Averages of quasi-continuous functions

Aleksander Maliszewski

Displaying similar documents to “Averages of quasi-continuous functions”

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $ℓ (y) \equiv \frac{1}{w (t)} (r (t) y)$ , $t \in [a, \infty)$ are established. These conditions are based on a recently proved relationship between spectral properties of $ℓ$ and oscillation of a certain associated second order differential equation.

Transitivity and partial order

Jiří Klaška (1997)

Mathematica Bohemica

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In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary $n$ -element set up to $n = 14$ .

Comparison theorems for differential equations of neutral type

Miroslava Růžičková (1997)

Mathematica Bohemica

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We are interested in comparing the oscillatory and asymptotic properties of the equations $L_{n} [x (t) - P (t) x (g (t))] + δ f (t, x (h (t))) = 0$ with those of the equations $M_{n} [x (t) - P (t) x (g (t))] + δ Q (t) q (x (r (t))) = 0 .$

Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra

Jan Ligęza (1998)

Mathematica Bohemica

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In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in $𝒢^{n} (ℝ)$ , where $𝒢 (ℝ)$ denotes the Colombeau algebra.