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Rδ-supercontinuous functions

Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.

Demonstratio Mathematica

2014

Vol. 47, nr 2

433--448

A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).

Breakthrough in Interval Data Fitting I. The Role of Hausdorff Distance

Gutowski M.W.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2009

z. 169

63-72

This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Probably the most often encountered application of global optimization methods is finding the so called best fitted values of various parameters, as well as their uncertainties, based on experimental data. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. The magic word and a key to success of interval approach appears the Hausdorff distance.

Remarks on connectivity and I-connectivity

Jędrzejewski J., Kowalczyk S.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

49-54

Stability of the pexider-type homogeneous equation

Jabłoński W.

Demonstratio Mathematica

1999

Vol. 32, nr 4

759-766

On Reflexivity of scalar-type spectral operators

Gok O.

Demonstratio Mathematica

1999

Vol. 32, nr 2

433-439