doc. Ing. Ľubomíra Dvořáková, Ph.D.
e-mail: | show e-mail |
telephone: | +420 22435 8559 |
room: | 09b |
www: | http://kmlinux.fjfi.cvut.cz/~balkolub |

Antipalindromy
advisor: | doc. Ing. Ľubomíra Dvořáková, Ph.D. |
e-mail: | show e-mail |
type: | bachelor thesis |
branch of study: | MI_MM, MI_AMSM, MINF, APIN |
key words: | palindrom, antipalindrom, prvočísla, dělitelnost |
description: | Každý jistě ví, že palindrom je slovo, které je stejné při čtení zepředu i pozpátku. O přirozeném čísle p řekneme, že je palindromem v bázi b, kde b je přirozené číslo, pokud jeho zápis p=a_0+a_1b+a_2b^2+...+a_nb^n v bázi b pomocí cifer 0 až b-1 splňuje, že a_0 a_1 a_2...a_n je palindrom, tj. a_k=a_{n-k} pro každé k od 0 do n. Podobně o přirozeném čísle a řekneme, že je antipalindromem v bázi b pokud jeho zápis a=a_0+a_1b+a_2b^2+...+a_nb^n v bázi b pomocí cifer 0 až b-1 splňuje a_k+a_{n-k}=b-1 pro každé k od 0 do n. Příkladem palindromu v bázi 10 je 9339 a příkladem antipalindromu v bázi 10 je 9360. Cílem práce je prostudovat pro antipalindromy vlastnosti, které jsou známé pro palindromy. Jmenujme namátkově: dělitelnost a prvočísla mezi antipalindromy, výskyt palindromů mezi antipalindromy a naopak, mocniny mezi antipalindromy, atd. Inspirací ke studiu antipalindromů nám byl výsledek z kombinatoriky na slovech, který říká, že jedno z nejslavnějších slov -- Thueovo-Moreovo slovo -- je bohaté na palindromy a antipalindromy zároveň [1]. |
references: |
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note: | Na tématu pracuje student Stanislav Kruml. |
last update: | 29.04.2020 22:15:10 |
Nekonečná slova s nízkou faktorovou komplexitou
advisor: | doc. Ing. Ľubomíra Dvořáková, Ph.D. |
e-mail: | show e-mail |
type: | phd thesis |
branch of study: | MI_MM, MINF |
key words: | dendric sets, tree sets, factor complexity, S-adic representation |
description: | Cílem práce bude studium některých charakteristik nedávno definované třídy faktorových jazyků nazvaných dendrické množiny [1]. Tato třída je zajímavá tím, že zobecňuje současně dvě velice podrobně prozkoumané třídy: slova definovaná Arnouxem a Rauzym v [2] a slova kódující výměnu intervalů. Přitom tyto dvě třídy jsou na vícepísmenné abecedě disjunktní. I když se dendrickým množinám věnuje v posledních letech velká pozornost, mnohé jejich charakteristiky zatím nejsou známé. Jedná se např. o kritický exponent, palindromickou komplexitu [3], popis podtřídy slov bohatých na palindromy, resp. zobecněné palindromy [4], vztah balancovaných slov k dendrickým množinám atd. Zdá se, že silným nástrojem při studiu těchto vlastností by mohla být znalost S-adické reprezentace dendrických slov objevená v [5]. Dalším z cílů práce bude i konstrukce nových typů dendrických množin. |
references: |
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last update: | 09.11.2019 17:35:16 |
Shape optimization for quantum systems with magnetic fields
advisor: | Vladimir Lotoreichik, Ph.D. |
e-mail: | show e-mail |
type: | bachelor thesis, master thesis |
branch of study: | MI_MM, APIN |
key words: | ground-state energy, eigenvalue optimization, magnetic fields |
attached file: | ![]() |
description: | The aim of the proposed project is to obtain optimization results for the ground-state energy in a family of model quantum systems with magnetic fields and non-trivial geometry. From the mathematical point of view, it means that there is a differential operator on a domain that describes the magnetic system, and the goal is to show that its smallest eigenvalue attains the maximal or the minimal value for some specific shape. Typically, the optimal shape for the ground-state energy is radially symmetric [1, 3], and it can, for example, be the disk or the annulus. Optimization with magnetic fields is much less understood than without them and even very fundamental questions remain open [2], but it is certainly possible to select the setting, which is feasible to analyze within the bachelor or diploma project. The outcome of the project is expected to be a rigorous mathematical proof that certain shape optimizes the ground-state energy. On the level of the bachelor project partial results in this direction will also be sufficient. |
references: |
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last update: | 25.11.2021 09:17:53 |
V3S Database
The application records results of science and research, and other academic activities. The V3S application serves as a tool for submitting data to the RIV database, exporting data for statistic analyses, and internal evaluation of research.
List of publications in V3S
Articles
2013
BiBTeX
title = {{Continued fractions of square roots of natural numbers}},
author = {Balkov{\' a}, L. and Hru{\v s}kov{\' a}, A.},
journal = {Acta Polytechnica},
year = {2013},
volume = {53},
number = {4},
pages = {322--328}
}
BiBTeX
title = {{Proof of the Brlek-Reutenauer conjecture}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Starosta, {\v S}.},
journal = {Theoretical Computer Science},
year = {2013},
volume = {475},
pages = {120--125},
month = {March}
}
BiBTeX
title = {{Ha{\v s}ovac{\'\i} funkce a kombinatorika na slovech}},
author = {Balkov{\' a}, L. and Legersk{\' y}, J.},
journal = {Pokroky matematiky, fyziky a astronomie},
year = {2013},
volume = {58},
number = {4},
pages = {274--284}
}
2012
BiBTeX
title = {{Corrigendum: "On Brlek-Reutenauer Conjecture"}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Starosta, {\v S}.},
journal = {Theoretical Computer Science},
year = {2012},
volume = {465},
pages = {73--74},
month = {December}
}
BiBTeX
title = {{Ramseyova teorie aneb p{\v r}{\'\i}klady, kter{\' e} jsou pro po{\v c}{\'\i}ta{\v c} p{\v r}{\'\i}li{\v s} slo{\v z}it{\' e}}},
author = {Balkov{\' a}, L. and Hru{\v s}kov{\' a}, A. and Mat{\' u}{\v s}, V. and Schusser, J. and {\v S}ubert, E. and Topfer, M.},
journal = {Rozhledy matematicko-fyzik{\' a}ln{\'\i}},
year = {2012},
volume = {87},
number = {4},
pages = {8--15}
}
BiBTeX
title = {{Factor frequencies in generalized Thue-Morse words}},
author = {Balkov{\' a}, L.},
journal = {Kybernetika},
year = {2012},
volume = {3},
number = {48},
pages = {371--385}
}
BiBTeX
title = {{Factor frequencies in languages invariant under symmetries preserving factor frequencies,}},
author = {Balkov{\' a}, L.},
journal = {Integers: Electronic Journal of Combinatorial Number Theory},
year = {2012},
volume = {12},
pages = {--}
}
2011
BiBTeX
title = {{Critical Exponent of Infinite Words Coding Beta-integers Associated with Non-simple Parry Numbers}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Klouda, K.},
journal = {Integers: Electronic Journal of Combinatorial Number Theory},
year = {2011},
volume = {11b},
pages = {1--25},
month = {December}
}
BiBTeX
title = {{Abelian Complexity of Infinite Words Associated with Quadratic Parry Numbers}},
author = {Balkov{\' a}, L. and Turek, O. and B{\v r}inda, K.},
journal = {Theoretical Computer Science},
year = {2011},
volume = {412},
number = {45},
pages = {6252--6260},
month = {October}
}
BiBTeX
title = {{Infinite words with finite defect}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Starosta, {\v S}.},
journal = {Advances in Applied Mathematics},
year = {2011},
volume = {47},
number = {3},
pages = {562--574}
}
BiBTeX
title = {{On Brlek-Reutenauer conjecture}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Starosta, {\v S}.},
journal = {Theoretical Computer Science},
year = {2011},
volume = {412},
number = {41},
pages = {5649--5655}
}
BiBTeX
title = {{Paul Erdos: {\v Z}ivot v cit{\' a}tech}},
author = {Balkov{\' a}, L.},
journal = {U{\v c}itel matematiky},
year = {2011},
volume = {19},
number = {4 (80},
pages = {227--237},
month = {May}
}
BiBTeX
title = {{Nahl{\' e}dnut{\'\i} pod pokli{\v c}ku kombinatoriky na nekone{\v c}n{\' y}ch slovech}},
author = {Balkov{\' a}, L.},
journal = {Pokroky matematiky, fyziky a astronomie},
year = {2011},
volume = {56},
number = {1},
pages = {9--18}
}
2010
BiBTeX
title = {{Jeden za osmn{\' a}ct a druh{\' y} bez dvou za dvacet aneb z{\' a}porn{\' e} cifry v z{\' a}pisu {\v c}{\'\i}sel}},
author = {Balkov{\' a}, L.},
journal = {Rozhledy matematicko-fyzik{\' a}ln{\'\i}},
year = {2010},
volume = {85},
number = {4},
pages = {3--11},
month = {prosinec}
}
BiBTeX
title = {{Sturmian Jungle (or Garden?) on Multiliteral Alphabets}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Starosta, {\v S}.},
journal = {RAIRO - Theoretical Informatics and Applications },
year = {2010},
volume = {44},
number = {4},
pages = {443--470}
}
BiBTeX
title = {{Beta-cel{\' a} {\v c}{\'\i}sla a kvazikrystaly}},
author = {Balkov{\' a}, L.},
journal = {{\v C}eskoslovensk{\' y} {\v c}asopis pro fyziku},
year = {2010},
volume = {60},
number = {6},
pages = {334--336},
month = {prosinec}
}
2009
BiBTeX
title = {{Palindromes in Infinite Ternary Words}},
author = {Pelantov{\' a}, E. and Balkov{\' a}, L. and Starosta, {\v S}.},
journal = {RAIRO - Theoretical Informatics and Applications },
year = {2009},
volume = {43},
number = {4},
pages = {687--702}
}
BiBTeX
title = {{A note on symmetries in the Rauzy graph and factor frequencies}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E.},
journal = {Theoretical Computer Science},
year = {2009},
volume = {410},
number = {27-29},
pages = {2779--2783},
month = {{\v c}erven}
}
BiBTeX
title = {{Palindromic complexity of infinite words associated with non-simple Parry numbers}},
author = {Balkov{\' a}, L. and Mas{\' a}kov{\' a}, Z.},
journal = {RAIRO - Theoretical Informatics and Applications },
year = {2009},
volume = {43},
number = {1},
pages = {145--163},
month = {March}
}
BiBTeX
title = {{Repetitions in beta-integers}},
author = {Balkov{\' a}, L. and Klouda, K. and Pelantov{\' a}, E.},
journal = {Letters in Mathematical Physics},
year = {2009},
volume = {87},
number = {1},
pages = {181--195},
month = {February}
}
BiBTeX
title = {{Noncommutative Reading of the Complex Plane through Delone Sequences}},
author = {Balkov{\' a}, L. and Ali, S.T. and Curado, E.M.F. and Gazeau, J.P. and Rego-Monteiro, M. A. and Rodrigues, L.M.C. and Sekimoto, K.},
journal = {Journal of Mathematical Physics},
year = {2009},
volume = {50},
number = {4},
pages = {043517--043544},
month = {duben}
}
2008
BiBTeX
title = {{Sequences with constant number of return words}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Steiner, W.},
journal = {Monatshefte f{\" u}r Mathematik},
year = {2008},
volume = {155},
number = {3-4},
pages = {251--263},
month = {December}
}
BiBTeX
title = {{Asymptotic Behavior of Beta-integers}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Gazeau, J.P.},
journal = {Letters in Mathematical Physics},
year = {2008},
volume = {84},
number = {2},
pages = {179--198},
month = {June}
}
2007
BiBTeX
title = {{Return Words and Recurrence Function of a Class of Infinite Words}},
author = {Balkov{\' a}, L.},
journal = {Acta Polytechnica},
year = {2007},
volume = {47},
number = {2-3},
pages = {15--19},
month = {February}
}
BiBTeX
title = {{Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers}},
author = {Balkov{\' a}, L. and Pelantov{\' a}, E. and Turek, O.},
journal = {RAIRO - Theoretical Informatics and Applications },
year = {2007},
volume = {2007},
number = {41},
pages = {307--328},
month = {September}
}
2006
BiBTeX
title = {{Complexity for Infinite Words Associated with Quadratic Nonsimple Parry Numbers}},
author = {Balkov{\' a}, L.},
journal = {Journal of Geometry and Symmetry in Physics},
year = {2006},
volume = {7},
number = {7},
pages = {1--11}
}
Contributions in proceedings
2013
BiBTeX
title = {{Infinite Words with Well Distributed Occurrences}},
author = {Balkov{\' a}, L. and De Luca, A. and Bucci, M. and Puzynina, S.},
address = {Berlin},
booktitle = {{Combinatorics on Words}},
publisher = {Springer-Verlag},
year = {2013},
pages = {46--57}
}
2007
BiBTeX
title = {{Factor Frequencies of Reversal Closed Languages}},
author = {Balkov{\' a}, L.},
address = {Praha},
booktitle = {{Doktorandsk{\' e} dny 2007}},
publisher = {{\v C}esk{\' a} technika - nakladatelstv{\'\i} {\v C}VUT},
year = {2007},
pages = {1--8}
}
2006
BiBTeX
title = {{All About Infinite Words Associated with Quadratic Non-simple Parry Numbers}},
author = {Balkov{\' a}, L.},
address = {Praha},
booktitle = {{Doktorandsk{\' e} dny 2006}},
publisher = {{\v C}esk{\' a} technika - nakladatelstv{\'\i} {\v C}VUT},
year = {2006},
pages = {1--10}
}
Others
2008
BiBTeX
title = {{Beta-integers and Quasicrystals}},
author = {Balkov{\' a}, L.},
address = {Prague},
year = {2008},
pages = {162},
school = {thesis of Faculty of Nuclear Sciences and Physical Engineering}
}