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| 23. 1. 2025 |
Irena Jadlovská – On the Lambert W function and its applications |
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Abstract:
In the talk, we discuss numerous applications of the Lambert W function - the multivalued inverse of the function $w \to w \exp^w$.
Particular attention is devoted to its role in both the quantitative and qualitative analysis of delay differential equations.
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| 5. 2. 2025 |
Ahmed Ibrahim Abosaied – Hardy-type inequalities |
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link to slides
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| 20. 2. 2025 |
Peter Mlynárčik – Kuratowski algebra and nondeterministic complexity |
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Abstract:
My presentation is divided to two parts.
- Common work with Galina Jirásková and Michal Hospodár.
- Essential part of my work is teaching at university and elementary school, so I present interesting problems
with wizard, elfs and hats.
The first part.
Kazimierz Kuratowski (1896-1980) was interested in the largest number
of distinct sets obtainable by repeatedly applying the set operations of closure and complement
to a given starting subset of a topological space. In 1922 he published that
at most 14 distinct sets is possible to obtain.
We investigate similar cases with regular languages and
instead of closure operation and complement in topological space
we consider positive Kleene closure and complement:
$$L^+=\bigcup\limits_{i=1}^{\infty}L^i,\ L^c=\Sigma^*\setminus L$$
With such two operations and their repeatedly applying on the set $L$
it is possible to obtain at most 10 distinct languages.
Next we consider nondetermnistic complexity of language $L$ with $\mathrm{nsc}(L)=n$
and nondeterministic complexities of 10 possible obtained languages.
Some of them have complexities $n$, $2^n$, and upper bounds $2^{2^n}$,
Dedekind number $M(n)$.
The second part.
We will look at several tasks where the main role is played by a wizard and elves.
The wizard has the elves in his power and amuses himself by casting spells colored hats
to the elves, gives them some rules and clues and elves must guess the color of their own hat...
In a way of solutions of such tasks we can find really nice mathematics
concerning to epistemic logic, algebra, probability...
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| 6. 3. 2025 |
Viktor Olejár – Descriptional and Computational Complexity of Regular Languages |
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Abstract:
We review some selected results obtained during the past few years of our PhD study.
We mostly focus on summarizing outcomes that fall into one of three key topics of our thesis:
closure properties, nondeterministic state complexity,
and computational complexity related to decision problems.
The talk serves as preparation and feedback for our thesis defense.
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