| 1. 10. 2020 |
Michal Hospodár – Right and left quotients on subclasses of convex languages |
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Abstract: We study the state complexity and nondeterministic state complexity of right quotient and left quotient
on the classes of prefix-, suffix-, factor-, and subword-free, -closed, and -convex regular languages,
and on the classes of right, left, two-sided, and all-sided ideal languages.
We get tight upper bounds in all cases except for state complexity of left quotient of all-sided ideals and subword-closed languages by a regular language,
and nondeterministic state complexity of left quotient on subword-convex languages.
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| 25. 6. 2020 |
Ján Haluška – Bitopology on $\mathbb{E}_4$ equipped with a skew circulated multiplication |
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Abstract: An operation of multiplication on $\mathbb{E}_4$ is introduced via a skew circulated matrix,
it is associative, commutative and distributive. The resulting algebra $\mathbb{W}$ over $\mathbb{R}$ is
isomorphic to $\mathbb{C}\times\mathbb{C}$ and with partially invertible elements.
The related algebraic, geometrical, and topological properties are given.
There are sub-planes of $\mathbb{W}$ isomorphic to the Gauss and Clifford complex number planes.
A topology on $\mathbb{W}$ are given via a norm which is sum of two non-equivalent seminorms.
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| 5. 3. 2020 |
Emília Halušková – On discrete properties of monotone functions |
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Abstract: A correspondence between monotone functions with respect a linear order and monounary algebras
which consist of at most four types of components will be described. Further, several properties of
monotone functions with respect a partial order will be given.
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| 20. 2. 2020 |
Ján Haluška – Generalized complex numbers |
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Abstract: An unified model of generalized complex numbers is defined
via an operation of multiplication in the form of a Toeplitz matrix.
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| 6. 2. 2020 |
Roman Frič – Lifting and sagging observables |
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Abstract: Important constructions in probability theory can be schematized
via two simple commutative triangle diagrams. We shall deal with joint experiments
and conditional probability.
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| 23. 1. 2020 |
Peter Eliaš – Ordered vector spaces in probability theory |