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The Origin of Mass in QCD and its RenormalizationApr 16 2019We present in the most general way how the mass scale parameter appears in the QCD ground state. The transversity of the full gluon self-energy has been investigated in detail. We have derived the Schwinger-Dyson equation of motion for the full gluon ... More

Non-extensive Motivated Parton Fragmentation FunctionsNov 05 2018A new form of fragmentation function is presented here, motivated by earlier non-extensive studies of jet fragmentation. We parametrized our Tsallis-like function on pion spectra and compared it to the most common fragmentation function parametrizations. ... More

A 'soft+hard' model for Pion, Kaon, and Proton Spectra and $v_2$ measured in PbPb Collisions at $\sqrt s = 2.76 A$TeVSep 21 2015Hadron spectra measured in high-energy collisions present distributions which can be derived from the non-extensive statistical and thermodynamical phenomena. Based on earlier theoretical developments, it seems, the methods are very applicable for jets ... More

FRG Approach to Nuclear Matter at Extreme ConditionsOct 16 2015Functional renormalization group (FRG) is an exact method for taking into account the effect of quantum fluctuations in the effective action of the system. The FRG method applied to effective theories of nuclear matter yields equation of state which incorporates ... More

Estimating the variation of neutron star observables by symmetric dense nuclear matter propertiesMay 06 2019Recent multi-channel astrophysics observations and the soon-to-be published new measured electromagnetic and gravitation data provide information on the inner structure of the compact stars. These macroscopic observations can significantly increase our ... More

Identified Two-particle Correlations and Quantum Number Conservations in p-p and Pb-Pb Collisions at LHC EnergiesFeb 04 2015In this paper we continue the investigation of the effect of quantum number conservations of pions, kaons, and protons, with very high transverse momenta (up to 25 GeV/c), during parton fragmentation and hadronization in p-p and Pb-Pb collisions at LHC ... More

The Effect of Quantum Fluctuations in the High-Energy Cold Nuclear Equation of State and in Compact Star ObservablesOct 12 2016We present a novel technique to obtain exact equation of state (EoS) by the Functional Renormalization Group (FRG) method, using the expansion of the effective potential in a base of harmonic functions at finite chemical potential. Within this theoretical ... More

Multiplicity Dependence of the Jet Structures in pp Collisions at LHC EnergiesSep 26 2018Oct 09 2018We study the event multiplicity dependence of the jet structure in pp collisions. We present evidence for jet shape modification due to multi-parton interactions using PYTHIA and HIJING++ Monte Carlo (MC) event generators as an input to our analysis. ... More

Application of the Non-extensive Statistical Approach to High Energy Particle CollisionsAug 04 2016In high-energy collisions the number of the created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution ... More

Mass hierarchy and energy scaling of the Tsallis--Pareto parameters in hadron productions at RHIC and LHC energiesOct 25 2017The latest, high-accuracy identified hadron spectra measurements in high-energy nuclear collisions led us to the investigation of the strongly interacting particles and collective effects in small systems. Since microscopical processes result in a statistical ... More

On the discrete Fuglede and Pompeiu problemsJul 08 2018Dec 17 2018We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu ... More

Correspondence of Many-flavor Limit and Kaluza-Klein Degrees of Freedom in the Description of Compact StarsJul 27 2016We present the correspondence between non-interacting multi-hadron fermion star equation of state in the many-flavor limit and the degrees of freedom of a Kaluza\,--\,Klein compact star. Many flavors can be interpreted in this framework as one extra compacti\-fied ... More

Testing a Possible Way of Geometrization of the Strong Interaction by a Kaluza-Klein StarSep 10 2015Geometrization of the fundamental interactions has been extensively studied during the century. The idea of introducing compactified spatial dimensions originated by Kaluza and Klein. Following their approach, several model were built representing quantum ... More

Hadronization within Non-Extensive Approach and the Evolution of the ParametersMay 14 2019We review transverse momentum distributions of various identified charged particles stemming from high energy collisions fitted by various non-extensive distributions as well as by the usual Boltzmann-Gibbs statistics. We investigate the best-fit formula ... More

Hadron Spectra Parameters within the Non-Extensive ApproachMay 21 2019We investigate how the non-extensive approach works in high-energy physics. Transverse momentum ($p_T$) spectra of several hadrons are fitted by various non-extensive momentum distributions and by the Boltzmann--Gibbs statistics.~It is shown that some ... More

Underlying Event Studies for LHC EnergiesJan 21 2011Underlying event was originally defined by the CDF collaboration decades ago. Here we improve the original definition to extend our analysis for events with multiple-jets. We introduce a definition for surrounding rings/belts and based on this definition ... More

Systematic Analysis of the Non-extensive Statistical Approach in High Energy Particle Collisions - Experiment vs. TheoryFeb 09 2017Feb 24 2017The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, ... More

On the Way to Future's High Energy Particle Physics Transport CodeDec 21 2015May 26 2016High Energy Physics (HEP) needs a huge amount of computing resources. In addition data acquisition, transfer, and analysis require a well developed infrastructure too. In order to prove new physics disciplines it is required to higher the luminosity of ... More

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

Introducing HIJING++: the Heavy Ion Monte Carlo Generator for the High-Luminosity LHC EraJan 14 2019Beyond 2025 we will enter the High-Luminosity era of the LHC, right after the upgrades of the third Long Shutdown of the Large Hadron Collider (LHC). The ongoing state-of-the-art experimental instrument upgrades require high-performance simulation support ... More

Testing and improving shear viscous phase space correction modelsJul 04 2017Comparison of hydrodynamic calculations with experimental data inevitably requires a model for converting the fluid to particles. In this work, nonlinear $2\to 2$ kinetic theory is used to assess the overall accuracy of various shear viscous fluid-to-particle ... More

First Results with HIJING++ on High-energy Heavy Ion CollisionsMay 07 2018We present preliminary results with HIJING++ (3.1.1) for identified hadron production in high-energy heavy ion collisions at LHC energies. The recently developed HIJING++ version is based on the latest version of PYTHIA8 and contains all the nuclear effects ... More

First Results with HIJING++ in High-Energy Heavy-Ion CollisionsJan 30 2017First calculated results with the new HIJING++ are presented for identified hadron production in high-energy heavy ion collisions. The recently developed HIJING++ version is based on the latest version of PYTHIA8 and contains all the nuclear effects has ... More

An analogue of the Szemeredi Regularity Lemma for bounded degree graphsSep 17 2008Apr 18 2009We show that a sufficiently large graph of bounded degree can be decomposed into quasi-homogeneous pieces. The result can be viewed as a "finitarization" of the classical Farrell-Varadarajan Ergodic Decomposition Theorem.

Sofic equivalence relationsJun 19 2009We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes' Embedding Conjecture as well as the Measurable Determinant Conjecture of L\"uck, Sauer and Wegner hold for treeable equivalence relations.

Magnetized baryons and the QCD phase diagram: NJL model meets the latticeMay 06 2019We determine the baryon spectrum of 1 + 1 + 1-flavor QCD in the presence of strong background magnetic fields using lattice simulations at physical quark masses for the first time. Our results show a splitting within multiplets according to the electric ... More

Importance weighting without importance weights: An efficient algorithm for combinatorial semi-banditsMar 17 2015Aug 31 2016We propose a sample-efficient alternative for importance weighting for situations where one only has sample access to the probability distribution that generates the observations. Our new method, called Geometric Resampling (GR), is described and analyzed ... More

Controlling Mackey--Glass chaosAug 18 2017The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for chaos control: ... More

A characterization of $n$-associative, monotone, idempotent functions on an interval that have neutral elementsSep 01 2016Oct 16 2017We investigate monotone idempotent $n$-ary semigroups. One of the main result of this article is the generalisation of Czogala-Drewniak Theorem, which describes the idempotent monotone associative functions having neutral element. Furthermore we present ... More

An efficient algorithm for learning with semi-bandit feedbackMay 13 2013We consider the problem of online combinatorial optimization under semi-bandit feedback. The goal of the learner is to sequentially select its actions from a combinatorial decision set so as to minimize its cumulative loss. We propose a learning algorithm ... More

Characterization ofn-associative, monotone,idempotent functions on an interval which haveneutral elementsSep 01 2016We investigate monotone idempotent $n$-ary semigroups. One of the main result of this article is the generalisation of Czogala-Drewniak Theorem, which describes the idempotent monotone associative functions having neutral element. Furthermore we present ... More

Associative idempotent nondecreasing functions are reducibleJul 13 2017Sep 04 2018An $n$-ary associative function is called reducible if it can be written as a composition of a binary associative function. We summarize known results when the function is defined on a chain and is nondecreasing. Our main result shows that associative ... More

Decomposition of balls in $\mathbb{R}^d$Jan 30 2014We investigate the decomposition problem of balls into finitely many congruent pieces in dimension $d=2k$. In addition, we prove that the $d$ dimensional unit ball $B_d$ can be divided into finitely many congruent pieces if $d=4$ or $d\ge 6$. We show ... More

On algebras that almost have finite dimensional representationsNov 21 2003We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.

Characterizing fully principal congruence representable distributive latticesJun 11 2017Motivated by a recent paper of G. Gr\"atzer, a finite distributive lattice $D$ is said to be fully principal congruence representable if for every subset $Q$ of $D$ containing $0$, $1$, and the set $J(D)$ of nonzero join-irreducible elements of $D$, there ... More

On the set of principal congruences in a distributive congruence lattice of an algebraMay 30 2017Jun 29 2017Let $Q$ be a subset of a finite distributive lattice $D$. An algebra $A$ represents the inclusion $Q\subseteq D$ by principal congruences if the congruence lattice of $A$ is isomorphic to $D$ and the ordered set of principal congruences of $A$ corresponds ... More

Almost maximally almost-periodic group topologies determined by T-sequencesMar 31 2005Nov 27 2005A sequence $\{a_n\}$ in a group $G$ is a {\em $T$-sequence} if there is a Hausdorff group topology $\tau$ on $G$ such that $a_n\stackrel\tau\longrightarrow 0$. In this paper, we provide several sufficient conditions for a sequence in an abelian group ... More

Precompact abelian groups and topological annihilatorsFeb 10 2005Jun 05 2005For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\chi \in K$ such that $\chi(a_n)\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\hat K$ (the Pontryagin dual of ... More

The number of permutations with k inversionsFeb 10 2010Let $n\geq 1$, $0\leq t\leq {n \choose 2}$ be arbitrary integers. Define the numbers $I_n(t)$ as the number of permutations of $[n]$ with $t$ inversions. Let $n,d\geq 1$ and $0\leq t\leq (d-1)n$ be arbitrary integers. Define {\em the polynomial coefficients} ... More

Extremal metrics and K-stabilityOct 18 2004Apr 02 2007We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. ... More

Hurwitzian continued fractions containing a repeated constant and an arithmetic progressionNov 12 2012May 25 2013We prove an explicit formula for infinitely many convergents of Hurwitzian continued fractions that repeat several copies of the same constant and elements of one arithmetic progression, in a quasi-periodic fashion. The proof involves combinatorics and ... More

$L^2$-spectral invariants and quasi-crystal graphsJul 07 2006Introducing and studying the pattern frequency algebra, we prove the analogue of L\"uck's approximation theorems on $L^2$-spectral invariants in the case of aperiodic order. These results imply a uniform convergence theorem for the integrated density ... More

Shifted Jacobi polynomials and Delannoy numbersSep 30 2009Dec 24 2009We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago, to all ... More

The amenability and non-amenability of skew fieldsNov 21 2003We investigate the amenability of skew filed extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable skew fields of infinite Gelfand-Kirillov ... More

Remark on the Calabi flow with bounded curvatureSep 12 2012In this short note we prove that if the curvature tensor is uniformly bounded along the Calabi flow and the Mabuchi energy is proper, then the flow converges to a constant scalar curvature metric.

Monte Carlo Studies of Identified Two-particle Correlations in p-p and Pb-Pb CollisionsMar 01 2014Mar 21 2014Azimuthal particle correlations have been extensively studied in the past at various collider energies in p-p, p-A, and A-A collisions. Hadron-correlation measurements in heavy-ion collisions have mainly focused on studies of collective (flow) effects ... More

Hermitian codes from higher degree placesJun 20 2012Matthews and Michel investigated the minimum distances in certain algebraic-geometry codes arising from a higher degree place $P$. In terms of the Weierstrass gap sequence at $P$, they proved a bound that gives an improvement on the designed minimum distance. ... More

Multivariable (φ,Γ)-modules and products of Galois groupsMar 14 2016We show that the category of continuous representations of the $d$th direct power of the absolute Galois group of $\mathbb{Q}_p$ on finite dimensional $\mathbb{F}_p$-vector spaces (resp. finitely generated $\mathbb{Z}_p$-modules, resp. finite dimensional ... More

Critical point in the QCD phase diagram for extremely strong background magnetic fieldsApr 30 2015Jul 16 2015Lattice simulations have demonstrated that a background (electro)magnetic field reduces the chiral/deconfinement transition temperature of quantum chromodynamics for eB < 1 GeV^2. On the level of observables, this reduction manifests itself in an enhancement ... More

First-order regret bounds for combinatorial semi-banditsFeb 23 2015Jun 10 2015We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making ... More

On Why-Questions in PhysicsJan 22 2011The aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.

A Geometrical Characterization of the Twin Paradox and its VariantsJul 11 2008Feb 19 2010The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent ... More

Renormalization group approach to the spin-1 Bose gasMay 26 2005Mar 13 2006A field theoretical renormalization group approach at two loop level is applied to the homogeneous spin-1 Bose gas in order to investigate the order of the phase transition. The beta function of the system with $d=4-\epsilon$ dimensions is determined ... More

Degenerations of $\mathbf{C}^n$ and Calabi-Yau metricsJun 01 2017We construct infinitely many complete Calabi-Yau metrics on $\mathbf{C}^n$ for $n \geq 3$, with maximal volume growth, and singular tangent cones at infinity. In addition we construct Calabi-Yau metrics in neighborhoods of certain isolated singularities ... More

Geometry of splice-quotient singularitiesDec 23 2008We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant ... More

Lattices embeddable in three-generated latticesDec 12 2015We prove that every finite lattice L can be embedded in a three-generated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely ... More

Finite semilattices with many congruencesJan 04 2018For an integer $n\geq 2$, let NCSL$(n)$ denote the set of sizes of congruence lattices of $n$-element semilattices. We find the four largest numbers belonging to NCSL$(n)$, provided that $n$ is large enough to ensure that $|$NCSL$(n)|\geq 4$. Furthermore, ... More

Free minimal actions of countable groups with invariant probability measuresMay 28 2018Jul 06 2018We prove that for any countable group G there exists a free minimal continuous action of G on the Cantor set admitting an invariant Borel probability measure.

Bifurcation of Periodic Delay Differential Equations at Points of 1:4 ResonanceJan 08 2010The time-periodic scalar delay differential equation $\dot x(t)=\gamma f(t,x(t-1))$ is considered, which leads to a resonant bifurcation of the equilibrium at critical values of the parameter. Using Floquet theory, spectral projection and center manifold ... More

Extremal metrics and K-stability (PhD thesis)Oct 31 2006In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to ... More

A second look at the toric h-polynomial of a cubical complexFeb 18 2010Jul 06 2010We provide an explicit formula for the toric $h$-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan's result on the non-negativity of these contributions. Our model allows for a variant of the Gessel-Shapiro ... More

Linear equations for the number of intervals which are isomorphic with Boolean lattices and the Dehn--Sommerville equationsFeb 10 2010Let $P$ be a finite poset. Let $L:=J(P)$ denote the lattice of order ideals of $P$. Let $b_i(L)$ denote the number of Boolean intervals of $L$ of rank $i$. We construct a simple graph $G(P)$ from our poset $P$. Denote by $f_i(P)$ the number of the cliques ... More

Coordinatization of join-distributive latticesAug 17 2012Oct 12 2012Join-distributive lattices are finite, meet-semidistributive, and semimodular lattices. They are the same as Dilworth's lattices in 1940, and many alternative definitions and equivalent concepts have been discovered or rediscovered since then. Let L be ... More

Extremal cross-polytopes and Gaussian vectorsAug 29 2012Jun 20 2013Let C = C(l_1, ..., l_n) be the n-dimensional orthogonal cross-polytope whose axes are of length l_1,..., l_n. Subject to the condition \sum l_i^2 = 1, the mean width of C is minimised when l_i = 1/sqrt{n} for every i, and it is maximised when C is at ... More

The existence of superluminal particles is consistent with the kinematics of Einstein's special theory of relativityFeb 26 2012Mar 28 2013Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that ... More

Multidimensional spline integration of scattered dataOct 14 2010Mar 01 2011We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing the deviation ... More

First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated ObserversMay 06 2010This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\'eka, Madar\'asz and N\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and general relativity; ... More

Multivariable $(\varphi,Γ)$-modules and smooth $o$-torsion representationsNov 03 2015Aug 15 2016Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of projective limits ... More

(φ,Γ)-modules over noncommutative overconvergent and Robba ringsAug 16 2012Apr 05 2013We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of \'etale $(\varphi,\Gamma)$-modules over certain completions of these rings are equivalent to the category of \'etale ... More

Thom polynomials of Morin singularities and the Green-Griffiths-Lang conjectureNov 21 2010Sep 16 2015The Green-Griffiths-Lang conjecture says that for every complex projective algebraic variety $X$ of general type there exists a proper algebraic subvariety of $X$ containing all nonconstant entire holomorphic curves $f:\mathbb{C} \to X$. We construct ... More

On the Popov-Pommerening conjecture for linear algebraic groupsApr 29 2013Oct 18 2016Let $G$ be a reductive group over an algebraically closed subfield $k$ of $\mathbb{C}$ of characteristic zero, $H \subseteq G$ an observable subgroup normalized by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. Popov and Pommerening ... More

On Induced Subgraphs of Finite Graphs not Containing Large Empty and Complete SubgraphsNov 16 2012Aug 18 2017In their celebrated paper [Ramsey-Type Theorems, Discrete Appl. Math. 25 (1989) 37-52], Erd\H{o}s and Hajnal asked the following: is it true, that for any finite graph H there exists a constant c(H) such that for any finite graph G, if G does not contain ... More

Greatest lower bounds on the Ricci curvature of Fano manifoldsMar 31 2009On a Fano manifold M we study the supremum of the possible t such that there is a K\"ahler metric in c_1(M) with Ricci curvature bounded below by t. This is shown to be the same as the maximum existence time of Aubin's continuity path for finding K\"ahler-Einstein ... More

Efron's coins and the Linial arrangementNov 14 2015Jun 14 2016We characterize the tournaments that are dominance graphs of sets of (unfair) coins in which each coin displays its larger side with greater probability. The class of these tournaments coincides with the class of tournaments whose vertices can be numbered ... More

On universal continuous actions on the Cantor setMar 14 2018Mar 16 2018Using the notion of proper Cantor colorings we prove the following theorem. For any countably infinite group $\Gamma$, there exists a free continuous action $\zeta: \Gamma \curvearrowright C$ on the Cantor set, which is universal in the following sense: ... More

Construction of locally plane graphs with many edgesOct 28 2011A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction of $k$-locally ... More

Degenerations of $\mathbf{C}^n$ and Calabi-Yau metricsJun 01 2017Apr 02 2019We construct infinitely many complete Calabi-Yau metrics on $\mathbf{C}^n$ for $n \geq 3$, with maximal volume growth, and singular tangent cones at infinity. In addition we construct Calabi-Yau metrics in neighborhoods of certain isolated singularities ... More

A remark on conical Kähler-Einstein metricsNov 12 2012We give some non-existence results for K\"ahler-Einstein metrics with conical singularities along a divisor on Fano manifolds. In particular we show that the maximal possible cone angle is in general smaller than the invariant R(M). We study this discrepancy ... More

Comments on "Cavitons and spontaneous hot flow anomalies in a hybrid-Vlasov global magnetospheric simulation" by Blanco-Cano et al. (2018)Jan 22 2019Blanco-Cano et al. (2018) intended to find a type of transient event in the solar wind before the terrestrial bow shock using a special type of simulation. However, the simulation results cannot reproduce the main features of the event. Not only are the ... More

A generalization of Croot-Lev-Pach's Lemma and a new upper bound for the size of difference sets in polynomial ringsMar 14 2018Mar 20 2018Croot, Lev and Pach used a new polynomial technique to give a new exponential upper bound for the size of three-term progression-free subsets in the groups $(\mathbb Z _4)^n$. The main tool in proving their striking result is a simple lemma about polynomials, ... More

Quasiplanar diagrams and slim semimodular latticesDec 31 2012A (Hasse) diagram of a finite partially ordered set (poset) P will be called quasiplanar if for any two incomparable elements u and v, either v is on the left of all maximal chains containing u, or v is on the right of all these chains. Every planar diagram ... More

What properties of numbers are needed to model accelerated observers in relativity?Sep 29 2012We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every real closed field. ... More

Critical velocity of antiferromagnetic spin-1 Bose-Einstein condensates at finite temperatureOct 06 2012We study the instability of a moving spinor Bose-Einstein condensate when the speed of flow reaches the critical velocity. This we identify on the basis of Landau's criterion, i.e. the velocity above which some elementary excitation energy becomes negative. ... More

Hierarchical Manifold Clustering on Diffusion Maps for Connectomics (MIT 18.S096 final project)Jul 20 2016In this paper, we introduce a novel algorithm for segmentation of imperfect boundary probability maps (BPM) in connectomics. Our algorithm can be a considered as an extension of spectral clustering. Instead of clustering the diffusion maps with traditional ... More

An additive problem in the Fourier coefficients of cusp formsJan 10 2001May 20 2003We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. ... More

Visual characterization of associative quasitrivial nondecreasing operations on finite chainsSep 21 2017Oct 26 2018In this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains. We also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains. Finally, we estimate ... More

A simultaneous representation of a group and a bounded poset with lattice automorphisms and principal congruencesAug 18 2015Aug 21 2015Given a poset $P$ with at least two elements and a group $G$, there exists a selfdual lattice of length 16 such that the collection of its principal congruences is order isomorphic to $P$ while its automorphism group to $G$.

A note on finite lattices with many congruencesDec 17 2017By a twenty year old result of Ralph Freese, an $n$-element lattice $L$ has at most $2^{n-1}$ congruences. We prove that if $L$ has less than $2^{n-1}$ congruences, then it has at most $2^{n-2}$ congruences. Also, we describe the $n$-element lattices ... More

Weak convergence of finite graphs, integrated density of states and a Cheeger type inequalitySep 03 2005May 23 2006In \cite{Elek} we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph sequences. We show that ... More

Characterizing circles by a convex combinatorial propertyNov 28 2016Jul 23 2017Let $K_0$ be a compact convex subset of the plane $\mathbb R^2$, and assume that $K_1\subseteq \mathbb R^2$ is similar to $K_0$, that is, $K_1$ is the image of $K_0$ with respect to a similarity transformation $\mathbb R^2\to\mathbb R^2$. Kira Adaricheva ... More

An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circlesOct 08 2016May 23 2017Kira Adaricheva and Madina Bolat have recently proved that if $U_0$ and $U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $j\in \{0,1,2\}$ and $k\in\{0,1\}$ such that $U_{1-k}$ is included in the convex hull of $U_k\cup(\{A_0,A_1, ... More

Circles and crossing planar compact convex setsFeb 18 2018Let $K_0$ be a compact convex subset of the plane $\mathbb R^2$, and assume that whenever $K_1\subseteq \mathbb R^2$ is congruent to $K_0$, then $K_0$ and $K_1$ are not crossing in a natural sense due to L. Fejes-T\'oth. A theorem of L. Fejes-T\'oth from ... More

Sunflowers and $L$-intersecting familiesJan 19 2016Let $f(k,r,s)$ stand for the least number so that if $\cal F$ is an arbitrary $k$-uniform, $L$-intersecting set system, where $|L|=s$, and $\cal F$ has more than $f(k,r,s)$ elements, then $\cal F$ contains a sunflower with $r$ petals. We give an upper ... More

An easy way to a theorem of Kira Adaricheva and Madina Bolat on convexity and circlesOct 08 2016Kira Adaricheva and Madina Bolat have recently proved that if $U_0$ and $U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $j\in \{0,1,2\}$ and $k\in\{0,1\}$ such that $U_{1-k}$ is included in the convex hull of $U_k\cup(\{A_0,A_1, ... More

The cobordism class of the multiple points of immersionsSep 29 2004May 31 2006Let f: M -> N be an even codimensional immersion between smooth manifolds. We derive an explicit formula for the Pontrjagin numbers and signature of the multiple point manifolds in terms of singular cohomology of M and N, the maps induced between these ... More

Filtrations and test-configurationsNov 21 2011Feb 14 2013We introduce a strengthening of K-stability, based on filtrations of the homogeneous coordinate ring. This allows for considering certain limits of families of test-configurations, which arise naturally in several settings. We prove that if a manifold ... More

Optimal test-configurations for toric varietiesSep 17 2007On a K-unstable toric variety we show the existence of an optimal destabilising convex function. We show that if this is piecewise linear then it gives rise to a decomposition into semistable pieces analogous to the Harder-Narasimhan filtration of an ... More

The Calabi functional on a ruled surfaceMar 19 2007We study the Calabi functional on a ruled surface over a genus two curve. For polarisations which do not admit an extremal metric we describe the behaviour of a minimising sequence splitting the manifold into pieces. We also show that the Calabi flow ... More

On the Popov-Pommerening conjecture for linear algebraic groupsApr 29 2013Sep 27 2015Let $G$ be a reductive group over an algebraically closed field $k$, $H \subseteq G$ an observable subgroup normalised by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. The Popov-Pommerening conjecture from 1985 says that the invariant ... More

A short proof for the characterisation of tight framesMar 28 2014With the aid of utilising tensor products, we give a simplified proof to the fundamental theorem of Benedetto and Fickus about the existence and characterisation of finite, normalised tight frames. We also establish unit-norm tensor resolutions for symmetric, ... More