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Density of 4-edge paths in graphs with fixed edge densityJan 06 2016We investigate the number of 4-edge paths in graphs with a fixed number of vertices and edges. An asymptotically sharp upper bound is given to this quantity. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge ... More

Forbidden subposet problems with size restrictionsAug 23 2016Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are closely related ... More

The method of double chains for largest families with excluded subposetsApr 24 2012For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $\mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many $P$ posets. These posets are built from seven base ... More

Union-intersecting set systemsMar 01 2014Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of any t sets. ... More

Incomparable copies of a poset in the Boolean latticeSep 27 2013Let $B_n$ be the poset generated by the subsets of $[n]$ with the inclusion as relation and let $P$ be a finite poset. We want to embed $P$ into $B_n$ as many times as possible such that the subsets in different copies are incomparable. The maximum number ... More

Triangle areas determined by arrangements of planar linesFeb 08 2019A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been generalized in ... More

A model with Suslin trees but no minimal uncountable linear orders other than $ω_1$ and $-ω_1$Mar 09 2018Mar 12 2018We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016Nov 09 2017Motivated by an old conjecture of P. Erd\H{o}s and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number ... More

Uncountable strongly surjective linear ordersJun 30 2017Jan 30 2018A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering questions of Camerlo, ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016A graph (digraph) has uncountable chromatic number if its vertices cannot be covered by countably many independent (acyclic) sets. Our aim is to investigate digraphs with uncountable chromatic number and orientations of undirected graphs with uncountable ... More

Ladder system uniformization on trees I & IIJun 11 2018Jan 04 2019Given a tree $T$ of height $\omega_1$, we say that a ladder system colouring $(f_\alpha)_{\alpha\in \lim\omega_1}$ has a $T$-uniformization if there is a function $\varphi$ defined on a subtree $S$ of $T$ so that for any $s\in S_\alpha$ of limit height ... More

Topological Analysis of Bitcoin's Lightning NetworkJan 15 2019Jan 16 2019Bitcoin's Lightning Network (LN) is a scalability solution for Bitcoin allowing transactions to be issued with negligible fees and settled instantly at scale. In order to use LN, funds need to be locked in payment channels on the Bitcoin blockchain (Layer-1) ... More

Infinite combinatorics plain and simpleMay 17 2017Feb 05 2018We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly ... More

The mass of asymptotically anti-de Sitter space-timesNov 29 2000Oct 04 2001We give a definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of gr-qc/0110014 which show that our definition provides ... More

HIJING++, a Heavy Ion Jet INteraction Generator for the High-luminosity Era of the LHC and BeyondNov 06 2018HIJING++ (Heavy Ion Jet INteraction Generator) is the successor of the widely used original HIJING, developed almost three decades ago. While the old versions (1.x and 2.x) were written in FORTRAN, HIJING++ was completely rewritten in C++. During the ... More

Characterization of projectively flat Finsler manifolds of constant curvature with finite dimensional holonomy groupApr 05 2013Apr 12 2013In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian.

t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More

Squares and their centersAug 05 2014Aug 24 2014We study the relationship between the sizes of two sets $B, S\subset\mathbb{R}^2$ when $B$ contains either the whole boundary, or the four vertices, of a square with axes-parallel sides and center in every point of $S$, where size refers to one of cardinality, ... More

Tractable hypergraph properties for constraint satisfaction and conjunctive queriesNov 04 2009Dec 06 2011An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where ... More

Complete intersection quiver settings with one dimensional verticesMay 16 2011Jul 17 2011We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction ... More

Applications of an intersection formula to dual conesApr 03 2017Oct 19 2017We give a succinct proof of a duality theorem obtained by R\'ev\'esz in 1991 which concerns extremal quantities related to trigonomertic polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show ... More

Forbidding rank-preserving copies of a posetOct 25 2017The maximum size, $La(n,P)$, of a family of subsets of $[n]=\{1,2,...,n\}$ without containing a copy of $P$ as a subposet, has been intensively studied. Let $P$ be a graded poset. We say that a family $\mathcal{F}$ of subsets of $[n]=\{1,2,...,n\}$ contains ... More

Infinite monochromatic sumsets for colourings of the realsOct 20 2017Jan 02 2019N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of $\mathbb R$ so that no infinite sumset $X+X=\{x+y:x,y\in X\}$ is monochromatic. Our aim in this paper is to prove a consistency result in the opposite ... More

Cleaning Interval GraphsMar 05 2010We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, ... More

Structure Theorem and Isomorphism Test for Graphs with Excluded Topological SubgraphsNov 04 2011Nov 13 2014We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological subgraph has a ... More

Obtaining a Planar Graph by Vertex DeletionDec 29 2008In the k-Apex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor closed class of graphs, hence by the deep results of Robertson and Seymour, there is an ... More

On the dimension of polynomial semiringsOct 08 2015In our previous work, motivated by the study of tropical polynomials, a definition for prime congruences was given for an arbitrary commutative semiring. It was shown that for additively idempotent semirings this class exhibits some analogous properties ... More

The Collins-Roscoe mechanism and D-spacesOct 18 2010We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space.

On the equations and classification of toric quiver varietiesFeb 20 2014Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with ... More

Observables and initial conditions for rotating and expanding fireballs with spheroidal symmetryNov 09 2015Utilizing a recently found class of exact, analytic rotating solutions of non-relativistic fireball hydrodynamics, we calculate analytically the single-particle spectra, the elliptic flows and two-particle Bose-Einstein correlation functions for rotating ... More

Saturation in random graphsOct 30 2015Apr 13 2016A graph $H$ is $K_s$-saturated if it is a maximal $K_s$-free graph, i.e., $H$ contains no clique on $s$ vertices, but the addition of any missing edge creates one. The minimum number of edges in a $K_s$-saturated graph was determined over 50 years ago ... More

Domination in 3-tournamentsFeb 04 2016A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set $X$ dominates $T$ if every vertex not in $X$ is contained in an edge whose tail is in $X$. The domination number of $T$ is the ... More

Rounds in a combinatorial search problemNov 30 2016We consider the following combinatorial search problem: we are given some excellent elements of $[n]$ and we should find at least one, asking questions of the following type: "Is there an excellent element in $A \subset [n]$?". G.O.H. Katona proved sharp ... More

Improved Ramsey-type results in comparability graphsOct 01 2018Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if $G$ is an $n$-vertex graph ... More

Triangle-different Hamiltonian pathsAug 18 2016Oct 11 2016Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$-different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian ... More

Kernelization of Packing ProblemsDec 07 2018Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size at least k ... More

Toric quiver cellsSep 12 2016It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension ... More

Toric quiver cellsSep 12 2016Jul 03 2017It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension ... More

EM Cygni: a study of its eclipse timingsSep 17 2007EM Cygni is a Z Cam-subtype eclipsing dwarf nova. Its orbital period variations were reported in the past but the results were in conflict to each other while other studies allowed the possibility of no period variation. In this study we report accurate ... More

A note on idempotents in finite AW*-factorsSep 25 2000We prove that the value of the quasi-trace on an idempotent element in a AW*-factor of type II_1 is the same as the dimension of its left (or right) support.

On the probability that two elements of a finite semigroup have the same right matrixJan 25 2016Feb 08 2016Let $\sigma$ be a binary relation on a non empty finite set $A$. Let $P_{\sigma}(A)$ denote the probability that a randomly selected couple $(a, b)\in A\times A$ belongs to $\sigma$. In this paper we investigate $P_{\sigma}(A)$ in special cases.

On Congruences on Ultraproducts of Algebraic StructuresNov 08 2015Let $I$ be a non-empty set and $\mathcal{D}$ an ultrafilter over $I$. For similar algebraic structures $B_i$, $i\in I$ let $\Pi (B_i|i\in I)$ and $\Pi _{\mathcal{D}}(B_i|i\in I)$ denote the direct product and the ultraproduct of $B_i$, respectively. Let ... More

Remarks on the paper "M. Kolibiar, On a construction of semigroups"Apr 27 2015Jan 29 2016In his paper "On a construction of semigroups", M. Kolibiar gives a construction for a semigroup $T$ (beginning from a semigroup $S$) which is said to be derived from the semigroup $S$ by a $\theta$-construction. He asserted that every semigroup $T$ can ... More

An Application of the Separator of Subsets of Semigroups in the Number TheoryJan 21 2015Jun 01 2015In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Global Controllability of Chemical ReactionsAug 13 2015Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global ... More

Digital Economy And Society. A Cross Country Comparison Of Hungary And UkraineJan 02 2019We live in the Digital Age in which both economy and society have been transforming significantly. The Internet and the connected digital devices are inseparable parts of our daily life and the engine of the economic growth. In this paper, first I analyzed ... More

On Congruence Permutable $G$-setsJan 14 2018An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For an arbitrary ... More

Halfspace depth does not characterize probability distributionsOct 22 2018We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.

Effect of the $ηη$ channel and interference phenomena in the two-pion transitions of charmonia and bottomoniaNov 23 2016The basic shape of di-pion mass spectra in the two-pion transitions of both charmonia and bottomonia states is explained by an unified mechanism based on contributions of the $\pi\pi$, $K\overline{K}$ and $\eta\eta$ coupled channels including their interference. ... More

The Berry connection of the Ginzburg-Landau vorticesNov 02 2015Apr 20 2016We analyze 2-dimensional Ginzburg-Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy ... More

Irreducible Ginzburg-Landau fields in dimension 2Jul 01 2016Aug 25 2016Ginzburg--Landau fields are the solutions of the Ginzburg--Landau equations which depend on two positive parameters, $\alpha$ and $\beta$. We give conditions on $\alpha$ and $\beta$ for the existence of irreducible solutions of these equations. Our results ... More

Left equalizer simple semigroupsApr 27 2015Sep 29 2015In this paper we characterize and construct semigroups whose right regular representation is a left cancellative semigroup. These semigroups will be called left equalizer simple semigroups. For a congruence $\varrho$ on a semigroup $S$, let ${\mathbb ... More

The separator of a subset of a semigroupJan 24 2015In this paper we introduce a new notion by the help of the idealizer. This new notion is the separator of a subset of a semigroup. We investigate the properties of the separator in an arbitrary semigroup and characterize the unitary subsemigroups and ... More

On Monoid Congruences of Commutative SemigroupsJan 18 2015In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the help of subsets ... More

The Impact Of Country Of Origin In Mobile Phone Choice Of Generation Y And ZJan 02 2019Mobile phones play a very important role in our life. Mobile phone sales have been soaring over the last decade due to the growing acceptance of technological innovations, especially by Generations Y and Z. Understanding the change in customers' requirement ... More

On Congruence Permutable $G$-setsJan 14 2018Feb 24 2018An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For an arbitrary ... More

On Special Rees Matrix Semigroups Over SemigroupsSep 30 2016In this paper we define the notion of the locally right regular sequence of semigroups. We show that, if $S$ is a semigroup and $\alpha$ is a congruence on $S$, then the sequence $S/\alpha ^{(0)}, S/\alpha ^{(1)}, \dots , S/\alpha ^{(n)}, \dots $ of factor ... More

Retractable state-finite automata without outputsOct 04 2015A homomorphism of an automaton ${\bf A}$ without outputs onto a subautomaton ${\bf B}$ of ${\bf A}$ is called a retract homomorphism if it leaves the elements of $B$ fixed. An automaton ${\bf A}$ is called a retractable automaton if, for every subautomaton ... More

Separators of Ideals in Multiplicative Semigroups of Unique Factorization DomainsAug 29 2015In this paper we show that if $I$ is an ideal of a commutative semigroup $C$ such that the separator $SepI$ of $I$ is not empty then the factor semigroup $S=C/P_I$ ($P_I$ is the principal congruence on $C$ defined by $I$) satisfies Condition $(*)$: $S$ ... More

On Commutative Monoid Congruences of SemigroupsJan 08 2015A subset A of a semigroup S is called a medial subset of S if xaby is in A if and only if xbay is in A for every elements x, y, a, b of S. In the paper we show how we can construct the commutative monoid congruences of a semigroup S by the help of medial ... More

Finding small separators in linear time via treewidth reductionOct 21 2011We present a method for reducing the treewidth of a graph while preserving all of its minimal $s-t$ separators up to a certain fixed size $k$. This technique allows us to solve $s-t$ Cut and Multicut problems with various additional restrictions (e.g., ... More

Known Algorithms on Graphs of Bounded Treewidth are Probably OptimalJul 30 2010We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot ... More

Decomposing random graphs into few cycles and edgesApr 12 2014Nov 26 2014Over 50 years ago, Erd\H{o}s and Gallai conjectured that the edges of every graph on $n$ vertices can be decomposed into $O(n)$ cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random graph $G(n,p)$ ... More

$\mathcal{O}(k)$-robust spanners in one dimensionMar 23 2018A geometric $t$-spanner on a set of points in Euclidean space is a graph containing for every pair of points a path of length at most $t$ times the Euclidean distance between the points. Informally, a spanner is $\mathcal{O}(k)$-robust if deleting $k$ ... More

Trees, ladders and graphsSep 09 2014We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number $\omega_1$ without uncountable $\omega$-connected ... More

A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisetsDec 05 2012Mar 09 2014There are many generalizations of the Erd\H{o}s-Ko-Rado theorem. We give new results (and problems) concerning families of $t$-intersecting $k$-element multisets of an $n$-set and point out connections to coding theory and classical geometry. We establish ... More

Covering random graphs by monochromatic trees and Helly-type results for hypergraphsFeb 13 2019How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given $r$-edge-coloured graph $G$? These problems were introduced in the 1960's and were intensively studied by various researchers over the last 50 years. ... More

Finding non-minority balls with majority and plurality queriesDec 20 2018Given a set of $n$ colored balls, a \textit{majority, non-minority or plurality ball} is one whose color class has size more than $n/2$, at least $n/2$ or larger than any other color class, respectively. We describe linear time algorithms for finding ... More

Linear groups as right multiplication groups of quasifieldsOct 05 2012For quasifields, the concept of parastrophy is slightly weaker than isotopy. Parastrophic quasifields yield isomorphic translation planes but not conversely. We investigate the right multiplication groups of finite quasifields. We classify all quasifields ... More

Remote-Sensing Quantum Hyperspace by Entangled Photon InterferometryJan 11 2011Jan 21 2011Even though ideas of extracting future-related, or Faster-Than-Light (FTL) information from hyperspace using quantum entanglement have generally been refuted in the last ten years, in this paper we show that the original 'Delayed Choice Quantum Eraser ... More

A class of simple proper Bol loopsMar 30 2007The existence of finite simple non-Moufang Bol loops was considered as one of the main open problems in the theory of loops and quasigroups. In this paper, we present a class of proper simple Bol loops. This class also contains finite and new infinite ... More

Group invariants of certain Burn loop classesNov 14 2004In this paper, we determine the collineation groups generated by the Bol reflections, the core, the automorphism groups and the full direction preserving collineation groups of the loops $B_{4n}$ and $C_{4n}$ given by R.P. Burn. We also prove some lemmas ... More

S-duality in Abelian gauge theory revisitedMay 31 2010Mar 31 2015Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated ... More

Declarativeness: the work done by something elseNov 25 2017Being declarative means that we do computer programming on higher levels of abstraction. This vague definition identifies declarativeness with the act of ignoring details, but it is a special case of abstraction. The unspecified part is some computational ... More

Full-speed Fuzzing: Reducing Fuzzing Overhead through Coverage-guided TracingDec 31 2018Jan 28 2019Of coverage-guided fuzzing's three main components: (1) testcase generation, (2) code coverage tracing, and (3) crash triage, code coverage tracing is a dominant source of overhead. Coverage-guided fuzzers trace every testcase's code coverage through ... More

Torsion in almost Kaehler geometryJan 08 2003We study almost K\"ahler manifolds whose curvature tensor satisfies the second curvature condition of Gray (shortly ${\cal{AK}}_2$). This condition is interpreted in terms of the first canonical Hermitian connection. It turns out that this condition forces ... More

Minimal quasivarieties of semilattices over commutative groupsAug 28 2012We continue some recent investigations of W. Dziobiak, J. Jezek, and M. Maroti. Let G=(G,\cdot) be a commutative group. A semilattice over G is a semilattice enriched with G as a set of unary operations acting as semilattice automorphisms. We prove that ... More

On the topology of elliptic singularitiesJan 18 2019For any elliptic normal surface singularity with rational homology sphere link we consider a new elliptic sequence, which differs from the one introduced by Laufer and S. S.-T. Yau. However, we show that their length coincide. Using the properties of ... More

Initial data for fluid bodies in general relativityJan 29 2002We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly ... More

Traces arising from regular inclusionsMay 18 2016We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of normalizers of ... More

Pseudo-Diagonals and Uniqueness TheoremsAug 29 2013We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.

Representations of Circular WordsMay 22 2014In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The latter form can ... More

Finite Permutable Putcha SemigroupsFeb 20 2014A semigroup $S$ is called a permutable semigroup if $\alpha \circ \beta =\beta \circ \alpha$ is satified for all congruences $\alpha$ and $\beta$ of $S$. A semigroup is called a Putcha semigroup if it is a semilattice of archimedean semigroups. In this ... More

Prolongations of Lie algebras and applicationsDec 10 2007Jun 05 2008We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness results for ... More

Connexions with totally skew-symmetric torsion and nearly-Kaehler geometrySep 08 2007We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor ... More

Bernstein type inequalities for rational functions on analytic curves and arcsDec 22 2015Apr 28 2016Borwein and Erd\'elyi proved a Bernstein type inequality for rational functions on the unit circle and on the real line. Here we establish asymptotically sharp extensions of their inequalities for rational functions on analytic Jordan arcs and curves. ... More

Algebraic reduction of certain almost Kaehler manifoldsFeb 24 2003We study almost Kaehler manifolds whose curvature tensor satisfies the third curvature condition of Gray. We show that the study of manifolds within this class reduces to the study of a subclass having the property that the torsion of the first canonical ... More

|{Math, Philosophy, Programming, Writing}| = 1Mar 06 2018Sep 19 2018Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and Philosophy itself. ... More

The Algebraic View of ComputationDec 09 2017We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.

A Note on Semigroup Algebras of Permutable SemigroupsNov 27 2015Let $S$ be a semigroup and $\mathbb F$ be a field. For an ideal $J$ of the semigroup algebra ${\mathbb F}[S]$ of $S$ over $\mathbb F$, let $\varrho _J$ denote the restriction (to $S$) of the congruence on ${\mathbb F}[S]$ defined by the ideal $J$. A semigroup ... More

Rigidity of Riemannian foliations with complex leaves on Kaehler manifoldsApr 03 2002We study Riemannian foliations with complex leaves on Kaehler manifolds. The tensor T, the obstruction to the foliation be totally geodesic, is interpreted as a holomorphic section of a certain vector bundle. This enables us to give classification results ... More

Polynomial and rational inequalities on Jordan arcs and domainsAug 07 2014Jun 04 2015In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitely many Jordan curves onto a complement to a system of the same number of ... More

On the number of k-dominating independent setsApr 13 2015May 07 2015We study the existence and the number of $k$-dominating independent sets in certain graph families. While the case $k=1$ namely the case of maximal independent sets - which is originated from Erd\H{o}s and Moser - is widely investigated, much less is ... More

The structure of AK_2-manifoldsJan 21 2003We study special almost Kaehler manifolds whose curvature tensor satisfies the second curvature condition of Gray. It is shown that for such manifolds, the torsion of the first canonical Hermitian is parallel. This enables us to show that every AK_2-manifold ... More

Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equationsAug 09 2017Feb 07 2018Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently modeled by generalizing ... More

Do the rich get richer? An empirical analysis of the BitCoin transaction networkAug 18 2013Mar 31 2014The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of ... More

Maps on classes of Hilbert space operators preserving measure of commutativityJul 03 2014In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily invariant norm ... More

3-nets realizing a diassociative loop in a projective planeMar 01 2016A \textit{$3$-net} of order $n$ is a finite incidence structure consisting of points and three pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one line ... More

Computing with small quasigroups and loopsSep 17 2015This is a companion to our lectures GAP and loops, to be delivered at the Workshops Loops 2007, Prague, Czech Republic. In the lectures we introduce the GAP package LOOPS, describe its capabilities, and explain in detail how to use it. In this paper we ... More

How to initialize a second class particle?Oct 16 2015Jan 14 2016We greatly generalize P. A. Ferrari and C. Kipnis' results on the behavior of the second class particle in the rarefaction fan of the totally asymmetric simple exclusion process (Ann. Inst. H. Poincar\'e Probab. Statist. 31(1), 1995). Versions of their ... More