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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

Uncountable dichromatic number without short directed cyclesMay 02 2019May 24 2019A. Hajnal and P. Erd\H{o}s proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example $ C_4 $ (among other obligatory subgraphs). It was shown recently by D. T. Soukup that, in contrast of the undirected ... 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

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

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

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

Uncountable dichromatic number without short directed cyclesMay 02 2019May 11 2019A. Hajnal and P. Erd\H{o}s proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example $ C_4 $ (among other obligatory subgraphs). It was shown recently by D. T. Soukup that, in contrast of the undirected ... More

Uncountable dichromatic number without short directed cyclesMay 02 2019A. Hajnal and P. Erd\H{o}s proved that a graph with uncountable chromatic number cannot avoid short cycles, it must contain for example $ C_4 $ (among other obligatory subgraphs). It was shown recently by D. T. Soukup that, in contrast of the undirected ... 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

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

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

Vertex-flames in countable rooted digraphs preserving an Erdős-Menger separation for each vertexOct 11 2017Apr 09 2019It follows from a theorem of Lov\'asz 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 quantities are equal: the local connectivity from $ r $ ... 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

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

Prime congruences of idempotent semirings and a Nullstellensatz for tropical polynomialsAug 17 2014Sep 13 2017A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ideals of commutative rings. In order to establish a good notion of radical ... 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 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

Measure on gauge invariant symmetric normsApr 16 2015The concept of a gauge invariant symmetric random norm is elaborated in this paper. We introduce norm processes and show that this kind of stochastic processes are closely related to gauge invariant symmetric random norms. We construct a gauge invariant ... 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

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 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

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

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

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

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

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

Fundamental Complexity Measures of LifeNov 16 2011At present, there is a great deal of confusion regarding complexity and its measures (reviews on complexity measures are found in, e.g. Lloyd, 2001 and Shalizi, 2006 and more references therein). Moreover, there is also confusion regarding the nature ... 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

Traffic Dynamics of Computer NetworksOct 07 2008Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I studied the ... More

New type astrophysical solution to the solar neutrino problems and its predicitons to the SNOMay 10 2000The anomalously slow rotation of the solar core is just one from a remarkable lists of fundamental indications showing that the solar core is somehow coupled to the surface activity cycle. On the other hand, the atmospheric, LSND and solar neutrino problems ... More

The dynamic energy source of the Sun and the duplicity of the stellar energy productionMar 04 1998Some possible ways of the energy production with fusion reactions in the Sun was explored theoretically in the first half of this century. Nowadays it is a standard view that the Sun produces its energy on a uniform level. I point out, that in the stellar ... More

Off-shell effects in the energy dependence of the Be7(p,gamma)B8 astrophysical S factorOct 28 1996I show that off-shell effects, like antisymmetrization and Be-7 distortions, can significantly influence the energy dependence of the nonresonant Be7(p,gamma)B8 astrophysical S factor at higher energies. The proper treatment of these effects results in ... 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.

Reflexive Unitary Subsemigroups of Left Simple SemigroupsJan 07 2015Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So it is a natural ... 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

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

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

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.

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.

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

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 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

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 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

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

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

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 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

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

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

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

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

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

Number systems over ordersAug 16 2017Let $\mathbb{K}$ be a number field of degree $k$ and let $\mathcal{O}$ be an order in $\mathbb{K}$. A 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

Evolutionary dynamics of cooperation in neutral populationsDec 06 2017Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the formation ... More

Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potentialApr 04 2016Jul 10 2017We 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

Blocking unions of arborescencesJul 03 2015Given a digraph $D=(V,A)$ and a positive integer $k$, a subset $B\subseteq A$ is called a \textbf{$k$-union-arborescence}, if it is the disjoint union of $k$ spanning arborescences. When also arc-costs $c:A\to \mathbb{R}$ are given, minimizing the cost ... 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

Individual wealth-based selection supports cooperation in spatial public goods gamesOct 05 2016In a social dilemma game group members are allowed to decide if they contribute to the joint venture or not. As a consequence, defectors, who do not invest but only enjoy the mutual benefit, prevail and the system evolves onto the tragedy of the common ... More

Collective influence in evolutionary social dilemmasApr 14 2016When evolutionary games are contested in structured populations, the degree of each player in the network plays an important role. If they exist, hubs often determine the fate of the population in remarkable ways. Recent research based on optimal percolation ... More

A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection gamesMay 14 2015As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data. The latter shows that crime is often recurrent, and that crime rates do not respond linearly to ... 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

On Simultaneous PalindromesMar 04 2014Jun 11 2014A palindrome in base $g$ is an integer $N$ that remains the same when its digit expansion in base $g$ is reversed. Let $g$ and $h$ be given distinct integers $>1$. In this paper we discuss how many integers are palindromes in base $g$ and simultaneously ... More

The minimal base size for a p-solvable linear groupOct 21 2013Sep 23 2014Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on $V$ of size at most $2$ unless $q \leq 4$ in which ... 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

Group-size effects on the evolution of cooperation in the spatial public goods gameDec 13 2011We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors. We find that ... More

Local density of states and Friedel oscillation in grapheneSep 15 2010We investigate the local density of states and Friedel oscillation in graphene around a well localized impurity in Born approximation. In our analytical calculations Green's function technique has been used taking into account both the localized atomic ... 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

Thermal metastabilities in the solar coreJan 18 2002Linear stability analysis indicates that solar core is thermally stable for infinitesimal internal perturbations. For the first time, thermal metastabilities are found in the solar core when outer perturbations with significant amplitude are present. ... More

On an implementation of the Solovay-Kitaev algorithmJun 08 2006In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological generating set of $SU(d)$. ... 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

Set-Direct Factorizations of GroupsJul 14 2017Oct 10 2018We consider factorizations $G=XY$ where $G$ is a general group, $X$ and $Y$ are normal subsets of $G$ and any $g\in G$ has a unique representation $g=xy$ with $x\in X$ and $y\in Y$. This definition coincides with the customary and extensively studied ... More

Set-Direct Factorizations of GroupsJul 14 2017We consider factorizations $G=XY$ where $G$ is a general group, $X$ and $Y$ are normal subsets of $G$ and any $g\in G$ has a unique representation $g=xy$ with $x\in X$ and $y\in Y$. This definition coincides with the customary and extensively studied ... 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

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

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

Topological statesJul 05 2019Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit coupling, transition ... 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

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 $\frac{1}{d} + \frac{1}{3d^3}$.

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

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

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

Simplest Cubic Number FieldsFeb 27 2012In this paper we intend to show that certain integers do not occur as the norms of principal ideals in a family of cubic fields studied by Cohn, Shanks, and Ennola. These results will simplify the construction of certain unramified quadratic extensions ... 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

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