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Gorecki H.,University of Lodz | Bialas S.,The School of Banking and Management in Cracow
Bulletin of the Polish Academy of Sciences: Technical Sciences | Year: 2010

It is proved that there exist the relations between coefficients of the transcendental equations and the infinite number of their roots, similar to Vieta's formulae. These relations may be obtained for the entire analytic functions using theorems of residues and argument principle. In particular the meromorphic functions will be considered. Source


Bialas S.,The School of Banking and Management in Cracow | Gorecki H.,University of Lodz
Bulletin of the Polish Academy of Sciences: Technical Sciences | Year: 2010

Two problems concerning polynomials are considered. For the first problem it is proved that the zeroes of the fractional polynomials of rational order fulfil relations similar to the Vieta's formulae for the polynomials. In the second problem it is presented the iterative method of generalization of the Graeffe-Lobachevsky method to solution of the algebraic equations. Source


The School of Banking and Management in Cracow | Entity website

The School of Banking and Management in Cracow has embarked on promoting and administering exams for the European Computer Driving Licence (ECDL). ECDL is a program designed by the Council of European Professional Informatics Societies, the aim of which is to standardize and document the knowledge level of the basics of computer use ...


The School of Banking and Management in Cracow | Entity website

ACCA odwied oficjaln stron: www.londonsam ...


Magdon-Maksymowicz M.S.,Agricultural University of Krakow | Maksymowicz A.Z.,The School of Banking and Management in Cracow
Theory in Biosciences | Year: 2015

Some modifications of the simple asexual Penna model, enriched by epigenetic contributions, are presented. The standard bit-string Penna model of biological aging and population evolution is based on an inherited DNA structure which defines the future life of a newly born individuals, when genes are activated by the biological clock, and the predefined genetic death is fully controlled by the number of defected genes. Epigenomes allow to introduce additional mechanism of gene activation or silencing without affecting the DNA genome itself. It may be either inherited or may reflect external, environmental factors. In the presented model, information read from the introduced epigenome may alter gene expression that may be stopped or re-activated. We concentrate on the influence of epigenetics on the age $$a$$a distribution of genetic mortality $$m(a)$$m(a). Changes in $$m(a)$$m(a) are strong for the case of inherited epigenetic contribution with nearly perfect inheritance and ‘positive’ epigenome that partly ignores the ‘bad’ mutations. We conclude that the epigenetic contribution may influence population structure $$m(a)$$m(a) and could be, at least partly, responsible for deviation of $$m(a)$$m(a) distribution from the Gompertz law. In short, we claim that proposed epigenetic contribution may be seen as a candidate for possible explanation of observed deviation from the Gompertz law, also among senior members of society. A very simple model was used in this paper and many crucial mechanisms of biological aging were omitted. Therefore, further work based on a more realistic models is necessary. © 2015, Springer-Verlag Berlin Heidelberg. Source

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