ◽  
pp. 37-48
Author(s):  
Jacek Hejduk ◽  
Renata Wiertelak ◽  
Wojciech Wojdowski
Keyword(s):  
Real Line ◽  
Baire Space ◽  
Baire Property ◽  
Density Topology ◽  
The Real ◽  
Real Functions

Abstract Some kind of abstract density topology in a topological Baire space is considered. The semiregularization of this type of topology on the real line in many cases is the coarsest topology for which real functions continuous with respect to the abstract density topology are continuous.

Porous subsets in the space of functions having the Baire property

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Gertruda Ivanova ◽  
Elżbieta Wagner-Bojakowska
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Baire Property ◽  
The Real ◽  
Porous Set ◽  
The Family

AbstractThe comparison of some subfamilies of the family of functions on the real line having the Baire property in porosity terms is given. We prove that the family of all quasi-continuous functions is strongly porous set in the family of all cliquish functions and that the family of all cliquish functions is strongly porous set in the family of all functions having the Baire property.We prove also that the family of all Świątkowski functions is lower 2/3-porous set in the family of cliquish functions and the family of functions having the internally Świątkowski property is lower 2/3-porous set in the family of cliquish functions.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real

DERIVATION BASES ON THE REAL LINE (I)

1982 ◽  
Vol 8 (1) ◽  
pp. 67 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real

Fracture Toughness of Large Forgings for Power Producing Industry

2013 ◽  
Vol 577-578 ◽  
pp. 593-596 ◽  
Author(s):  
Václav Mentl
Keyword(s):  
Fracture Toughness ◽  
Chemical Composition ◽  
Steam Turbine ◽  
Mechanical Treatment ◽  
Material Degradation ◽  
The Real ◽  
Operational Safety ◽  
Local Properties ◽  
Thermo Mechanical Treatment ◽  
Shape And Size

The steam turbine rotors represent large components both in radial and axial directions. Their local properties generally differ from one forging to another, or if we compare head and bottom parts of the original ingot, or central and circumferential localities of one rotor body respectively, or if we compare the properties of separate discs e.g. in the case of welded rotors. These differences stem from both even slight changes in the chemical composition (of separate heats or even within one ingot) and thermo-mechanical treatment and in the differences in technology with respect to the real shape and size of the forgings in question. In the paper, the consequences of the differences in fracture toughness characteristics in various rotor localities are discussed with respect to the rotors operational safety taking into account the existence of cracks and material degradation.

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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