Seminar of the Extension of the Mathematical Institute SAS in Košice

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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.
 
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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
 
Old page of the seminar (2010–2017): https://im.saske.sk/seminar/2017.html