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Dominating sets in projective planesMar 09 2016We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result which shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set ... More

Permutations over cyclic groupsNov 29 2012Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements $a_1,...,a_m$ of the cyclic group of order $m$, there is a permutation $\pi$ such that $1a_{\pi(1)}+...+ma_{\pi(m)}=0$. ... 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

Density version of the Ramsey problem and the directed Ramsey problemJan 27 2014Jan 21 2016We discuss a variant of the Ramsey and the directed Ramsey problem. First, consider a complete graph on $n$ vertices and a two-coloring of the edges such that every edge is colored with at least one color and the number of bicolored edges $|E_{RB}|$ is ... More

Partition dimension of projective planesNov 29 2016We determine the partition dimension of the incidence graph $G(\Pi_q)$ of the projective plane $\Pi_q$ up to a constant factor $2$ as $(2+o(1))\log_2{q}\leq \mathrm{pd}(G(\Pi_q))\leq (4+o(1))\log_2{q}.$

The Density Turán problemJul 29 2014Let $H$ be a graph on $n$ vertices and let the blow-up graph $G[H]$ be defined as follows. We replace each vertex $v_i$ of $H$ by a cluster $A_i$ and connect some pairs of vertices of $A_i$ and $A_j$ if $(v_i,v_j)$ was an edge of the graph $H$. As usual, ... More

A simple proof of the Zeilberger-Bressoud q-Dyson theoremNov 28 2012As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the q-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.

On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair methodJan 04 2015Mar 12 2015We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\subseteq \binom{[n]}{k}$. Improving a bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of $\log M(n,k)$ by proving that for ... More

The Turán number of blow-ups of treesApr 15 2019A conjecture of Erd\H{o}s from 1967 asserts that any graph on $n$ vertices which does not contain a fixed $r$-degenerate bipartite graph $F$ has at most $Cn^{2-1/r}$ edges, where $C$ is a constant depending only on $F$. We show that this bound holds for ... More

Time-scale effects on the gain-loss asymmetry in stock indicesAug 16 2016Aug 17 2016The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations ... More

A new approach to constant term identities and Selberg-type integralsDec 22 2013Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation ... More

Universal Random Access Error Exponent for Codebooks with Different Word-LengthsJul 07 2016Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. It is shown that simultaneously for each codebook an error exponent can be achieved that equals the random coding exponent ... 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

Avoider-Enforcer star gamesFeb 11 2013Jan 30 2015In this paper, we study $(1 : b)$ Avoider-Enforcer games played on the edge set of the complete graph on $n$ vertices. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. ... More

Universal Random Access Error Exponents for Codebooks of Different Word-LengthsJul 07 2016Oct 26 2016Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent for this codebook ... More

Next-to-leading order calculation of four-jet observables in electron-positron annihilationJun 09 1998Sep 12 2000The production of four jets in electron-positron annihilation allows for measuring the strong coupling and the underlying group structure of the strong interaction simultaneously. This requires next-to-leading order perturbative prediction for four-jet ... More

Next-to-Leading Order Calculation of Four-Jet Shape VariablesJul 10 1997Dec 22 1997We present the next-to-leading order calculation of two four-jet event shape variables, the D parameter and acoplanarity differential distributions. We find large, more than 100% radiative corrections. The theoretical prediction for the D parameter is ... More

Calculation of QCD jet cross sections at next-to-leading orderOct 27 1996A general method for calculating \NLO cross sections in perturbative QCD is presented. The algorithm is worked out for calculating $N$-jet cross sections in hadron-hadron collisions. The generalization of the scheme to performing caclulations for other ... More

Proceedings 14th International Conference on Automata and Formal LanguagesMay 21 2014The 14th International Conference Automata and Formal Languages (AFL 2014) was held in Szeged, Hungary, from the 27th to the 29th of May, 2014. The conference was organized by the Department of Foundations of Computer Science of the University of Szeged. ... More

On the luminosity-redshift relation in brane-worlds with cosmological constantJun 27 2006In this paper we calculate the luminosity distance - redshift relation for a special type of flat Friedmann brane with cosmological constant. This special case is singled out by its simplicity, the luminosity distance being given in terms of elementary ... More

Perturbations of rotating cosmological black holesNov 18 2002Nov 25 2002Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.

Super-d-complexity of finite wordsApr 22 2011In this paper we introduce and study a new complexity measure for finite words. For positive integer $d$ special scattered subwords, called super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are defined. We give methods to compute super-$d$-complexity ... More

On arc-disjoint Hamiltonian cycles in De Bruijn graphsMar 07 2010Dec 30 2013We give two equivalent formulations of a conjecture [2,4] on the number of arc-disjoint Hamiltonian cycles in De Bruijn graphs.

Thermodynamic model for electron emission and negative- and positive-ion formation in keV molecular collisionsAug 18 2016A statistical-type model is developed to describe the ion production and electron emission in collisions of (molecular) ions with atoms. The model is based on the Boltzmann population of the bound electronic energy levels of the quasi molecule formed ... More

2-cancellative hypergraphs and codesMar 10 2011A family of sets F (and the corresponding family of 0-1 vectors) is called t-cancellative if for all distict t+2 members A_1,... A_t and B,C from F the union of A_1,..., A_t and B differs from the union of A_1, ..., A_t and C. Let c(n,t) be the size of ... More

On scattered subword complexityApr 22 2011Special scattered subwords, in which the gaps are of length from a given set, are defined. The scattered subword complexity, which is the number of such scattered subwords, is computed for rainbow words.

Modelling dynamic programming problems by generalized d-graphsNov 30 2010In this paper we introduce the concept of generalized d-graph (admitting cycles) as special dependency-graphs for modelling dynamic programming (DP) problems. We describe the d-graph versions of three famous single-source shortest algorithms (The algorithm ... More

G_{δσδ} Haar null sets without G_δ hulls in Z^ωOct 21 2016We show that in the non-locally-compact abelian Polish group Z^{\omega} there exists a \Pi^0_4 Haar null set that is not contained in any \Pi^0_2 Haar null set. This partially answers a question of M. Elekes and Z. Vidny\'anszky.

Degeneracy induced scaling of the correlation length for periodic modelsApr 02 2012Jun 27 2012The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition ... 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

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

Scattering of charged particles on two spatially separated time-periodic optical fieldsJun 29 2018We consider a monoenergetic beam of moving charged particles interacting with two separated oscillating electric fields. Time-periodic linear potential is assumed to model the light-particle interaction using a nonrelativistic, quantum mechanical description ... More

Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI modelFeb 21 2011We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based ... More

Lectures on renormalization and asymptotic safetyNov 17 2012Aug 13 2014A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and ... 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

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.

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.

A Subdirect Decomposition of a Semigroup of all Fuzzy Sets of a SemigroupMar 12 2018A mapping from a semigroup $S$ to the unit interval $[0, 1]$ is called a fuzzy set of $S$. It is known that the set ${\cal F}(S)$ of all fuzzy sets of a semigroup $S$ is a semigroup under the operation $\circ$ defined by \[(f\circ g)(s)=\begin{cases} ... More

On Special Semigroups Derived From an Arbitrary SemigroupOct 18 2015Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of $\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation $\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form a semigroup which is denoted ... More

Notes on a problem on weakly exponential $Δ$-semigroupsMay 23 2013Aug 29 2015A semigroup $S$ is called a weakly exponential semigroup if, for every couple $(a,b)\in S\times S$ and every positive integer $n$, there is a non-negative integer $m$ such that $(ab)^{n+m}=a^nb^n(ab)^m=(ab)^ma^nb^n$. A semigroup $S$ is called a $\Delta$-semigroup ... More

Sum of embedded submanifoldsMay 10 2017In an $n$-manifold $X$ each element of $H_{n-1}(X; \mathbb{Z}_2)$ can be represented by an embedded codimension-1 submanifold. Hence for any two such submanifolds there is a third one that represents the sum of their homology classes. We construct such ... 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.

Parton shower evolution with subleading colorFeb 20 2012Jun 14 2012Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color approximation, which is the leading term in an expansion in powers of $1/N_c^2$, where $N_c = 3$ is the number ... 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

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

Generalized eccentric vs. true anomaly parametrizations in the perturbed Keplerian motionOct 10 2006The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly parametrization ... More

Irradiated closed Friedmann brane-worldsOct 10 2006We consider the evolution of a closed Friedmann brane irradiated by a bulk black hole. Both absorption on the brane and transmission across the brane are allowed, the latter representing a generalization over a previously studied model. Without transmission, ... More

The history of degenerate (bipartite) extremal graph problemsJun 21 2013Jun 29 2013This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions. ... More

About the projective Finsler metrizability: First steps in the non-isotropic caseMay 20 2017We consider the projective Finsler metrizability problem: under what conditions the solutions of a given system of second-order ordinary differential equations (SODE) coincide with the geodesics of a Finsler metric, as oriented curves. SODEs with isotropic ... More

About the integrability of the Rapcsák equationMay 19 2015In [17] A. Rapcs\'ak obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential equations. In this paper we investigate the integrability of the Rapcs\'ak system, consisting of ... More

Naively Haar null sets in Polish groupsAug 10 2015Let $(G,\cdot)$ be a Polish group. We say that a set $X \subset G$ is Haar null if there exists a universally measurable set $U \supset X$ and a Borel probability measure $\mu$ such that for every $g, h \in G$ we have $\mu(gUh)=0$. We call a set $X$ naively ... More

Nuclear-resonant electron scatteringApr 07 2008We investigate nuclear-resonant electron scattering as occurring in the two-step process of nuclear excitation by electron capture (NEEC) followed by internal conversion. The nuclear excitation and decay are treated by a phenomenological collective model ... More

Covering complete partite hypergraphs by monochromatic componentsApr 11 2016A well-known special case of a conjecture attributed to Ryser states that k-partite intersecting hypergraphs have transversals of at most k-1 vertices. An equivalent form was formulated by Gy\'arf\'as: if the edges of a complete graph K are colored with ... More

Coding objects related to Catalan numbersMar 06 2010A coding method using binary sequences is presented for different computation problems related to Catalan numbers. This method proves in a very easy way the equivalence of these problems.

A complexity problem for Borel graphsOct 13 2017Dec 09 2018We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift graph on $[\mathbb{N}]^{<\mathbb{N}}$ with finite (or, equivalently, $\leq ... More

Geometric inequalities in spherically symmetric spacetimesJul 01 2016ADM mass is usually preferred against using quasi-local notions of mass in deriving geometric inequalities. We are interested in testing if usage of quasi-local mass provide any benefits. In spherical symmetry there is a highly accepted notion: the Misner-Sharp ... More

New tools in GeoGebra offering novel opportunities to teach loci and envelopesMay 30 2016GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians and programmers ... More

The Assembly of Supermassive Black Holes at High RedshiftsJul 29 2008Apr 28 2009The supermassive black holes (SMBHs) massive enough to power the bright redshift ~6 quasars observed in the Sloan Digital Sky Survey (SDSS) are thought to have assembled by mergers and/or gas accretion from less massive "seed" BHs. If the seeds are the ... More

Sprays metrizable by Finsler functions of constant flag curvatureDec 06 2012In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem we provide the necessary and sufficient conditions that can be used to decide whether ... More

Measures and functions with prescribed homogeneous multifractal spectrumFeb 11 2013In this paper we construct measures supported in $[0,1]$ with prescribed multifractal spectrum. Moreover, these measures are homogeneously multifractal (HM, for short), in the sense that their restriction on any subinterval of $[0,1]$ has the same multifractal ... More

A Fixed Point Theorem for Non-Monotonic FunctionsFeb 03 2014Feb 07 2015We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of monotonic functions ... More

Proceedings 8th Workshop on Fixed Points in Computer ScienceFeb 14 2012This volume contains the proceedings of the Eighth Workshop on Fixed Points in Computer Science which took place on 24 March 2012 in Tallinn, Estonia as an ETAPS-affiliated workshop. Past workshops have been held in Brno (1998, MFCS/CSL workshop), Paris ... More

A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms IJul 03 2008In previous articles we outlined a subtraction scheme for regularizing doubly-real emission and real-virtual emission in next-to-next-to-leading order (NNLO) calculations of jet cross sections in electron-positron annihilation. In order to find the NNLO ... More

List colorings with distinct list sizes, the case of complete bipartite graphsNov 01 2011Let $f:V \rightarrow \mathbb{N}$ be a function on the vertex set of the graph $G=(V,E)$. The graph $G$ is {\em $f$-choosable} if for every collection of lists with list sizes specified by $f$ there is a proper coloring using colors from the lists. The ... More

Composition Closure of Linear Extended Top-down Tree TransducersJan 08 2013Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, ... More

Isentropes and Lyapunov exponentsApr 05 2018We consider skew tent maps $T_{{\alpha}, {\beta}}(x)$ such that $( {\alpha}, {\beta})\in[0,1]^{2}$ is the turning point of $T {_ { {\alpha}, {\beta}}}$, that is, $T_{{\alpha}, {\beta}}=\frac{{\beta}}{{\alpha}}x$ for $0\leq x \leq {\alpha}$ and $T_{{\alpha}, ... More

On 3-uniform hypergraphs without a cycle of a given lengthDec 27 2014Dec 30 2014We study the maximum number of hyperedges in a 3-uniform hypergraph on $n$ vertices that does not contain a Berge cycle of a given length $\ell$. In particular we prove that the upper bound for $C_{2k+1}$-free hypergraphs is of the order $O(k^2n^{1+1/k})$, ... More

Multifractal properties of typical convex functionsApr 10 2017Oct 25 2017We study the singularity (multifractal) spectrum of continuous convex functions defined on $[0,1]^{d}$. Let $E_f({h}) $ be the set of points at which $f$ has a pointwise exponent equal to $h$. We first obtain general upper bounds for the Hausdorff dimension ... More

Can We Detect the Anisotropic Shapes of Quasar HII Regions During Reionization Through The Small-Scale Redshifted 21cm Power Spectrum?May 07 2007Sep 17 2007Light travel time delays distort the apparent shapes of HII regions surrounding bright quasars during early stages of cosmic reionization. Individual HII regions may remain undetectable in forthcoming redshifted 21 cm experiments. However, the systematic ... More

QCD Corrections to Photon Production in Association with Hadrons in $e^+e^-$ AnnihilationJul 10 1992A detailed investigation of the theoretical ambiguities present in the QCD description of photon production in $e^+e^-$ annihilation is given. It is pointed out that in a well-defined perturbative analysis it is necessary to subtract the quark-photon ... More

Petrov types of slowly rotating fluid ballsNov 18 1999Jun 11 2000Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the ... More

Hyers--Ulam stability of derivations and linear functionsJul 02 2013In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, ... More

Relaxation times in the ASEP model using a DMRG methodApr 03 2002Dec 11 2002We compute the largest relaxation times for the totally asymmetric exclusion process (TASEP) with open boundary conditions with a DMRG method. This allows us to reach much larger system sizes than in previous numerical studies. We are then able to show ... More

A change of variables theorem for the multidimensional Riemann integralApr 15 2008The most general change of variables theorem for the Riemann integral of functions of a single variable has been published in 1961 (by Kestelman). In this theorem, the substitution is made by an `indefinite integral', that is, by a function of the form ... More

Dimension distortion by projections on Riemannian surfaces of constant curvatureJul 15 2015We apply the theory of Peres and Schlag to obtain estimates for generic Hausdorff dimension distortion under orthogonal projections on simply connected two dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions ... More

A unified approach to equilibrium statistics in closed systems with random dynamicsJun 18 2016In a balanced version of decay and growth processes a simple master equation arrives at a final state including the Poisson, Bernoulli, negative binomial and P\'olya distribution. Such decay and growth rates incorporate a symmetry between the observed ... More

Parity violation effects in the Josephson junction of a $p$-wave superconductorNov 07 2014Feb 16 2015The phenomenon of the parity violation due to weak interaction may be studied with superconducting systems. Previous research considered the case of conventional superconductors. We here theoretically investigate the parity violation effect in an unconventional ... More

Gravitational dynamics in s+1+1 dimensionsJul 06 2005Mar 06 2006We present the concomitant decomposition of an (s+2)-dimensional spacetime both with respect to a timelike and a spacelike direction. The formalism we develop is suited for the study of the initial value problem and for canonical gravitational dynamics ... More

On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional caseDec 21 2007Jun 26 2008The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is not a representant of ... More

Triple point in the $O(2)$ ghost model with higher-order gradient termAug 06 2016The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field $\phi$ has been investigated in Wegner and Houghton's renormalization group framework, including higher-derivatives in the kinetic term. ... More

The Thickness of High-Redshift Quasar Ionization Fronts as a Constraint on the Ionizing Spectral Energy DistributionDec 20 2007Jan 10 2008High-redshift quasars (z >~ 6) drive ionization fronts into the intergalactic medium (IGM). If the thickness of the front can be measured, it can provide a novel constraint on the ionizing spectral energy distribution (SED). Here we follow the propagation ... More

GeoGebra Tools with Proof CapabilitiesMar 03 2016We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a result, a number ... More

Haar null and Haar meager sets: a survey and new resultsJun 21 2016We survey results about Haar null subsets of (not neccessarily locally compact) Polish groups, focusing on the methods that can be applied easily in proving new results. We also discuss alternative definitions and show some counterexamples for plausible, ... More

Schreier decomposition of loopsMay 13 2015The aims of this paper are to find algebraic characterizations of Schreier loops and explore the limits of the non-associative generalization of the theory of Schreier extensions. A loop can have Schreier decomposition with respect to a normal subgroup ... More

Rogue active regions and the inherent unpredictability of the solar dynamoApr 10 2018New developments in surface flux transport modeling and theory of flux transport dynamos have given rise to the notion that certain large active regions with anomalous properties (location, tilt angle and/or Hale/non-Hale character) may have a major impact ... More

Interplay of fixed points in scalar modelsDec 14 2010Oct 25 2013We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified ... More

Functional renormalization group for quantized anharmonic oscillatorSep 21 2010Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of the gradient ... More

EPR Steering inequalities with Communication AssistanceMar 16 2016Mar 22 2016In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model ... More

The kinetic energy operator in the subspaces of wavelet analysisJul 18 2007At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is ``canonically'' chosen as the projection of the operator $-\Delta/2$ onto the subspace of the given resolution. It ... More

Higher Markov and Bernstein inequalities and fast decreasing polynomials with prescribed zerosApr 24 2017Jul 21 2017Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities we assume that ... 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

A class of finite simple Bol loops of exponent 2Sep 28 2007In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by $S_5$. The construction uses the description of the structure of ... 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

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

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 Abel map for surface singularities III. Elliptic germsFeb 20 2019If $(\widetilde{X},E)\to (X,o)$ is the resolution of a complex normal surface singularity and $c_1:{\rm Pic}(\widetilde{X})\to H^2(\widetilde{X},{\mathbb Z})$ is the Chern class map, then ${\rm Pic}^{l'}(\widetilde{X}):= c_1^{-1}(l')$ has a (Brill--Noether ... 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

Data-driven Analysis of Complex Networks and their Model-generated CounterpartsOct 19 2018Oct 25 2018Data-driven analysis of complex networks has been in the focus of research for decades. An important question is to discover the relation between various network characteristics in real-world networks and how these relationships vary across network domains. ... More

Refinement trajectory and determination of eigenstates by a wavelet based adaptive methodAug 10 2006The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in ... More