EUDML

A compact set $T \subset 𝐑^{2}$ is constructed such that each horizontal or vertical line intersects $T$ in at most one point while the $α$ -dimensional measure of $T$ is infinite for every $α \in (0, 2)$ .

Integration of some very elementary functions

Jan Mařík — 1993

Mathematica Bohemica

Let $m$ be a natural number. Let $f, g$ and $Q$ be real polynomials such that ${d e g f, d e g g} \subset {1, 2}, d e g Q < m d e g f, g$ is not a square and $f$ has imaginary roots, if it is not linear. Effective methods for the integration of $Q / (f^{m} \sqrt{g}$ are exhibited.

Integrating factor

Jan Mařík — 1994

Mathematica Bohemica

The problem of integrating factor for ordinary differential equations is investigated. Conditions are given which guarantee that each solution of $\partial_{1} F (x, y) + y^{'} \partial_{2} F (x, y) = 0$ is also a solution of $M (x, y) + y^{'} N (x, y) = 0$ where $\partial_{1} F = μ M$ and $\partial_{2} F = μ N$ .

A note on integration of rational functions

Jan Mařík — 1991

Mathematica Bohemica

Let $P$ and $Q$ be polynomials in one variable with complex coefficients and let $n$ be a natural number. Suppose that $Q$ is not constant and has only simple roots. Then there is a rational function $ϕ$ with $ϕ^{'} = P / Q^{n + 1}$ if and only if the Wronskian of the functions $Q^{'}, {(Q^{2})}^{'}, ..., {(Q^{n})}^{'}, P$ is divisible by $Q$ .

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Les fonctionnelles sur l'ensemble des fonctions continues bornées, définies dans un espace topologique

Mocninné řady na obvodě konvergenčního kruhu

Odhad prosté hodnoty integrálů a kriteria pro konvergenci nevlastních integrálů

Transformation of $m$ -dimensional Lebesgue integrals

Eine Bemerkung über elliptische Differentialgleichungen

The surface integral

Extensions of additive mappings

Заметка к теории поверхностного интеграла

Book reviews. Černý, Ilja: Základy analysy v komplexním oboru. (Fundaments of analysis in the comlex domain)

Приводимость определителя с неизвестными в качестве элементов, если его принять за полином над коммутативным кольцом

The Baire and Borel measure

Представление функционала в виде интеграла

Конспект статьи „Основы теории интеграла в евклидовых пространствах”

The Hausdorff dimension of some special plane sets

Integration of some very elementary functions

Integrating factor

A note on integration of rational functions

O kvadratických polynomech, které nabývají mnoha prvočíselných hodnot

Poznámka o řídkých množinách v $E_{m}$

O popularisaci matematiky