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The Complete Lattice of Erdős-Menger SeparationsApr 12 2019F. Escalante and T. Gallai studied in the seventies the structure of different kind of separations and cuts between a vertex pair in a (possibly infinite) graph. One of their results is that if there is a finite separation, then the optimal (i.e. minimal ... More

Highly connected infinite digraphs without edge-disjoint back and forth paths between a certain vertex pairMay 01 2017We construct for all $ k\in \mathbb{N} $ a $ k $-edge-connected digraph $ D $ with $ s,t\in V(D) $ such that there are no edge-disjoint $ s \rightarrow t $ and $t\rightarrow s $ paths. We use in our construction "self-similar" graphs which technique could ... More

Vertex-flames of countable digraphs preserving an Aharoni-Berger cut for each vertexOct 11 2017In the finite case an $ r $-vertex-flame is a finite directed graph $ F $ with $ r\in V(F) $ in which for every vertex $ v\neq r $ the indegree of $ v $ is equal to $ \kappa_F(r,v) $ (the local connectivity from $ r $ to $ v $ in $ F $). G. Calvillo Vives ... More

On partitioning the edges of an infinite digraph into dicyclesApr 28 2017Oct 12 2018Nash-Williams proved in \cite{nash1960decomposition} that for an undirected graph $ G $ the set $ E(G) $ can be partitioned into cycles if and only if every cut has either even or infinite number of edges. C. Thomassen gave a simpler proof for this and ... More

Gomory-Hu trees of infinite graphs with finite total weightApr 23 2017Gomory and Hu proved that if $ G $ is a finite graph with non-negative weights on its edges, then there exists a tree $ T $ (called now Gomory-Hu tree) on $ V(G) $ such that for all $ u\neq v\in V(G) $ there is an $ e\in E(T) $ such that the two components ... More

Edmonds' Branching Theorem in Digraphs without Forward-infinite PathsMay 01 2017Let $ D $ be a finite digraph, and let $ V_0,\dots,V_{k-1} $ be nonempty subsets of $ V(D) $. The (strong form of) Edmonds' branching theorem states thatthere are pairwise edge-disjoint spanning branchings $ \mathcal{B}_0,\dots, \mathcal{B}_{k-1} $ in ... More

On partitioning the edges of an infinite digraph into directed cyclesApr 28 2017Nash-Williams proved in that for an undirected graph $ G $ the set $ E(G) $ can be partitioned into cycles if and only if every cut has either even or infinite number of edges. At the and of his article he stated the following directed analogue of his ... More

Vertex-flames in countable rooted digraphs preserving an Erdős-Menger separation for each vertexOct 11 2017Feb 12 2019From a theorem of Lov\'asz (Theorem 2 of \cite{lovasz1973connectivity}) it follows that if $ D $ is a finite digraph with $ r\in V(D) $, then there is a spanning subdigraph $ E $ of $ D $ such that for every vertex $ v\neq r $ the following three quantities ... More

On partitioning the edges of an infinite digraph into dicyclesApr 28 2017Feb 12 2019Nash-Williams proved in \cite{nash1960decomposition} that for an undirected graph $ G $ the set $ E(G) $ can be partitioned into cycles if and only if every cut has either even or infinite number of edges. C. Thomassen gave a simpler proof for this and ... More

Independent and maximal branching packing in infinite matroid-rooted digraphsMay 02 2017We prove a common generalization of the maximal independent arborescence packing theorem of Cs. Kir\'aly and two of our earlier works about packing branchings in infinite digraphs.

T-joins in infinite graphs as edge-disjoint system of paths matching the vertices in $ T $Apr 24 2017We characterize the class of infinite connected graphs $ G $ for which there exists a $ T $-join for any choice of an infinite $ T \subseteq V(G) $. We also show that the following well-known fact remains true in the infinite case. If $ G $ is connected ... More

Countable Menger theorem with finitary matroid constraints on the ingoing edgesApr 30 2017We present a strengthening of the countable Menger theorem (edge version) of R. Aharoni. Let $ D=(V,A) $ be a countable digraph with $ s\neq t\in V $ and let $\mathcal{M}=\bigoplus_{v\in V}\mathcal{M}_v $ be a matroid on $ A $ where $ \mathcal{M}_v $ ... More

King-serf duo by monochromatic paths in k-edge-coloured tournamentsMay 02 2017An open conjecture of Erd\H{o}s states that for every positive integer $k$ there is a (least) positive integer $f(k)$ so that whenever a tournament has its edges colored with $k$ colors, there exists a set $S$ of at most $f(k)$ vertices so that every ... More

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

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

Invariance of separability probability over reduced states in 4x4 bipartite systemsOct 05 2016Jan 04 2017The geometric separability probability of composite quantum systems is extensively studied in the last decades. One of most simple but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit quantum states ... More

Volume of the space of qubit channels and some new results about the distribution of the quantum Dobrushin coefficientJul 05 2016The simplest building blocks for quantum computations are the qbit-qbit quantum channels. In this paper we analyse the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. ... More

Invariance of separability probability over reduced states in 4x4 bipartite systemsOct 05 2016The geometric separability probability of composite quantum systems is extensively studied in the last decades. One of most simple but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit quantum states ... More

Means of unbounded setsFeb 05 2018Feb 25 2018We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be extended to ... More

Means of infinite sets IIISep 26 2018We study various topics, e.g. accumulation points by a mean, two types of derivative by a mean, two new continuity and a boundedness concepts, we construct new means from old ones, finally we investigate the limit of means.

The Lefschetz Property for Componentwise Linear Ideals and Gotzmann IdealsJul 16 2003For standard graded Artinian $K$-algebras defined by componentwise linear ideals and Gotzmann ideals, we give conditions for the weak Lefschetz property in terms of numerical invariants of the defining ideals.

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

Invariance of separability probability over reduced states in 4x4 bipartite systemsOct 05 2016Oct 15 2016The geometric separability probability of composite quantum systems is extensively studied in the last decades. One of most simple but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit quantum states ... More

On the notation of quantum copulasFeb 22 2019Working with multivariate probability distributions Sklar introduced the notion of copula in 1959, which turned out to be a key concept to understand the structure of distributions of composite systems. Roughly speaking Sklar proved that a joint distribution ... More

Volume of the space of qubit-qubit channels and state transformations under random quantum channelsAug 23 2017The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states ... More

Refinement of Robertson-type uncertainty principles with geometric interpretationNov 20 2013May 21 2015A generalisation of the classical covariance for quantum mechanical observables has previously been presented by Gibilisco, Hiai and Petz. Gibilisco and Isola has proved that the usual quantum covariance gives the sharpest inequalities for the determinants ... More

Be7(p,gamma)B8 and the high-energy solar neutrino fluxApr 23 1997The importance of the Be7(p,gamma)B8 reaction in predicting the high-energy solar neutrino flux is discussed. I present a microscopic eight-body model and a potential model for the calculation of the Be7(p,gamma)B8 cross section.

Points accessible in average by rearrangement of sequences IDec 14 2018Mar 04 2019We investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible points.

On the monotonicity conjecture for the curvature of the Kubo-Mori metricOct 29 2003The canonical correlation or Kubo-Mori scalar product on the state space of a finite quantum system is a natural generalization of the classical Fisher metric. This metric is induced by the von Neumann entropy or the relative entropy of the quantum mechanical ... 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

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

The complexity of the equation solvability problem over semipattern groupsMar 18 2016The complexity of the equation solvability problem is known for nilpotent groups, for not solvable groups and for some semidirect products of Abelian groups. We provide a new polynomial time algorithm for deciding the equation solvability problem over ... 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

Universality of vector sequences and universality of Tverberg partitionsMay 18 2018A result of Rosenthal says that for every $q>1$ and $n \in \mathbb{N}$ there is $N \in \mathbb{N}$ such that every sequence of $N$ distinct positive numbers contains, after a suitable translation and possible multiplication by $-1$, a subsequence $a_1,\ldots,a_n$ ... More

Few-body resonances in light nucleiOct 31 2000We have localized several few-body resonances in light nuclei, using methods which can properly handle two- or three-body resonant states. Among other results, we predict the existence of a three-neutron resonance, small spin-orbit splittings between ... More

A Dynamic Solar Core Model: On the Activity-Related Changes of the Neutrino FluxesOct 08 1998The energy sources of the Sun may actually involve a thermonuclear runaway energy source present in stellar energy producing regions. I consider the conjectures of the derived model for the solar neutrino fluxes in case of a solar core allowed to vary ... More

On mean-setsAug 11 2018We introduce a new type of means. It is new in two ways: its domain consists of sets and its values are sets too. We investigate the properties and behavior of such generalization. We also present many naturally arisen examples for such means.

Measuring sets by meansAug 16 2017We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get another way ... 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

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

On the geometry of generalized Gaussian distributionsJun 05 2007In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some methods to endow ... More

On the cardinality of $π(δ)$Jan 18 2019We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least $2^{2^{\aleph_0}}$ if there exist at least two transitive quasi-uniformities in the class. The transitive elements of $\pi(\delta)$ are characterized ... More

Means of infinite sets IIMay 17 2017Sep 25 2018We continue the study of how one can define means of infinite sets. We introduce many new properties, investigate their relations to each other and how they can typify a mean. We collect the properties in property groups e.g. for monotonicity and continuity ... More

Means of infinite sets IApr 24 2017Jun 06 2018We open a new field on how one can define means on infinite sets. We investigate many different ways on how such means can be constructed. One method is based on sequences of ideals, other deals with accumulation points, one uses isolated points, other ... More

Dimension structuresNov 02 2017Dec 14 2017We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.

Measures by means, means by measuresJun 12 2017Jul 31 2018We construct measure which determines an ordinary mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also study the properties ... More

Extending means to several variablesApr 05 2017Oct 31 2018We begin the study of how to extend few variable means to several variable ones and how to shrink means of several variables to less variables. With the help of one of the techniques we show that it is enough to check an inequality between two quasi-arithmetic ... More

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.

Extending means to several variablesApr 05 2017We begin the study of how to extend few variable means to several variable ones and how to shrink means of several variables to less variables. With the help of one of the techniques we show that it is enough to check an inequality between two quasi-arithmetic ... More

Importance of core polarization in halo nucleiApr 23 1997A comment on the importance of core polarization in halo nuclei. I point out that although core polarization is suppressed in neutron halos, it plays an essential role in their binding mechanism.

Novelty and Foreseeing Research Trends; The Case of Astrophysics and AstronomyApr 08 2018Metrics based on reference lists of research articles or on keywords have been used to predict citation impact. The concept behind such metrics is that original ideas stem from the reconfiguration of the structure of past knowledge, and therefore atypical ... More

Volume of the quantum mechanical state spaceApr 14 2006Apr 27 2006The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant ... More

On the curvature of the quantum state space with pull-back metricsApr 14 2006The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these Riemannian manifolds. ... More

Monotone Riemannian metrics on density matrices with non-monotone scalar curvatureMay 29 2003The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted as an average ... More

Uncertainty principle with quantum Fisher informationJul 08 2007Oct 11 2007In this paper we prove a nontrivial lower bound for the determinant of the covariance matrix of quantum mechanical observables, which was conjectured by Gibilisco, Isola and Imparato. The lower bound is given in terms of the commutator of the state and ... More

Large nilpotent subgroups of finite subgroups of the birational automorphism group of a varietyMar 18 2019We call a group $G$ nilpotently Jordan of class at most $c$ $(c\in\mathbb{N})$ if there exists a constant $J\in\mathbb{Z}^+$ such that every finite subgroup $H\leqq G$ contains a nilpotent subgroup $K\leqq H$ of class at most $c$ and index at most $J$. ... More

Remarks on GraphonsJan 14 2018The notion of the graphon (a symmetric measurable fuzzy set of $[0, 1]^2$) was introduced by L. Lov\'asz and B. Szegedy in 2006 to describe limit objects of convergent sequences of dense graphs. In their investigation the integral \[t(F,W)=\int _{[0, ... More

Short note on the perturbation of operators with dyadic productsOct 07 2008In this paper we use abstract vector spaces and their duals without any canonical basis. Some of our results can be extended to infinite dimensional vector spaces too, but here we consider only finite dimensional spaces. We focus on a general perturbation ... More

Parameter Tuning of Three-Flavor Dynamical Anisotropic Clover ActionSep 28 2007In this work, we perform parameter tuning with dynamical anisotropic clover lattices using the Schr\"odinger functional and stout-smearing in the fermion field. We find that $\xi_R/\xi_0$ is relatively close to 1 in our parameter search, which allows ... 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

Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link SmearingMar 27 2008Mar 27 2008In this work we perform the parameter tuning of three flavors of dynamical clover quarks on anisotropic lattices. The fermion action uses three-dimensional spatial stout-link smearing. The gauge anisotropy is determined in a small box with Schr\"odinger ... More

Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potentialApr 04 2016Jul 02 2016We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use ... More

Phason modes in spin-density wave in the presence of long-range Coulomb interactionNov 24 1993We study the effect of long-range Coulomb interaction on the phason in spin-density wave (SDW) within mean field theory. In the longitudinal limit and in the absence of SDW pinning the phason is completely absorbed by the plasmon due to the Anderson-Higgs ... More

Discretized rotation has infinitely many periodic orbitsJun 18 2012Dec 20 2012For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.

An improvement on the trivial lower bound for the depth of a centerlineMar 03 2016We prove that for every $d \geq 3$ and for every probability measure $\mu$ in $\mathbb R^d$ there exists a (1-dimensional) line $\ell$ with depth at least $\frac{1}{d} + \frac{1}{3d^3}$.

Unsupervised 3D Shape Learning from Image Collections in the WildNov 26 2018Nov 27 2018We present a method to learn the 3D surface of objects directly from a collection of images. Previous work achieved this capability by exploiting additional manual annotation, such as object pose, 3D surface templates, temporal continuity of videos, manually ... More

Punishment and inspection for governing the commons in a feedback-evolving gameJul 15 2018Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of ... 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.

Seeing beyond the light: Vison and photon electrodynamics in quantum spin iceFeb 22 2019Understanding the nature and behaviour of excitations in quantum spin liquids, and in topological phases of matter in general, is of fundamental importance, and has proven crucial for experimental detection and characterisation of candidate materials. ... 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

Pairwise preferences in the stable marriage problemSep 30 2018We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to declare a draw ... More

Social diversity and promotion of cooperation in the spatial prisoner's dilemma gameAug 13 2007Jan 17 2008The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma ... More

Cluster mean-field study of the parity conserving phase transitionFeb 03 2005May 02 2005The phase transition of the even offspringed branching and annihilating random walk is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing to reach zero branching rate a phase transition can be seen for any N <= 12.The ... More

Phase transitions for rock-scissors-paper game on different networksJul 16 2004Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness ... More

Evolutionary solving of the debts' clearing problemFeb 26 2014The debts' clearing problem is about clearing all the debts in a group of n entities (persons, companies etc.) using a minimal number of money transaction operations. The problem is known to be NP-hard in the strong sense. As for many intractable problems, ... More

Comment on "Fermion production in a magnetic field in a de Sitter universe"Oct 25 2016We point out that the transition probabilities used in a recent perturbative calculation of pair creation in an external magnetic field in the expanding de Sitter space with the $in$ and $out$ fermion states defined by the Bunch-Davies modes [C. Crucean ... More

On the dynamics of the Pappus-Steiner mapAug 14 2017We extract a two-dimensional dynamical system from the theorems of Pappus and Steiner in classical projective geometry. We calculate an explicit formula for this system, and study its elementary geometric properties. Then we use Artin reciprocity to characterise ... More

Electronic Raman scattering in unconventional density wavesDec 03 2003Nov 27 2005We investigate the electronic Raman scattering in pure, quasi-one dimensional conductors with density wave ground state. In particular, we develop the theory of light-scattering on spin and charge density waves, both conventional and unconventional. We ... More

Non-power-law universality in one-dimensional quasicrystalsMar 26 2018Oct 08 2018We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground state, usually ... More

Number systems over ordersAug 16 2017May 10 2018Let $\mathbb{K}$ be a number field of degree $k$ and let $\mathcal{O}$ be an order in $\mathbb{K}$. A \emph{generalized number system over $\mathcal{O}$} (GNS for short) is a pair $(p,\mathcal{D})$ where $p \in \mathcal{O}[x]$ is monic and $\mathcal{D}\subset\mathcal{O}$ ... More

Reliable estimation of the radius of convergence in finite density QCDApr 03 2019We study different estimators of the radius of convergence of the Taylor series of the pressure in finite density QCD. We adopt the approach in which the radius of convergence is estimated first in a finite volume, and the infinite-volume limit is taken ... More

Forbidden Families of Minimal Quadratic and Cubic ConfigurationsMar 16 2017A matrix is \emph{simple} if it is a (0,1)-matrix and there are no repeated columns. Given a (0,1)-matrix $F$, we say a matrix $A$ has $F$ as a \emph{configuration}, denoted $F\prec A$, if there is a submatrix of $A$ which is a row and column permutation ... More

An improvement on the Rado bound for the centerline depthMar 03 2016Oct 16 2017Let $\mu$ be a Borel probability measure in $\mathbb R^d$. For a $k$-flat $\alpha$ consider the value $\inf \mu(H)$, where $H$ runs through all half-spaces containing $\alpha$. This infimum is called the half-space depth of $\alpha$. Bukh, Matou\v{s}ek ... More

On the Connection of Gamma-Ray Bursts and X-Ray Flashes in the BATSE and RHESSI DatabasesOct 25 2016Classification of gamma-ray bursts (GRBs) into groups has been intensively studied by various statistical tests in previous years. It has been suggested that there was a distinct group of GRBs, beyond the long and short ones, with intermediate durations. ... More

On the number of $p'$-degree characters in a finite groupDec 24 2014Let $p$ be a prime divisor of the order of a finite group $G$. Then $G$ has at least $2 \sqrt{p-1}$ complex irreducible characters of degrees prime to $p$. In case $p$ is a prime with $\sqrt{p-1}$ an integer this bound is sharp for infinitely many groups ... More

Finite Computational Structures and ImplementationsOct 19 2016What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only partial answers to ... More

Phase transition in a double branching annihilating random walkMay 27 2016This paper investigates the long-time behavior of double branching annihilating random walkers with nearest-neighbor dependent rates. The system consists of even number of particles which can execute nearest-neighbor random walk and they can as well give ... More

Character degree sums of finite groupsMay 13 2013Sep 14 2013We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.

Colourings of the Cartesian Product of Graphs and Multiplicative Sidon SetsNov 10 2005Oct 20 2008Let $F$ be a family of connected bipartite graphs, each with at least three vertices. A proper vertex colouring of a graph $G$ with no bichromatic subgraph in $F$ is $\F$-free. The $F$-free chromatic number $\chi(G,F)$ of a graph $G$ is the minimum number ... More

The Big-Line-Big-Clique Conjecture is False for Infinite Point SetsAug 18 2010The big-line-big-clique conjecture states that for all $k,\ell\geq2$ there is an integer $n$ such that every finite set of at least $n$ points in the plane contains $\ell$ collinear points or $k$ pairwise visible points. We show that this conjecture is ... More

Normal coverings of linear groupsJun 19 2012For a non-cyclic finite group $G$, let $\gamma(G)$ denote the smallest number of conjugacy classes of proper subgroups of $G$ needed to cover $G$. Bubboloni, Praeger and Spiga, motivated by questions in number theory, have recently established that $\gamma(S_n)$ ... More

Average dimension of fixed point spaces with applicationsJan 21 2010Let $G$ be a finite group, $F$ a field, and $V$ a finite dimensional $FG$-module such that $G$ has no trivial composition factor on $V$. Then the arithmetic average dimension of the fixed point spaces of elements of $G$ on $V$ is at most $(1/p) \dim V$ ... More

On the number of conjugacy classes of $π$-elements in finite groupsJun 04 2013Jan 18 2014Let $G$ be a finite group and $\pi$ be a set of primes. We show that if the number of conjugacy classes of $\pi$-elements in $G$ is larger than $5/8$ times the $\pi$-part of $|G|$ then $G$ possesses an abelian Hall $\pi$-subgroup which meets every conjugacy ... More

On Visibility and BlockersDec 07 2009This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.

How to initialize a second class particle?Oct 16 2015Feb 06 2017We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively (including zero-range, ... More