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Equation f ( p ( x ) ) = q ( f ( x ) ) for given real functions p , q

Oldřich Kopeček (2012)

Czechoslovak Mathematical Journal

We investigate functional equations f ( p ( x ) ) = q ( f ( x ) ) where p and q are given real functions defined on the set ℝ of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions p , q which are strictly increasing and continuous on ℝ . In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present a construction...

Equilibrium search model with endogenous growth rate of human capital

Wansheng Tang, Chi Zhou, Chaoqun Xiao, Ruiqing Zhao (2016)

Kybernetika

This article studies an equilibrium search problem when jobs provided by firms can be either unskilled or skilled and when workers differing in their education level can be either low-educated or high-educated. The structure proportion of jobs affects the equilibrium which indicates a threshold that can distinguish whether the equilibrium is separating or cross-skill. In addition, the cross-skill equilibrium solution implies the high-educated workers are more likely to obtain higher pay rates than...

Food Webs, Competition Graphs, and Habitat Formation

M. Cozzens (2011)

Mathematical Modelling of Natural Phenomena

One interesting example of a discrete mathematical model used in biology is a food web. The first biology courses in high school and in college present the fundamental nature of a food web, one that is understandable by students at all levels. But food webs as part of a larger system are often not addressed. This paper presents materials that can be used in undergraduate classes in biology (and mathematics) and provides students with the opportunity...

Fraktály a jak o nich učit

Barbora Divišová (2013)

Učitel matematiky

The article focuses on basic information about fractals in a popular way. It brings about a way to provide glimpses of the theory of fractals for pupils at the primary and secondary schools. A strictly geometrical definition of fractals is given together with three examples of fractals (Cantor discontinuum, Koch snowflake, Sierpinski triangle). Next two other definitions of fractals are presented. The main part of the article consists of the examples of fractals in biology and in arts which can...

Generalized Nets Model of an E-Learning System Software Architecture

Dimov, Aleksandar, Ilieva, Sylvia (2007)

Serdica Journal of Computing

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.Component-based software engineering and software architecture are tightly connected areas in computer science. Software architecture presents the functionality of the system as decomposition into components, the properties of these components and the connectors between them. This paper illustrates a methodology for application...

GeoGebra jako nástroj objevování a dokazování

Roman Hašek (2014)

Učitel matematiky

Using examples from elementary mathematics, the article presents some possibilities of using GeoGebra as a tool of active discovery of the mathematical basis of problems. The solving procedures are described by individual steps so that the reader can try them him/herself. The problems were chosen so that different solving strategies can be used in GeoGebra: analytic, synthetic, algebraic.

Geometrické důkazy v matematické analýze

Antonín Slavík (2019)

Pokroky matematiky, fyziky a astronomie

Článek představuje alternativní pohled na některé známé výsledky z matematické analýzy. Ukazuje jejich geometrickou interpretaci, případně využívá vhodných ilustrací ke zdůvodnění platnosti příslušných tvrzení. Uvedené postupy nejsou vždy zcela precizní, na rozdíl od formálně přesných důkazů však umožňují hlubší porozumění problematice.

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