total 207670took 0.12s

Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019In this paper we study the $\eta'$ mass in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip ... More

Chiral observables and topology in hot QCD with two families of quarksMay 15 2018Nov 08 2018We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected ... More

Topology (and axion's properties) from lattice QCD with a dynamical charmMay 04 2017We present results on QCD with four dynamical flavors in the temperature range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic ... More

Pair ${(bc)}$ diquarks production in high energy proton--proton collisionsJun 13 2016The cross section of pair double heavy diquark production process $pp\to(bc)+(\bar b \bar c)+X$ is calculated in the leading order of gluonic fusion channel with all four possible color and spin combinations $[^1S_0]_{\bar3}$, $[^1S_0]_{6}$, $[^3S_1]_{\bar3}$, ... More

Penetration of Josephson vortices and measurement of the c-axis penetration depth in $Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}$: Interplay of Josephson coupling, surface barrier and defectsJun 23 2000The first penetration field H_{J}(T) of Josephson vortices is measured through the onset of microwave absorption in the locked state, in slightly overdoped $\rm{Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ single crystals (T_{c} ~ 84 K). The magnitude of H_{J}(T) ... More

Finite temperature gluon spectral functions from $N_f=2+1+1$ lattice QCDJan 30 2017We investigate gluon spectral functions at finite temperature in Landau gauge, based on a subset of lattice QCD ensembles with $N_f=2+1+1$ dynamical twisted mass quarks flavors, generated by the tmfT collaboration. Our study uses a novel Bayesian approach ... More

Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019Mar 25 2019In this paper we study the $\eta'$ in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip in ... More

On heat transfer in a thermally perturbed harmonic chainAug 06 2017Unsteady heat transfer in a harmonic chain is analyzed. Two types of thermal perturbations are considered: 1) initial instant temperature perturbation, 2) external heat supply. Closed equations describing the heat propagation are obtained and their analytical ... More

c-axis penetration depth in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals measured by ac-susceptibility and cavity perturbation techniqueJun 23 2000The $c$-axis penetration depth $\Delta\lambda_c$ in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) single crystals as a function of temperature has been determined using two techniques, namely, measurements of the ac-susceptibility at a frequency of 100 kHz ... More

Super-Teichmüller spaces and related structuresNov 25 2018This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2 September - 8 ... More

Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat sourceJan 07 2019Apr 26 2019We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system of stochastic ... More

Fast and slow thermal processes in harmonic scalar latticesFeb 28 2017Nov 13 2017An approach for analytical description of thermal processes in harmonic lattices is presented. We cover longitudinal and transverse vibrations of chains and out-of-plane vibrations of two-dimensional lattices with interactions of an arbitrary number of ... More

Homotopy Algebras of Differential (Super)forms in Three and Four DimensionsFeb 12 2017We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding $A_{\infty}$-structures. In $N=2$ ... More

Quantum Group as Semi-infinite CohomologyDec 09 2008Apr 15 2010We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is constructed from the ... More

Normal state resistivity of Ba$_{1-x}$K$_x$Fe$_2$As$_2$: evidence for multiband strong-coupling behaviorNov 08 2010Jul 12 2011We present theoretical analysis of the normal state resistivity in multiband superconductors in the framework of Eliashberg theory. The results are compared with measurements of the temperature dependence of normal state resistivity of high-purity Ba$_{0.68}$K$_{0.32}$Fe$_{2}$As$_{2}$ ... More

Verbally closed virtually free subgroupsFeb 24 2017Jul 05 2017A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbally closed subgroups are retracts in any finitely generated group.

Thermal equilibration in a one-dimensional harmonic crystal surrounded by a viscous environmentApr 26 2019May 04 2019The features for the unsteady process of thermal equilibration (the fast motions) in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements of all the particles ... More

Dynamics of spatially localized states in transitional plane Couette flowJun 26 2018Jan 16 2019Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider ... More

Microwave surface impedance anisotropy of YBa$_2$Cu$_3$O$_x$ single crystals with different oxygen contentFeb 25 2003The linear microwave response of ultra high-quality YBa$_2$Cu$_3$O$_x$ single crystals grown in BaZrO$_3$ crucibles is measured at 9.4 GHz in rf magnetic fields parallel and perpendicular to the $ab$-plane in the temperature range 5$\leq T\leq 200$ K. ... More

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supplyOct 03 2017We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential ... More

Quantum K-theory of Quiver Varieties and Many-Body SystemsMay 30 2017May 11 2018We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic ... More

Thermal echo in a finite one-dimensional harmonic crystalJul 10 2018Aug 03 2018An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude described by ... More

Extended Vertical Lists for Temporal Pattern Mining from Multivariate Time SeriesApr 26 2018Temporal Pattern Mining (TPM) is the problem of mining predictive complex temporal patterns from multivariate time series in a supervised setting. We develop a new method called the Fast Temporal Pattern Mining with Extended Vertical Lists. This method ... More

Baxter Q-operator from quantum K-theoryDec 27 2016Jan 16 2019We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove that the spectrum ... More

Flocking from a quantum analogy: Spin-orbit coupling in an active fluidAug 02 2017Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of the fluid can ... More

Discrete and Continuum ThermomechanicsJul 29 2017In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal, quasi-one-dimensional crystal ... More

Completeness property of one-dimensional perturbations of normal and spectral operators generated by first order systemsJul 14 2018The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \times 2$ system \begin{equation} L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad ... More

On the stability of redundancy modelsMar 11 2019We investigate the stability condition of redundancy-$d$ multi-server systems. Each server has its own queue and implements popular scheduling disciplines such as First-Come-First-Serve (FCFS), Processor Sharing (PS), and Random Order of Service (ROS). ... More

Relativistic corrections to double charmonium production in high energy proton-proton interactionJul 13 2012On the basis of pertubative QCD and the relativistic quark model we calculate relativistic corrections to the process of pair $J/\psi$ production in proton-proton collisions at LHC energy $\sqrt S=7$ TeV. Relativistic terms in the production amplitude ... More

Pair double heavy diquark production in high energy proton-proton collisionsMay 05 2014Oct 21 2014On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of double heavy diquarks. Relativistic factors in the production amplitude connected with the relative ... More

Relativistic corrections to η_c-pair production in high energy proton-proton collisionsFeb 27 2013On the basis of perturbative QCD and the relativistic quark model we calculate relativistic corrections to the double $\eta_c$ meson production in proton-proton interactions at LHC energies. Relativistic terms in the production amplitude connected with ... More

Relativistic description of the double P-wave charmonium production in e^+e^- annihilationJun 14 2011Aug 10 2011On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of P-wave charmonium states. Relativistic factors in the production amplitude connected with ... More

Anisotropy of microwave conductivity of YBaCuO in superconducting and normal states: Crossover 3D-2DJun 06 2003Imaginary part of the microwave conductivity \sigma''(T<T_c) and the resistivity \rho(T)=1/\sigma(T>T_c) along (\sigma_{ab}'' and \rho_{ab}) and perpendicular to (\sigma_c'' and \rho_c) cuprate ab-planes of YBa_2Cu_3O_{7-x} crystal were measured in the ... More

Relativistic corrections to the pair double heavy diquark production in e^+e^- annihilationAug 19 2013Aug 23 2013On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of double heavy diquarks. Relativistic factors in the production amplitude connected with the relative ... More

$(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical dualityNov 25 2018Dec 16 2018A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe ... More

Cluster formation via sonic depletion forces in levitated granular matterAug 11 2018The properties of small clusters can differ dramatically from the bulk phases of the same constituents. In equilibrium, cluster assembly has been recently explored, whereas out of equilibrium, the physical principles of clustering remain elusive. These ... More

The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spinsFeb 23 2008Feb 24 2009We prove upper and lower bounds on the free energy in the Sherrington-Kirkpatrick model with multidimensional (e.g., Heisenberg) spins in terms of the variational inequalities based on the corresponding Parisi functional. We employ the comparison scheme ... More

The Aizenman-Sims-Starr scheme for the SK model with multidimensional spinsNov 14 2007Nov 24 2007This paper has been temporarily withdrawn for revision by the authors.

On intrinsic isometries to Euclidean spaceMar 29 2010I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.

Irreducible Ulrich bundles on isotropic GrassmanniansApr 06 2016May 13 2016We classify irreducible equivariant Ulrich vector bundles on isotropic Grassmannians.

Optimal Prediction of Stiff Oscillatory MechanicsJan 18 2000We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by examples that optimal ... More

A search for an optimal start system for numerical homotopy continuationMay 22 2011We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start systems is a hard ... More

Numerical Algebraic Geometry for Macaulay2Nov 09 2009May 22 2011Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic geometry. We present ... More

Torus actions of complexity one and their local propertiesFeb 24 2018We consider an effective action of a compact (n-1)-torus on a smooth 2n-manifold with isolated fixed points. We prove that under certain conditions the orbit space is a closed topological manifold. In particular, this holds for certain torus actions with ... More

Building Large Free Subshifts Using the Local LemmaFeb 20 2018Feb 15 2019Gao, Jackson, and Seward proved that every countably infinite group $\Gamma$ admits a nonempty free subshift $X \subseteq 2^\Gamma$. Here we strengthen this result by showing that free subshifts can be "large" in various senses. Specifically, we prove ... More

Ruijsenaars-Schneider three-body models with N=2 supersymmetryFeb 22 2018Apr 09 2018The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of ... More

Sentiment Protocol: A Decentralized Protocol Leveraging Crowd Sourced WisdomOct 31 2017May 05 2018The wisdom of the crowd is a valuable asset in today's society. It is not only important in predicting elections but also plays an essential role in marketing and the financial industry. Having a trustworthy source of opinion can make forecasts more accurate ... More

An impure solution to the problem of matching fansOct 20 2017Apr 01 2018We propose an algorithm to solve the problem of matching fans in interaction net implementations of optimal reduction for the pure untyped lambda calculus without use of any additional agent types. The algorithm relies upon a specific interaction nets ... More

Phenomenology of charged-particle multiplicity distributionsOct 05 2017Charged-particle multiplicity distributions are an interesting tool to study both soft- and hard-QCD processes in hadronic collisions. Since last century a significant range of center-of-mass energies has been probed, ranging from a few GeV to 13 TeV ... More

The Johansson--Molloy Theorem for DP-ColoringAug 13 2017Jul 26 2018The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound $\chi(G) \leq (1+o(1))\Delta(G)/\ln \Delta(G)$ for triangle-free graphs $G$, avoiding the technicalities of the entropy compression method ... More

On Baire Measurable Colorings of Group ActionsAug 31 2017The field of descriptive combinatorics investigates the question, to what extent can classical combinatorial results and techniques be made topologically or measure-theoretically well-behaved? This paper examines a class of coloring problems induced by ... More

One-skeleta of $G$-parking function ideals: resolutions and standard monomialsAug 15 2017Jun 15 2018Given a graph $G$, the $G$-parking function ideal $M_G$ is an artinian monomial ideal in the polynomial ring $S$ with the property that a linear basis for $S/M_G$ is provided by the set of $G$-parking functions. It follows that the dimension of $S/M_G$ ... More

Rationality proofs by curve countingMay 08 2017Dec 10 2018We propose an approach for showing rationality of an algebraic variety $X$. We try to cover $X$ by rational curves of certain type and count how many curves pass through a generic point. If the answer is $1$, then we can sometimes reduce the question ... More

Discrete Games in Endogenous Networks: Equilibria and PolicyMay 09 2017In games of friendship links and behaviors, I propose $k$-player Nash stability---a family of equilibria, indexed by a measure of robustness given by the number of permitted link changes, which is (ordinally and cardinally) ranked in a probabilistic sense. ... More

Two-step General Linear Methods for Retarded Functional Differential EquationsApr 15 2017This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems the uniform ... More

Weighted prime geodesic theoremsFeb 11 2019Prime geodesic theorems for weighted infinite graphs and weighted building quotients are given. The growth rates are expressed in terms of the spectral data of suitable translation operators inspired by a paper of Bass.

Upward confluence in the interaction calculusJun 19 2018Oct 14 2018The lambda calculus is not upward confluent, one of counterexamples known thanks to Plotkin. This paper investigates upward confluence in the interaction calculus. Can an interaction system have this property? We positively answer this question and also ... More

A Categorical Construction of Bachmann-Howard Fixed PointsSep 18 2018Sep 19 2018Peter Aczel has given a categorical construction for fixed points of normal functors, i.e. dilators which preserve initial segments. For a general dilator $X\mapsto T_X$ we cannot expect to obtain a well-founded fixed point, as the order type of $T_X$ ... More

$Π^1_1$-Comprehension as a Well-Ordering PrincipleSep 18 2018Sep 19 2018A dilator is a particularly uniform transformation $X\mapsto T_X$ of linear orders that preserves well-foundedness. We say that $X$ is a Bachmann-Howard fixed point of $T$ if there is an almost order preserving collapsing function $\vartheta:T_X\rightarrow ... More

On the bounded derived category of $\mathsf{IGr}(3, 7)$Apr 18 2018May 30 2018We construct a mininal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian $\mathsf{IGr}(3,7)$. Moreover, we show that $\mathsf{IGr}(3, 7)$ admits a full exceptional collection consisting of equivariant ... More

Spherical parking functions, uprooted trees, and yet another way to count $n^n$Jun 12 2018Parking functions are a widely studied class of combinatorial objects, with connections to several branches of mathematics. The number of parking functions of length $n$ is given by $(n+1)^{n-1}$, which by Cayley's formula is equal to the number of spanning ... More

Stein's method for steady-state diffusion approximationsApr 27 2017Diffusion approximations have been a popular tool for performance analysis in queueing theory, with the main reason being tractability and computational efficiency. This dissertation is concerned with establishing theoretical guarantees on the performance ... More

Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspectiveFeb 07 2017Feb 14 2017Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can ... More

Face rings of cycles, associahedra, and standard Young tableauxMar 20 2015Aug 22 2016We show that J_n, the Stanley-Reisner ideal of the n-cycle, has a free resolution supported on the (n-3)-dimensional simplicial associahedron A_n. This resolution is not minimal for n > 5; in this case the Betti numbers of J_n are strictly smaller than ... More

Topological model for h"-vectors of simplicial manifoldsFeb 19 2015Any manifold with boundary gives rise to a Poincare duality algebra in a natural way. Given a simplicial poset $S$ whose geometric realization is a closed orientable homology manifold, and a characteristic function, we construct a manifold with boundary ... More

Distributed recovery of jointly sparse signals under communication constraintsNov 08 2016The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and ... More

Non-perturbative quark, gluon and meson correlators of unquenched QCDJun 20 2017We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving ... More

Tangent Developable Orbit Space of an OctupoleJul 12 2018The orbit space of an octupole, a traceless symmetric third-rank tensor of $SO(3)$, is shown to be a three-dimensional body with three cusps and two cuspidal edges. It is demonstrated that for a unique choice of orbit space coordinates its boundary turns ... More

Virtually free finite-normal-subgroup-free groups are strongly verbally closedDec 09 2017Jun 22 2018Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.

Microwave Response of V3Si Single Crystals: Evidence for Two-Gap SuperconductivitySep 09 2005The investigation of the temperature dependences of microwave surface impedance and complex conductivity of V3Si single crystals with different stoichiometry allowed to observe a number of peculiarities which are in remarkable contradiction with single-gap ... More

Holomorphic torsion for Hermitian locally symmetric spacesMar 05 1996Sep 27 1996The holomorphic torsion of a compact locally symmetric manifold is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.

A Lefschetz formula for flowsDec 01 1995For the geodesic flow of an odd dimensional hyperbolic manifold we prove a Lefschetz type formula. The local terms are Fuller indices of the closed orbits. The global "Frobenius operator" is the generator of the flow and its action on tangential cohomology. ... More

Schemes over $F_1$Apr 08 2004Jul 26 2006Using the approach of Kurokawa, Ochiai, and Wakayama to 'absolute mathematics' we define a corresponding notion of schemes.

Euler-Poincar'e functionsJan 24 2002A new construction of Euler-Poincar\'e functions for real reductive groups is given. This construction also works for non-connected groups and representations that do not lift.

Differential operators on equivariant vector bundles over symmetric spacesMay 19 2000Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger ... More

On the growth of modular symbolsFeb 09 2007It is shown that the modular symbol of a cusp form of weight two has logarithmic growth.

Lefschetz formulae for p-adic groupsMay 19 2005Lefschetz formulae for torus actions on p-adic groups are proven.

Mellin transforms of p-adic Whittaker functionsSep 18 2001It is shown that Mellin transforms of p-adic Whittaker functions exist for generic characters. For good choices of vectors they are rational functions. For class one vectors they can be calculated explicitly. It turns out that they are automorphic L-factors ... More

Pentagrams, inscribed polygons, and Prym varietiesJul 13 2016Sep 19 2016The pentagram map is a discrete integrable system on the moduli space of planar polygons. The corresponding first integrals are so-called monodromy invariants $E_1, O_1, E_2, O_2,\dots$ By analyzing the combinatorics of these invariants, R.Schwartz and ... More

Measurable versions of the Lovász Local Lemma and measurable graph coloringsApr 25 2016Aug 07 2016In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a function $f \colon ... More

Trident pair production in strong laser pulsesNov 17 2010Jan 14 2011We calculate the trident pair production amplitude in a strong laser background. We allow for finite pulse duration, while still treating the laser fields nonperturbatively in strong-field QED. Our approach reveals explicitly the individual contributions ... More

A quest for 5-point condition a la AlexandrovNov 19 2014Here I give a description of Alexandrov 4-point comparison via quadratic forms and then propose a natural 5-point condition which might have some future. Consider this note as a letter from me --- do not take it seriously.

RoCK blocks, wreath products and KLR algebrasNov 25 2015Oct 14 2016We consider RoCK (or Rouquier) blocks of symmetric groups and Hecke algebras at roots of unity. We prove a conjecture of Turner asserting that a certain idempotent truncation of a RoCK block of weight $d$ of a symmetric group $\mathfrak S_n$ defined over ... More

Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebrasJul 23 2011Aug 08 2012In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry. The most important ... More

Interior Nucleation of Martensite in a Cubic-to-Tetragonal Phase TransformationJul 20 2015Using a variational model based on non-linear elasticity we investigate whether in a cubic-to-tetragonal phase transformation it is energetically preferable to nucleate martensite within austenite. Under minimal growth assumptions on the free energy density ... More

The problem of Buchstaber number and its combinatorial aspectsMar 02 2010For any simplicial complex on m vertices a moment-angle complex Z_K embedded in C^m can be defined. There is a canonical action of a torus T^m on Z_K, but this action fails to be free. The Buchstaber number is the maximal integer s(K) for which there ... More

Infinite energy solutions for critical wave equation with fractional damping in unbounded domainsNov 14 2015This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known results for bounded ... More

Homology of torus spaces with acyclic proper faces of the orbit spaceMay 19 2014Let $X$ be 2n-dimensional compact manifold with a locally standard action of a compact torus. The orbit space $X/T$ is a manifold with corners. Suppose that all proper faces of $X/T$ are acyclic. In the paper we study the homological spectral sequence ... More

Bi-Lipschitz extension from boundaries of certain hyperbolic spacesDec 12 2011Tukia and Vaisala showed that every quasi-conformal map of $\R^n$ extends to a quasi-conformal self-map of $\R^{n+1}$. The restriction of the extended map to the upper half-space $\R^n \times \R^+$ is, in fact, bi-Lipschitz with respect to the hyperbolic ... More

Integrating by Spheres: Summary of Blaschke-Petkantschin FormulasApr 24 2019In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type, that help to pass from integration over $k$-tuples of points in space ... More

Schwarzian mechanics via nonlinear realizationsMay 06 2019The method of nonlinear realizations is used to clarify some conceptual and technical issues related to the Schwarzian mechanics. It is shown that the Schwarzian derivative arises naturally, if one applies the method to SL(2,R) times R group and decides ... More

Superfluid density in the underdoped YBa_2Cu_3O_{7-x}: Evidence for d-density wave order of pseudogapDec 22 2003The investigation of the penetration depth \lambda_{ab}(T,p) in YBa_2Cu_3O_{7-x} crystals allowed to observe the following features of the superfluid density n_s(T,p)\propto \lambda_{ab}^{-2}(T,p) as a function of temperature T<Tc/2 and carrier concentration ... More

Pseudogap in the microwave response of YBa_2Cu_3O_{7-x}Dec 23 2003The in-plane and out-of-plane surface impedance and microwave conductivity components of one and the same YBa_2Cu_3O_{7-x} (0.07\le x\le 0.47) single crystal are determined in the wide ranges of temperature T and carrier concentration p in CuO_2 planes. ... More

Non-Elitist Genetic Algorithm as a Local Search MethodJul 12 2013Mar 28 2014Sufficient conditions are found under which the iterated non-elitist genetic algorithm with tournament selection first visits a local optimum in polynomially bounded time on average. It is shown that these conditions are satisfied on a class of problems ... More

Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear Schrodinger Equation on DomainsDec 29 2005We prove wellposedness of the Cauchy problem for the nonlinear Schrodinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on ... More

On a conjecture of Kuznetsov and PolishchukMay 12 2015We prove a conjecture by A. Kuznetsov and A. Polishchuk on the existence of some particular full exceptional collections in bounded derived categories of coherent sheaves on Grassmannian varieties.

Toric manifolds over 3-polytopesJul 12 2016Dec 01 2016In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not ... More

High-dimensional Gaussian fields with isotropic increments seen through spin glassesAug 26 2011We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational representation in terms of a Parisi-type functional for the free energy in the ... More

Expanders are order diameter non-hyperbolicJan 30 2015Feb 25 2015We show that expander graphs must have Gromov-hyperbolicity at least proportional to their diameter, with a constant of proportionality depending only on the expansion constant and maximal degree. In other words, expanders contain geodesic triangles which ... More

Dimensions of multi-fan algebrasJul 13 2016Dec 01 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More