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Speaker diarisation using 2D self-attentive combination of embeddingsFeb 08 2019Speaker diarisation systems often cluster audio segments using speaker embeddings such as i-vectors and d-vectors. Since different types of embeddings are often complementary, this paper proposes a generic framework to improve performance by combining ... More

An Expandable Local and Parallel Two-Grid Finite Element SchemeSep 09 2015An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel finite element ... More

North Atlantic Right Whale Contact Call DetectionApr 30 2013Jun 07 2013The North Atlantic right whale (Eubalaena glacialis) is an endangered species. These whales continuously suffer from deadly vessel impacts alongside the eastern coast of North America. There have been countless efforts to save the remaining 350 - 400 ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More

Signature-Based Gröbner Basis Algorithms --- Extended MMM Algorithm for computing Gröbner basesAug 11 2013Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a view of signature-based ... More

Investigating Static and Dynamic Light ScatteringOct 08 2011A new size, static radii $R_{s}$, can be measured accurately using Static Light Scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute homogenous spherical particles in dispersion. The method proposed in this work not ... More

Investigating Diffusion Coefficient Using Dynamic Light Scattering TechniqueDec 12 2006In this work, the Z-average, effective, apparent diffusion coefficients and their poly-dispersity indexes were investigated for dilute poly-disperse homogeneous spherical particles in dispersion where the Rayleigh-Gans-Debye approximation is valid. The ... More

Three Different Sizes Obtained Using Light Scattering TechniquesNov 23 2004Dec 08 2004The average scattered intensity is determined by the optical characteristics of particles in dispersion. The normalized time auto-correlation function of the scattered light intensity $g^{(2)}(\tau) $ includes both the optical and hydrodynamic information ... More

Discussing the Relationship between the Static and Dynamic Light ScatteringOct 11 2004Dec 08 2004Both the static $(SLS) $ and dynamic $(DLS) $ light scattering techniques are used to obtain the size information from the scattered intensity, but the static radius $R_{s}$ and the apparent hydrodynamic radius $R_{h,app}$ are different. In this paper, ... More

New Interpretation for Laser Light Scattering TechniqueNov 18 2005The new method proposed in this work not only measures the particle size distribution and the average molar mass accurately using the static light scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute poly-disperse ... More

The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Aug 25 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More

Potential Polynomials and Motzkin PathsMay 28 2008A {\em Motzkin path} of length $n$ is a lattice path from $(0,0)$ to $(n,0)$ in the plane integer lattice $\mathbb{Z}\times\mathbb{Z}$ consisting of horizontal-steps $(1, 0)$, up-steps $(1,1)$, and down-steps $(1,-1)$, which never passes below the x-axis. ... More

Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop SolvabilitiesSep 07 2015Sep 15 2015This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas ... More

Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\mathbb{S}^{n+1}(1)$Jul 28 2016Aug 01 2016In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere $\mathbb{S}^{n+1}(1)$, i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition $\int_{\Omega_{1}}|\nabla ... More

Accurate and Efficient Solution of the Electronic Schrödinger Equation with the Coulomb Singularity by the Distributed Approximating Functional MethodApr 04 2016We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the solutions ... More

Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic PathsAug 30 2016Gutzwiller's famous semiclassical trace formula plays an important role in theoretical and experimental quantum mechanics with tremendous success. We review the physical derivation of this deep periodic orbit theory in terms of the phase space formulation ... More

Generic Base Change, Artin's Comparison Theorem, and the Decomposition Theorem for Complex Artin stacksNov 04 2015We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables us to deduce ... More

Enumeration of standard Young tableaux of shifted strips with constant widthJun 24 2015Let $g_{n_1,n_2}$ be the number of standard Young tableau of truncated shifted shape with $n_1$ rows and $n_2$ boxes in each row. By using of the integral method this paper derives the recurrence relations of $g_{3,n}$, $g_{n,4}$ and $g_{n,5}$ respectively. ... More

The physical origin of hydrophobic effectsJan 26 2016Aug 15 2016The strength of hydrogen bonding in water is stronger than that of van der waals interaction, therefore water may play an important role in the process of hydrophobic effects. When a hydrophobic solute is dissolved into water, an interface appears between ... More

Recovery of sparsest signals via $\ell^q$-minimizationMay 03 2010In this paper, it is proved that every $s$-sparse vector ${\bf x}\in {\mathbb R}^n$ can be exactly recovered from the measurement vector ${\bf z}={\bf A} {\bf x}\in {\mathbb R}^m$ via some $\ell^q$-minimization with $0< q\le 1$, as soon as each $s$-sparse ... More

Exact Decoding on Latent Variable Conditional Models is NP-HardJun 18 2014Latent variable conditional models, including the latent conditional random fields as a special case, are popular models for many natural language processing and vision processing tasks. The computational complexity of the exact decoding/inference in ... More

On the Coordinate System of Space-Weather HMI Active Region Patches (SHARPs): A Technical NoteSep 10 2013We describe the coordinate systems of two streams of HMI active region vector data. A distinction is made between (a) the 2D grid on which the field vector is measured (or sampled), and (b) the 3D coordinate established at each grid point, in which the ... More

Structure Regularization for Structured Prediction: Theories and ExperimentsNov 23 2014Jan 30 2015While there are many studies on weight regularization, the study on structure regularization is rare. Many existing systems on structured prediction focus on increasing the level of structural dependencies within the model. However, this trend could have ... More

Moduli spaces of SL(r)-bundles on singular irreducible curvesMar 17 2003For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset $\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves of rank $r$ and degree ... More

Monte Carlo studies of three-dimensional O(1) and O(4) \boldmath{$φ^4$} theory related to BEC phase transition temperaturesSep 20 2002The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2) symmetric $\phi^4$ ... More

Degeneration of SL(n)-bundles on a reducible curveDec 07 2001We constructed a projective moduli space of semistable torsion free sheaves with `fixed determinant' on a reducible curve. When a family of smooth curves degenerates to the reducible curve, our moduli space is a degeneration of the moduli spaces of semistable ... More

Toroidal Dimer Model and Temperley's BijectionMar 02 2016Temperley's bijection relates the toroidal dimer model to cycle rooted spanning forests ($CRSF$) on the torus. The height function of the dimer model and the homology class of $CRSF$ are naturally related. When the size of the torus tends to infinity, ... More

Parabolic Flow for Generalized complex Monge-Ampère type equationsJan 18 2015We study the parabolic flow for generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} $C^\infty$ estimates for normalized solutions, and then prove the $C^\infty$ convergence.

Generalized complex Monge-Ampère type equations on closed Hermitian manifoldsDec 28 2014Jun 28 2016We study generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} estimates and then prove the existence of admissible solutions. Moreover, the gradient estimate is improved.

On representations of real Jacobi groupsApr 30 2010Oct 12 2010We consider a category of continuous Hilbert space representations and a category of smooth Frechet representations, of a real Jacobi group $G$. By Mackey's theory, they are respectively equivalent to certain categories of representations of a real reductive ... More

W-Operator and Hurwitz NumberNov 15 2016W-operators are differential operators on the polynomial ring. Mironov, Morosov and Natanzon construct the generalized Hurwitz numbers. They use the W-operator to prove a formula for the generating function of the generalized Hurwitz numbers. A special ... More

A simple bijection between binary trees and colored ternary treesMay 09 2008In this short note, we first present a simple bijection between binary trees and colored ternary trees and then derive a new identity related to generalized Catalan numbers.

Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert SpacesNov 15 2016Nov 16 2016Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by Eckstein and Bertsakas ... More

A supercharacter theory for Sylow $p$-subgroups of the Steinberg triality groupsNov 28 2016Aug 09 2018We determine a supercharacter theory for the matrix Sylow $p$-subgroup ${^3}D_4^{syl}(q^3)$ of the Steinberg triality group ${^3}D_4(q^3)$, and establish the supercharacter table of ${^3}D_4^{syl}(q^3)$.

Laguerre and Jacobi analogues of the Warren processOct 05 2016Jul 24 2017We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of K\"onig-O'Connell and ... More

A new integral formula for Heckman-Opdam hypergeometric functionsJun 14 2014Dec 07 2015We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald ... More

On the Entropy of Parabolic Allen-Cahn EquationDec 20 2018In this paper we define the entropy of Radon measures, especially the measures associated to the parabolic Allen-Cahn equation. We show that when the entropy of the initial data is small enough (less than twice of the energy of the one dimensional standing ... More

NonLERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groupsAug 17 2016Aug 23 2018We will show that, for any noncompact arithmetic hyperbolic $m$-manifold with $m> 3$, and any compact arithmetic hyperbolic $m$-manifold with $m> 4$ that is not a $7$-dimensional arithmetic hyperbolic manifold defined by octonions, its fundamental group ... More

Finite dimensional representations of the rational Cherednik algebra for $G_4$Oct 29 2009In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group $G_4$. In particular, we classify the irreducible finite dimensional representations and compute their characters.

Investigation of Volume Phase Transition from the Different Properties of ParticlesNov 18 2005In this work, three different particle sizes: the static radius $R_{s}$, hydrodynamic radius $R_{h}$ and apparent hydrodynamic radius $ R_{h,app}$ obtained using the light scattering technique, are investigated for dilute poly-disperse homogenous spherical ... More

Zero entropy invariant measures for some skew product diffeomorphismsDec 15 2008In this paper we study some skew product diffeomorphisms with nonuniformly hyperbolic structure along fibers. We show that there is an invariant measure with zero entropy which has atomic conditional measures along fibers.

A probabilistic approach for enumeration of certain Young tableauxFeb 04 2013In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially standard Young ... More

Entropy and Ergodic Measures for Toral AutomorphismsMar 06 2011We show that for every linear toral automorphism, especially the non-hyperbolic ones, the entropies of ergodic measures form a dense set on the interval from zero to the topological entropy.

OPESCI-FD: Automatic Code Generation Package for Finite Difference ModelsMay 20 2016In this project, we introduce OPESCI-FD, a Python package built on symbolic mathematics to automatically generate Finite Difference models from a high-level description of the model equations. We investigate applying this framework to generate the propagator ... More

Tilt-stability, vanishing theorems for stable sheaves and applicationsSep 12 2016We study the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters. For a stable sheaf, we give some effective bounds of these parameters such that the stable sheaf is tilt-stable. ... More

Probe Anomalous $tqγ$ couplings through Single Top Photoproduction at the LHCFeb 08 2014Jul 17 2014In this work we study the constraints on the anomalous $tq\gamma$ ($q=u$, $c$) couplings by photon-produced leading single top production and single top jet associated production through the main reaction $pp\rightarrow p\gamma p\rightarrow pt\rightarrow ... More

The nonvanishing hypothesis at infinity for Rankin-Selberg convolutionsJul 20 2013Dec 02 2015We prove the nonvanishing hypothesis at infinity for Rankin-Selberg convolutions for $\GL(n)\times \GL(n-1)$.

Stability Criterion for Convolution-Dominated Infinite MatricesJul 22 2009Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the $\ell^p$-stability ... More

Logarithmic heat projective operatorsSep 21 2000Let $f:\Cal C\to S$ be a flat family of curves over a smooth curve $S$ such that $f$ is smooth over $S_0=S\ssm\{s_0\}$ and $f^{-1}(s_0)=\Cal C_0$ is irreducible with one node. We have an associated family $\Cal M_{S_0}\to S_0$ of moduli spaces of semistable ... More

Degeneration of moduli spaces and generalized theta functionsJul 29 1999We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.

Topological Symmetries of R^3, IIMar 10 2016If a fintie group G acts topologically and faithfully on R^3, then G is a subgroup of O(3)

Convergence of Coalescing Nonsimple Random Walks to the Brownian WebJan 10 2005The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $\R\times\R$. It was first introduced by Arratia, and later analyzed in detail by T\'{o}th and Werner. More recently, Fontes, Isopi, Newman and ... More

Model actions for almost reduced groups on UHF algebrasSep 24 2014For any countable discrete group $G$ with a reduced abelian subgroup of finite index, we construct an action $\alpha$ of $G$ on the universal UHF algebra $\Qq$ using an infinite tensor product of permutation representations of $G$ and show that these ... More

The general $J$-flowsJul 31 2015We study the general $J$-flows. We use Moser iteration to obtain the uniform estimate.

Physical Angular Momentum Separation for QEDAug 18 2016We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts ... More

Covering a cubic graph by 5 perfect matchingsJan 13 2016Feb 29 2016Berge Conjecture states that every bridgeless cubic graph has 5 perfect matchings such that each edge is contained in at least one of them. In this paper, we show that Berge Conjecture holds for two classes of cubic graphs, cubic graphs with a circuit ... More

Laguerre and Jacobi analogues of the Warren processOct 05 2016We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of K\"onig-O'Connell and ... More

Traces of intertwiners for quantum affine sl_2 and Felder-Varchenko functionsAug 17 2015Dec 06 2015We show that the traces of $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of Etingof-Schiffmann-Varchenko valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction ... More

Character tables of Sylow $p$-subgroups of the Steinberg triality groups ${^3}D_4(q^3)$Jun 20 2016Aug 08 2018We determine the character tables of Sylow $p$-subgroups $U$ of the Steinberg triality groups ${^3}D_4(q^3)$, where $q$ is a power of an odd prime $p$.

Necessity of numerical smoothnessJul 12 2012Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial smoothness indicators ... More

Different Particle Sizes Obtained from Static and Dynamic Laser Light ScatteringMay 31 2004Dec 08 2004Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) ... More

Note on K-stability of pairsAug 23 2011Nov 23 2012We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.

Infinite Mixtures of Multivariate Gaussian ProcessesJul 26 2013This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture ... More

Independence of $\ell$ for the supports in the Decomposition TheoremDec 04 2015In this note, we prove a result on the independence of $\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence ... More

An exact axisymmetric spiral solution of incompressible 3D Euler equationsJan 29 2011Jul 31 2011Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, ... More

Rank $n$ swapping algebra for the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin componentNov 11 2014Oct 24 2015F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce ... More

A representation-theoretic proof of the branching rule for Macdonald polynomialsDec 01 2014We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal ... More

The Star of David RuleMay 09 2008In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are ... More

Measures of Intermediate Entropies for Skew Product DiffeomorphismsJun 10 2009Jan 18 2010In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. ... More

Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped DomainsJul 20 2015We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is ... More

W-Operators and Permutation GroupsOct 20 2016W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of ... More

Dark Matter Searches in Jet plus Missing Energy in $\rm γp$ collision at CERN LHCJul 21 2014Aug 01 2014In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus missing energy signal to set limits on the couplings of the fermionic dark matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow p\gamma p\rightarrow p \chi\chi ... More

Counting Hypergraphs in Data StreamsApr 28 2013We present the first streaming algorithm for counting an arbitrary hypergraph $H$ of constant size in a massive hypergraph $G$. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, ... More

Pluricanonical maps of varieties of Albanese fiber dimension twoNov 28 2012Feb 23 2014In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions. ... More

On the Clifford theorem for surfacesMar 04 2012We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Oct 17 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More

Universal central extensions of twisted forms of split simple Lie algebras over ringsNov 17 2010Nov 19 2010We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by ... More

On uniform estimate of complex elliptic equations on closed Hermitian manifoldsDec 16 2014Feb 10 2015In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed K\"ahler manifolds. ... More

On a class of fully nonlinear elliptic equations on closed Hermitian manifoldsOct 01 2013We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive $C^\infty$ {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch ... More

A New Formula for the Inverse Wavelet TransformJun 20 2010Aug 30 2010Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

Shifted convolution sums of $GL_3$ cusp forms with $θ$-seriesSep 25 2015Sep 10 2016Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $\phi(x)$ be a smooth function compactly ... More

Stability of sheaves of locally closed and exact formsMay 13 2009For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of exact 1-forms ... More

Direct images of bundles under Frobenius morphismsNov 13 2006Mar 31 2008Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded ... More

Suspicion on Engrafting HBT From Astronomy to Heavy Ion CollisionDec 13 2004Aug 19 2005HBT method in astronomy and heavy ion collision is contrasted in present article.Some differences are found and validity of using HBT in heavy ion collision is suspected.

Factorization of generalized theta functions at reducible caseApr 17 2000We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.

Topological Phases of Fermionic Ladders with Periodic Magnetic FieldsDec 14 2015In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting ... More

Two laws of large numbers for sublinear expectationsNov 18 2015In this paper, we consider the sublinear expectation on bounded random vari- ables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the no- tion of independence for ... More

A probabilistic approach to enumeration of Gessel walksMar 02 2009We consider Gessel walks in the plane starting at the origin $(0, 0)$ remaining in the first quadrant $i, j \geq 0$ and made of West, North-East, East and South-West steps. Let $F(m; n_1, n_2)$ denote the number of these walks with exact $m$ steps ending ... More

Frobenius morphism and semi-stable bundlesApr 09 2009This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008, Seoul. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct ... More

Virtual Domination of $3$-manifoldsJan 27 2014For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M'$, such that there exists a degree-$2$ map $f:M'\rightarrow N$, i.e. $M$ virtually $2$-dominates $N$.

Virtual Homological Torsion of Closed Hyperbolic 3-manifoldsSep 05 2013Jun 05 2014In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. ... More

Ordinary p-adic automorphic formsSep 18 2017Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of "ordinary $p$-adic automorphic forms along a parabolic subgroup" and show that they interpret all classical ordinary automorphic forms.

A Transcendental Invariant of Pseudo-Anosov MapsSep 12 2012May 09 2013For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will ... More

Investigation Solvation Dynamics and Isomerization of Dye IR-140 Using pump supercontinuum-probing TechniqueNov 06 2001The solvation dynamics and isomerization process of an organic dye, IR-140, in polar solvents and nonpolar solvents have been investigated using pump supercontinuum-probing (PSCP) technique. In all solvents, the dynamics exhibits solvent-dependent. Solvent ... More

Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover which has a homological eigenvalue with modulus greater than $1$, then the monodromy of any fibered structure of any finite cover of $M_{\phi}$ has this property.

On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection ruleApr 18 2015In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given ... More

Decomposition Theorem for Perverse sheaves on Artin stacks over finite fieldsSep 22 2010Mar 11 2012We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.

L-series of Artin stacks over finite fieldsAug 22 2010Mar 28 2011We reprove the Lefschetz trace formula for stacks (in the context of derived categories and the six operations for stacks developed by Laszlo and Olsson), and give the meromorphic continuation of L-series (in particular, zeta functions) of Artin stacks ... More

Axisymmetrically Tropical Cyclone-like Vortices with Secondary CirculationsSep 07 2013The secondary circulation of the tropical cyclone (TC) is related to its formation and intensification, thus becomes very important in the studies. The analytical solutions have both the primary and secondary circulation in a three-dimensionally nonhydrostatic ... More