Seminar of the Extension of the Mathematical Institute SAS in Košice

TBA Jozef PócsAggregation functions and their connection to universal algebra
Abstract: Aggregation functions form a composition closed family, i.e., a clone. We show that any generating set of this clone enables to define an algebraic structure, such that aggregation functions form free algebra in the variety generated by the mentioned algebraic structure.
1. 10. 2020 Michal Hospodár – Right and left quotients on subclasses of convex languages
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.
25. 6. 2020 Ján Haluška – Bitopology on $\mathbb{E}_4$ equipped with a skew circulated multiplication
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.
5. 3. 2020 Emília Halušková – On discrete properties of monotone functions
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.
20. 2. 2020 Ján Haluška – Generalized complex numbers
Abstract: An unified model of generalized complex numbers is defined via an operation of multiplication in the form of a Toeplitz matrix.
6. 2. 2020 Roman Frič – Lifting and sagging observables
Abstract: Important constructions in probability theory can be schematized via two simple commutative triangle diagrams. We shall deal with joint experiments and conditional probability.
23. 1. 2020 Peter Eliaš – Ordered vector spaces in probability theory
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