# Seminar of the Extension of the Mathematical Institute SAS in Košice

 next: TBA 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.

 previous:
 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