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S-matrix analysis of the baryon electric charge correlationOct 07 2017We compute the correlation of the net baryon number with the electric charge ($\chi_{BQ}$) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable $\chi_{BQ}$ is particularly sensitive to the details of the ... More

Matching the Hagedorn mass spectrum with Lattice QCD resultsJul 23 2015Nov 06 2015Based on recent Lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of Hadron Resonance Gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved ... More

Repulsive interactions and their effects on the thermodynamics of hadron gasFeb 28 2017We compare two approaches in modeling repulsive interactions among hadrons: the excluded volume approximation and the S-matrix formalism. These are applied to study the thermodynamics of the $\pi N \Delta$ system. It is shown that the introduction of ... More

Strangeness fluctuations from $K-π$ interactionsJul 15 2015Nov 06 2015Motivated by recent lattice QCD studies, we explore the effects of interactions on strangeness fluctuations in strongly interacting matter at finite temperature. We focus on S-wave $K\pi$ scattering and discuss the role of the $K_0^*(800)$ and $K^*(1430)$ ... More

Effects of $ρ$-meson width on pion distributions in heavy-ion collisionsAug 24 2016Apr 01 2017The influence of the finite width of $\rho$ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find ... More

Thermal contribution of unstable statesFeb 08 2019Within the framework of the Lee model, we analyze in detail the difference between the energy derivative of the phase shift and the standard spectral function of the unstable state. The fact that the model is exactly solvable allows us to demonstrate ... More

Restoration of tetragonal $C_4$ symmetry coexistent with filamentary superconductivity in the pressure induced intermediate phase in the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$Jul 07 2015Jul 09 2015The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where A=Na or K) show a particular rich phase diagram. It was observed that an intermediate re-entrant tetragonal phase forms within the orthorhombic antiferromagnetically-ordered stripe-type ... More

Confinement Models at Finite Temperature and DensityAug 27 2009Feb 12 2010In-medium chiral symmetry breaking in confining potential models of QCD is examined. Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature. We argue that previous attempts to circumvent this ... More

Polyakov loop fluctuations and deconfinement in the limit of heavy quarksJun 16 2014We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows ... More

Overlap between Lattice QCD and HRG with in-medium effects and parity doublingNov 29 2017We investigate the fluctuations and correlations involving baryon number in hot hadronic matter with modified masses of negative-parity baryons, in the context of the hadron resonance gas. Temperature-dependent masses are adopted from the recent lattice ... More

Polyakov loop fluctuations in the presence of external fieldsJan 24 2018We study the implications of the spontaneous and explicit Z(3) center symmetry breaking for the Polyakov loop susceptibilities. To this end, ratios of the susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop ... More

Thermodynamics of strange baryon system from coupled-channel analysis and missing statesJun 06 2018Dec 14 2018We study the thermodynamics of the strange baryon system using an S-matrix formulation of statistical mechanics. For this purpose, we employ an existing coupled-channel study involving $\bar{K} N$, $\pi \Lambda$, and $\pi \Sigma$ interactions in the $S=-1$ ... More

Possible coexistence of double-Q magnetic order and chequerboard charge order in the re-entrant tetragonal phase of Ba0.76K0.24Fe2As2May 18 2017We investigate the re-entrant tetragonal phase in the iron-based superconductor Ba0 .76K0.24Fe2As2 by DC magnetization and thermoelectrical measurements. The reversible magnetization confirms by a thermodynamic method that the spin alignment in the re-entrant ... More

Fourier coefficients of the net-baryon number density and chiral criticalityMay 11 2018Jun 28 2018We investigate the Fourier coefficients $b_k(T)$ of the net--baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large $k$ is determined by the singularities of the partition ... More

Effects of $ρ$-meson width on pion distributions in heavy-ion collisionsAug 24 2016The influence of the finite width of $\rho$ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find ... More

The thermal proton yield anomaly in Pb-Pb collisions at the LHC and its resolutionAug 09 2018Jan 27 2019We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical ... More

Polyakov loop fluctuations in SU(3) lattice gauge theory and an effective gluon potentialJul 23 2013We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute ... More

Probing Deconfinement with Polyakov Loop SusceptibilitiesJun 21 2013The susceptibilities of the real and imaginary parts, as well as of the modulus of the Polyakov loop, are computed in SU(3) lattice gauge theory. We show that the ratios of these susceptibilities are excellent probes of the deconfinement transition, independent ... More

On finding all positive integers $a,b$ such that $b\pm a$ and $ab$ are palindromicDec 20 2018Jan 13 2019It is proven that the only integer solutions $(a,b)$ such that $a+b$ and $ab$ are palindromic are $(2,5\cdot 10^k-3)$, $(3,24)$ and $(9,9)$, and in a similar fashion, $b-a$ and $ab$ are only palindromic at $(a,b)=(3,147\cdot 10^{4(k+1)}+5247\sum_{i=0}^k10^{4i})$, ... More

Interplay between antiferromagnetic order and spin polarization in ferromagnetic metal/electron-doped cuprate superconductor junctionsAug 24 2009Recently we proposed a theory of point-contact spectroscopy and argued that the splitting of zero-bias conductance peak (ZBCP) in electron-doped cuprate superconductor point-contact spectroscopy is due to the coexistence of antiferromagnetic (AF) and ... More

Ground states of supersymmetric Yang-Mills-Chern-Simons theorySep 09 2012We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus. The Witten index may be computed in the weak coupling limit, where the ground state wave-functions localize on the moduli space of flat gauge ... More

World-sheet aspects of mirror symmetryOct 20 1994(Talk given at the Oskar Klein centenary symposium 19-21 September 1994 in Stockholm, Sweden, to appear in the proceedings.) The first half of this talk is a non-technical discussion of some general aspects of string theory, in particular the problem ... More

Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-modelMay 07 2004Nov 10 2004We consider the (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. ... More

On a class of nonlinear Schrödinger equation on finite graphsMar 13 2019Suppose that $G=(V, E)$ is a finite graph with the vertex set $V$ and the edge set $E$. Let $\Delta$ be the usual graph Laplacian. Consider the following nonlinear Schr$\ddot{o}$dinger type equation of the form $$ \left \{ \begin{array}{lcr} -\Delta u-\alpha ... More

Zero-mode dynamics in supersymmetric Yang-Mills-Chern-Simons theoryDec 20 2012We consider minimally supersymmetric Yang-Mills theory with a Chern-Simons term on a flat spatial two-torus in the limit when the torus becomes small. The zero-modes of the fields then decouple from the non-zero modes and give rise to a spectrum of states ... More

Surface observables and the Weyl anomalyAug 27 1999I review the computation of the conformal anomaly of a Wilson surface observable in free two-form gauge theory in six dimensions.

Boundary conditions for GL-twisted N=4 SYMJun 20 2011Jul 04 2011We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. ... More

The low-energy spectrum of (2,0) theory on T^5 x RSep 24 2008We consider the ADE-series of (2, 0) supersymmetric quantum theories on T^5 \times R, where the first factor is a flat spatial five-torus, and the second factor denotes time. The quantum states of such a theory \Phi are characterized by a discrete quantum ... More

Wilson-'t Hooft operators and the theta angleMar 24 2006We consider $(3+1)$-dimensional $SU(N)/\mathbb Z_N$ Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle $\theta\to\theta+2\pi$, a 't Hooft operator $T(\gamma)$ ... More

The partition bundle of type A_{N-1} (2, 0) theoryDec 20 2010Dec 27 2010Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss ... More

Automorphic properties of (2, 0) theory on T6Nov 30 2009We consider ADE-type (2, 0) theory on a family of flat six-tori endowed with flat Sp(4) connections coupled to the R-symmetry. Our main objects of interest are the components of the `partition vector' of the theory. These constitute an element of a certain ... More

Dynamics of spinor Bose-Einstein condensate subject to dissipationFeb 02 2016We investigate the internal dynamics of the spinor Bose-Einstein Condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along specific orbital in ... More

Commutation relations for surface operators in six-dimensional (2, 0) theoryDec 08 2000The A_{N - 1} (2, 0) superconformal theory has an observable associated with every two-cycle in six dimensions. We make a natural guess for the commutation relations of these operators, which reduces to the commutation relations of Wilson and 't Hooft ... More

BPS-spectra in four dimensions from M-theoryNov 11 1997I review my work together with Piljin Yi on the spectrum of BPS-saturated states in N = 2 supersymmetric Yang-Mills theories. In an M-theory description, such states are realized as certain two-brane configurations. We first show how the central charge ... More

Gradient estimates for the weighted porous medium equation on graphsMar 13 2019In this paper, we study the gradient estimates for the positive solutions of the weighted porous medium equation $$\Delta u^{m}=\delta(x)u_{t}+\psi u^{m}$$ on graphs for $m>1$, which is a nonlinear version of the heat equation. Moreover, as applications, ... More

Moduli of PT-Semistable Objects INov 25 2010We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold $X$. Then we show that the stack of objects in the heart $\langle \Coh_{\leq 1}(X), \Coh_{\geq 2}(X)[1] \rangle$ satisfies a version of the valuative ... More

BPS states in (2,0) theory on R x T5Jan 07 2009We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where the first factor denotes time, and the second factor is a flat spatial five-torus. In addition to their energy, quantum states are characterized by their spatial momentum, 't ... More

Mirror symmetry for the Kazama-Suzuki modelsFeb 21 1994Apr 13 1994We study the $N = 2$ coset models in their formulation as supersymmetric gauged Wess-Zumino-Witten models. A model based on the coset $G/H$ is invariant under a symmetry group isomorphic to $\Z_{k+Q}$, where $k$ is the level of the model and $Q$ is the ... More

A class of six-dimensional conformal field theoriesJun 29 2000Dec 06 2000We describe a class of six-dimensional conformal field theories that have some properties in common with and possibly are related to a subsector of the tensionless string theories. The latter theories can for example give rise to four-dimensional $N = ... More

Existences of rainbow matchings and rainbow matching coversJun 10 2015Let $G$ be an edge-coloured graph. A rainbow subgraph in $G$ is a subgraph such that its edges have distinct colours. The minimum colour degree $\delta^c(G)$ of $G$ is the smallest number of distinct colours on the edges incident with a vertex of $G$. ... More

An edge-coloured version of Dirac's theoremDec 30 2012Dec 10 2013Let $G$ be an edge-coloured graph. The minimum colour degree $ \delta^c(G) $ of $G$ is the largest integer $k$ such that, for every vertex $v$, there are at least $k$ distinct colours on edges incident to $v$. We say that $G$ is properly coloured if no ... More

On the Exponential Decay of the n-point Correlation Functions and the Analyticity of the PressureApr 11 2007Jun 13 2007The goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n-point correlation functions for certain unbounded models of Kac type. The methods are based on estimating higher order derivatives of the solution ... More

Witten Laplacian Methods for the Decay of CorrelationsNov 01 2006Mar 24 2007The aim of this paper is to apply direct methods to the study of integrals that appear naturally in Statistical Mechanics and Euclidean Field Theory. We provide weighted estimates leading to the exponential decay of the two-point correlation functions ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfacesOct 12 2017On a Weierstra{\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted $Z^l$-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of $X$. We show that a slope ... More

Stability and Fourier-Mukai transforms on elliptic fibrationsJun 19 2012Jan 17 2014We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an application, we ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves on a product elliptic threefoldOct 09 2017On the product elliptic threefold $X = C \times S$ where $C$ is an elliptic curve and $S$ is a K3 surface of Picard rank 1, we define a notion of limit tilt stability, which satisfies the Harder-Narasimhan property. We show that under the Fourier-Mukai ... More

On some moduli of complexes on K3 surfacesMar 07 2012We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of ... More

A relation between higher-rank PT stable objects and quotients of coherent sheavesOct 02 2018On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime assumption on ... More

T-structures on elliptic fibrationsSep 10 2015We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures ... More

Fourier-Mukai transforms of slope stable torsion-free sheaves and stable 1-dimensional sheaves on Weierstrass elliptic threefoldsOct 10 2017We focus on a class of Weierstrass elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically $K$-trivial surface. In the first half of this article, we define the notion of limit tilt stability, which is closely related ... More

Moduli of PT-semistable objects IINov 29 2010May 04 2011We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ ... More

Uniqueness Theorem for non-compact mean curvature flow with possibly unbounded curvaturesSep 01 2017Feb 03 2019In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These generalize the ... More

Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetriesApr 15 2018Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D ... More

Photon-number tomography of multimode states and positivity of the density matrixMar 06 2019For one-mode and multimode light, the photon-number tomograms of Gaussian quantum states are explicitly calculated in terms of multivariable Hermite polynomials. Positivity of the tomograms is shown to be necessary condition for positivity of the density ... More

Ring to Mountain Transition in Deposition Pattern of DryingFeb 16 2016When a droplet containing a non-volatile component is dried on a substrate, it leaves a ringlike deposit on the substrate. We propose a theory which predicts the deposit distribution based on a model of fluid flow and contact line motion of the droplet. ... More

Excluded Volume Effects in Gene StretchingJun 17 2002We investigate the effects excluded volume on the stretching of a single DNA in solution. We find that for small force F, the extension h is not linear in F but proportion to F^{\chi}, with \chi=(1-\nu)/\nu, where \nu is the well-known universal correlation ... More

Quantum Tomography Approach in Signal AnalysisJun 02 1999Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to the fractional ... More

ML(n)BiCGStab: Reformulation, Analysis and ImplementationNov 24 2010With the aid of index functions, we re-derive the ML(n)BiCGStab algorithm in a paper by Yeung and Chan in 1999 in a more systematic way. It turns out that there are n ways to define the ML(n)BiCGStab residual vector. Each definition will lead to a different ... More

On differential characteristic classesNov 15 2013Oct 16 2014In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin ... More

The flat Grothendieck-Riemann-Roch theorem without adiabatic techniquesMar 15 2012May 31 2016In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation ... More

Compact Hermitian manifolds with quasi-negative curvatureOct 17 2018Nov 14 2018In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of Chern-Ricci curvature will be preserved if the initial metric has non-positive bisectional curvature. As an application, we show that the canonical ... More

To theory of tornado formation: mass condensation into droplets, their polarization by the Earth electric fields and rotation by magnetic fieldDec 07 2009Vapor condensation with removing of latent heat by emission of characteristic frequencies allows fast droplets formation in big volumes, which becomes possible with spatial redistribution and spreading of condensation nuclei and ions formed in long lightning ... More

Zero-energy states of N = 4 SYM on T^3: S-duality and the mapping class groupFeb 05 2008We continue our studies of the low-energy spectrum of N=4 super-Yang-Mills theory on a spatial three-torus. In two previous papers, we computed the spectrum of normalizable zero-energy states for all choices of gauge group and all values of the electric ... More

Weyl anomaly for Wilson surfacesMay 22 1999We consider a free two-form in six dimensions and calculate the conformal anomaly associated with a Wilson surface observable.

On the $L^{n\over 2}$-norm of Scalar CurvatureAug 03 1995Comparisons on $L^{n\over 2}$-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.

Photon-number tomography and fidelityDec 23 2012The scheme of photon-number tomography is discussed in the framework of star-product quantization. The connection of dual quantization scheme and observables is reviewed. The quantizer and dequantizer operators and kernels of star product of tomograms ... More

Tunneling solutions in topological field theory on R x S^3 x IDec 13 2011Feb 07 2012We consider a topologically twisted version, recently introduced by Witten, of five-dimensional maximally supersymmetric Yang-Mills theory on a five-manifold of the form M_5 =R x W_3 x I. If the length of the interval I is sufficiently large, the supersymmetric ... More

Gauss-Bonnet-Chern theorem and differential charactersFeb 04 2015Jan 31 2017In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.

On an index theorem by BismutJan 07 2015Jul 16 2015In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

Growth estimates on positive solutions of the equation $Δu + K u^{{n + 2}\over {n - 2}} = 0$ in ${\R}^n$Feb 01 2000We construct unbounded positive $C^2$-solutions of the equation $\Delta u + K u^{(n + 2)/(n - 2)} = 0$ in ${\R}^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive numbers in ${\R}^n$, the conformal metric $g = u^{4/(n ... More

Symplectic tomography of nonlinear coherent states of a trapped ionMar 03 2019Squeezed and rotated quadrature of an ion in a Paul trap is discussed in connection with reconstructing its quantum state using symplectic-tomography method. Marginal distributions of the quadrature for squeezed and correlated states and for nonlinear ... More

Construction of Blow-up Sequence for the Conformal Scalar Curvature Equation on S^n. I, II, and AppendixOct 06 2011Using the Lyapunov-Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S^n, (n > 5), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive ... More

Bayesian Nonparametric Estimation of a Unimodal Density via two $\mathbf{S}$-pathsSep 02 2006A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of densities generalize ... More

Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary SystemsJan 21 2004May 07 2004(Abridged) A diversity of 2:1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets ... More

On the Early In Situ Formation of Pluto's Small SatellitesMar 06 2018The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra - remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close ... More

A short representation of the six-dimensional (2, 0) algebraApr 20 2001We construct a BPS-saturated representation of the six-dimensional (2, 0) algebra with a certain non-zero value of the `central' charge. This representation is naturally carried by strings with internal degrees of freedom rather than by point particles. ... More

The light spectrum near the Argyres-Douglas pointJun 07 1999We consider N = 2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges ... More

The Holographic Weyl anomalyJun 11 1998Jun 17 1998We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. ... More

Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-dualityMar 19 2007Jun 10 2007We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions ... More

Uniqueness of Positive Solutions of the Conformal Scalar Curvature Equation and Applications to Conformal TransformationsOct 25 1996We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete Riemannian manifolds ... More

Arcwise connectedness of the boundaries of connected self-similar setsFeb 24 2003Let T be the attractor of injective contractions f_1,...,f_m on R^2 that satisfy the Open Set Condition. If T is connected, \partial T is arcwise connected. In particular, the boundary of the Levy dragon is arcwise connected.

A Predictable Rogue Wave and Generating MechanismsMar 05 2018Feb 08 2019Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and exists in all ... More

A multiple scattering theory approach to solving the time-dependent Schrödinger equation with an asymmetric rectangular potentialJun 29 2015An exact time-dependent solution for the wave function $\psi(r,t)$ of a particle moving in the presence of an asymmetric rectangular well/barrier potential varying in one dimension is obtained by applying a novel for this problem approach using multiple ... More

An exact solution of the time-dependent Schrödinger equation with a rectangular potential for real and imaginary timeSep 09 2015A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and transmission processes ... More

Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groupsJun 19 2007The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the ... More

Holography and the Weyl anomalyDec 03 1998We review our calculation of the Weyl anomaly for d-dimensional conformal field theories that have a description in terms of a (d + 1)-dimensional gravity theory.

Refined hexagons for differential cohomologyOct 02 2013Dec 07 2014Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential cohomology theories ... More

Refined estimates for simple blow-ups of the scalar curvature equation on S^nJul 08 2017In their work on a sharp compactness theorem for the Yamabe problem, Khuri, Marques and Schoen apply a refined blow-up analysis (what we call `second order blow-up argument' in this article) to obtain highly accurate approximate solutions for the Yamabe ... More

Simplicial Monoid Actions and The Associated Universal Simplicial Monoid ConstructionMar 15 2013The reduced universal monoid on the action category associated to a pointed simplicial M-set has appeared in the guise of various simplicial monoid and group constructions. These include the classical constructions of Milnor and James, as well as their ... More

On a class of quasilinear elliptic equation with indefinite weights on graphsMar 13 2019Suppose that $G=(V, E)$ is a connected locally finite graph with the vertex set $V$ and the edge set $E$. Let $\Omega\subset V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph $G$ $$ \left \{ \begin{array}{lcr} -\Delta_{p}u= ... More

Quantum Coding Theorem for Mixed StatesApr 04 1995Apr 19 1995We prove a theorem for coding mixed-state quantum signals. For a class of coding schemes, the von Neumann entropy $S$ of the density operator describing an ensemble of mixed quantum signal states is shown to be equal to the number of spin-$1/2$ systems ... More

Is baryon number violated when electroweak strings intercommute?Sep 15 1994Oct 14 1994We reexamine the self-helicity and the intercommutation of electroweak strings. A plausible argument for baryon number conservation when electroweak strings intercommute is presented. The connection between a segment of electroweak strings and a sphaleron ... More

Codegree Turán density of complete $r$-uniform hypergraphsJan 04 2018Apr 05 2018Let $r\ge 3$. Given an $r$-graph $H$, the minimum codegree $\delta_{r-1}(H)$ is the largest integer $t$ such that every $(r-1)$-subset of $V(H)$ is contained in at least $t$ edges of $H$. Given an $r$-graph $F$, the codegree Tur\'an density $\gamma(F)$ ... More

A multipartite version of the Hajnal-Szemerédi theorem for graphs and hypergraphsAug 21 2011Dec 30 2012A perfect $K_t$-matching in a graph $G$ is a spanning subgraph consisting of vertex disjoint copies of $K_t$. A classic theorem of Hajnal and Szemer\'edi states that if $G$ is a graph of order $n$ with minimum degree $\delta(G) \ge (t-1)n/t$ and $t| n$, ... More

Some examples of tilt-stable objects on threefoldsSep 12 2012We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which every slope ... More

Non-Asymptotic Convergence Analysis of Inexact Gradient Methods for Machine Learning Without Strong ConvexityAug 31 2013Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact gradient computations ... More

Nonnegative Trigonometric Polynomials, Sturms Theorem, and Symbolic ComputationFeb 27 2014Apr 26 2016In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This technique has been ... More

Spinors and the AdS/CFT correspondenceMar 30 1998Apr 03 1998We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject to a projection. ... More

Conformal Scalar Curvature Equations in Open SpacesOct 10 2001The article contains a brief description on the study of conformal scalar curvature equations, and discusses selected topics and questions concerning the equations in open spaces.

Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifoldsOct 30 1996Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant if the total ... More