Displaying similar documents to “On results of Jan Mařík in the theory of derivatives”

Symmetrized and continuous generalization of transversals

Martin Kochol (1996)

Mathematica Bohemica

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The theorem of Edmonds and Fulkerson states that the partial transversals of a finite family of sets form a matroid. The aim of this paper is to present a symmetrized and continuous generalization of this theorem.

Killing's equations in dimension two and systems of finite type

Gerard Thompson (1999)

Mathematica Bohemica

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A PDE system is said to be of finite type if all possible derivatives at some order can be solved for in terms lower order derivatives. An algorithm for determining whether a system of finite type has solutions is outlined. The results are then applied to the problem of characterizing symmetric linear connections in two dimensions that possess homogeneous linear and quadratic integrals of motions, that is, solving Killing's equations of degree one and two.

On non-absolutely convergent integrals

Štefan Schwabik (1996)

Mathematica Bohemica

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The influence of Jan Marik in the field of non absolute integration is described in the plane of Czech mathematics. A short historical account on the development of integration theory in the Czech region is presented in this connection together with the recent Riemann sum approach to the general Perron integral.

On the equation ϕ ( | x m - y m | ) = 2 n

Florian Luca (2000)

Mathematica Bohemica

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In this paper we investigate the solutions of the equation in the title, where φ is the Euler function. We first show that it suffices to find the solutions of the above equation when m = 4 and x and y are coprime positive integers. For this last equation, we show that aside from a few small solutions, all the others are in a one-to-one correspondence with the Fermat primes.