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Orbit configuration spaces of small covers and quasi-toric manifoldsNov 29 2011Nov 05 2012In this article, we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology, such as small covers, quasi-toric manifolds and (real) moment-angle manifolds; especially for the cases ... More

Dispersion of velocity gradients: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity provides a robust measure of magnetic field direction. In this paper, we use velocity centroids as the measures of velocity and propose a new way of studying media magnetization. ... More

Slick PacketsJan 08 2012Source-controlled routing has been proposed as a way to improve flexibility of future network architectures, as well as simplifying the data plane. However, if a packet specifies its path, this precludes fast local re-routing within the network. We propose ... More

Gravitational instantons with faster than quadratic curvature decay (III)Mar 28 2016Oct 06 2016This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, ... More

Gravitational instantons with faster than quadratic curvature decay (II)Aug 31 2015Jun 23 2016This is our second paper in a series to study gravitational instantons, i.e. complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models ... More

Characterizations of asymptotic distributions of continuous-time Pólya processesNov 29 2016Sep 02 2018We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the process, coupled ... More

Gröbner-Shirshov bases for metabelian Lie algebrasJun 13 2011In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov bases for partial commutative metabelian Lie algebras related to circuits, trees and some cubes.

Faster Deterministic Algorithms for Packing, Matching and $t$-Dominating Set ProblemsJun 15 2013In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively. Although recently ... More

Exact Sample Size Methods for Estimating Parameters of Discrete DistributionsNov 08 2012Nov 19 2012In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal property assumptions, ... More

Principal boundary of moduli spaces of abelian and quadratic differentialsNov 05 2016The seminal work of Eskin-Masur-Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe ... More

Gravitational instantons with faster than quadratic curvature decay (I)May 07 2015In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In ALG and ... More

Exact Methods for Multistage Estimation of a Binomial ProportionFeb 13 2013We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, ... More

Some sufficient conditions for infinite collisions of simple random walks on a wedge combOct 26 2010In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\{f(n), n\in \ZZ\}$. One interesting result is that if $f(n)$ has a growth order as $n\log n$, then two independent ... More

Embedding of tenable and balanced urn scheme into continuous-time Pólya processNov 29 2016We study poissonized tenable and balanced urns on two colors, say white and blue. In particular, we look at the process obtained by embedding a generalized P\'{o}lya-Eggenberger urn into continuous time. We analyze the number of white and blue balls after ... More

HSEARCH: fast and accurate protein sequence motif search and clusteringJan 02 2017Protein motifs are conserved fragments occurred frequently in protein sequences. They have significant functions, such as active site of an enzyme. Search and clustering protein sequence motifs are computational intensive. Most existing methods are not ... More

Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficientsAug 30 2017Sep 24 2017Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide a rigourous mathematical theory of two types of nonequilibrium FDTs for inhomogeneous ... More

Delay-Optimal Buffer-Aware Probabilistic Scheduling with Adaptive TransmissionSep 09 2015Cross-layer scheduling is a promising way to improve Quality of Service (QoS) given a power constraint. In this paper, we investigate the system with random data arrival and adaptive transmission. Probabilistic scheduling strategies aware of the buffer ... More

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-foldsAug 27 2014Feb 02 2015For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $\varphi_{-m}$ is birational onto its image for all ... More

Orthogonal Quantum Group Invariants of LinksJul 09 2010We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition ... More

Minimum K_2,3-saturated GraphsDec 19 2010Nov 11 2012A graph is K_{2,3}-saturated if it has no subgraph isomorphic to K_{2,3}, but does contain a K_{2,3} after the addition of any new edge. We prove that the minimum number of edges in a K_{2,3}-saturated graph on n >= 5 vertices is sat(n, K_{2,3}) = 2n ... More

Adaptivity vs PostselectionJun 13 2016We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes $\mathcal{C}$, we have $\mathsf{P}^{\mathcal{C}}$ ... More

Bounded Rationality, Strategy Simplification, and EquilibriumFeb 24 2010Jun 26 2011It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization ... More

On the fundamental domain of affine Springer fibersMar 19 2013Mar 11 2014For $G$ a connected reductive group, $\gamma\in \kg(F)$ semisimple regular integral, we introduce a fundamental domain $F_{\gamma}$ for the affine Springer fibers $\xx_{\gamma}$. There is a beautiful way to reduce the purity conjecture of $\xx_{\gamma}$ ... More

Product Formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito IntegralsDec 05 2014We present the product formula for complex multiple Wiener-Ito integrals. As applications, we show the Ustunel-Zakai independent criterion, the Nourdin-Rosinski asymptotic moment-independent criterion and joint convergence criterion for complex multiple ... More

A Geometric Method to Obtain the Generation Probability of a SentenceJun 04 2014"How to generate a sentence" is the most critical and difficult problem in all the natural language processing technologies. In this paper, we present a new approach to explain the generation process of a sentence from the perspective of mathematics. ... More

Optimistic versus Pessimistic--Optimal Judgemental Bias with Reference PointOct 10 2013This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment ... More

The spatial meaning of Pareto's scaling exponent of city-size distributionSep 19 2013The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the fractal dimension. ... More

Scalar field quasinormal frequencies of Reissner-Nordström black hole surrounded by quintessenceMay 27 2016Jun 03 2016We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for ... More

Renormalization Group Flow of Four-fermi with Chern-Simons InteractionMay 09 1994Aug 25 1994We introduce Chern-Simons interaction into the three dimensional four-fermi theory, ad suggest a possible line of non-Gaussian infrared stable fixed points of the four-fermi operator, this line is characterized by the Chern-Simons coupling.

Topological Invariance at Finite TemperatureJun 08 1994We examine the thermal behavior of a theory with charged massive vector matter coupled to Chern-Simons gauge field. We obtain a critical temperature Tc, at which the effective mass of vector field vanishes, and the system transfers from a symmetry broken ... More

Localization Formulas About Two Killing Vector FieldsApr 13 2013In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.

Sequential change-point detection based on nearest neighborsApr 12 2016We propose a new framework for the detection of change points in online, sequential data analysis. The approach utilizes nearest neighbor information and can be applied to multivariate or object data sequences. Different stopping rules are explored, and ... More

The Cartan Model for Equivariant CohomologyAug 12 2016In this article, we will discuss a new operator $d_{C}$ on $W(\mathfrak{g})\otimes\Omega^{*}(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and ... More

A simple proof of Jordan normal formNov 24 2011In this note, a simple proof Jordan normal form and rational form of matrices over a field is given.

On bootstrap approximations for high-dimensional U-statistics and random quadratic formsSep 30 2016This paper establishes a unified theory of bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when $d$ is large. Specifically, we show that the empirical bootstrap with the ... More

Computing the Mazur and Swinnerton-Dyer critical subgroup of elliptic curvesDec 09 2014Jan 16 2015Let $E$ be an optimal elliptic curve defined over $\mathbb{Q}$. The critical subgroup of $E$ is defined by Mazur and Swinnerton-Dyer as the subgroup of $E(\mathbb{Q})$ generated by traces of branch points under a modular parametrization of $E$. We prove ... More

Some birationality criteria on 3-folds with $p_g>1$Nov 28 2011Jul 23 2014We give some birationality criteria for $\phi_m$ (m=4,5,6,7) on general type 3-folds with $p_g\geq 2$ by means of an intensive classification.

Normalizing and Classifying Shape Indexes of Cities by Ideas from FractalsAug 31 2016A standard scientific study comprises two processes: one is to describe a thing, and the other is to understand how the thing works. In order to understand the principle of urban growth, a number of shape indexes are proposed to describe the size and ... More

Universal Logarithmic Scrambling in Many Body LocalizationAug 09 2016Aug 28 2016Out of time ordered correlator (OTOC) is recently introduced as a powerful diagnose for quantum chaos. To go beyond, here we present an analytical solution of OTOC for a non-chaotic many body localized (MBL) system, showing distinct feature from quantum ... More

Equivalent Relation between Normalized Spatial Entropy and Fractal DimensionAug 06 2016Sep 25 2016Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy to fractal dimension is ... More

Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue SpacesNov 04 2015Feb 02 2016We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\] in some domain $Q\subset \mathbb{R}^{n+1}$. We prove growth ... More

Wave equations with moving potentialsOct 30 2016In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave operators ... More

Natural Exponential Families: Resolution of A Conjecture and Existence of Reduction FunctionsOct 14 2015Mar 19 2016One-parameter natural exponential family (NEF) plays fundamental roles in probability and statistics. This article contains two independent results: (a) A conjecture of Bar-Lev, Bshouty and Enis states that a polynomial with a simple root at $0$ and a ... More

Noether's problem for p-groups with three generatorsJan 17 2013Apr 22 2013Let $p$ be an odd prime and $G$ be a nonabelian group of order $p^{n}$ with the presentation $$<\alpha,\beta,\gamma\mid \alpha^{p^{a}}=\beta^{p^{b}}=\gamma^{p^{c}}=1, [\alpha,\gamma]=1,[\gamma,\beta]=\alpha^{p^{r}},[\alpha,\beta]=\gamma^{p^{e}}>,$$ where ... More

Multiplicity One Theorem for the Ginzburg-Rallis Model: the tempered caseAug 12 2016Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove the multiplicity one theorem for the Ginzburg-Rallis model over the Vogan packets in the tempered case. In ... More

The excluded minors for the class of matroids that are graphic or bicircular liftSep 10 2016Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph $G$, the circuits of its bicircular lift matroid $L(G)$ are the edge sets of those subgraphs of $G$ that contain at least two cycles, and are minimal ... More

Generalized Yang-Baxter Equations and Braiding Quantum GatesAug 26 2011Solutions to the Yang-Baxter equation - an important equation in mathematics and physics - and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum information science. ... More

Commuting involutions on surfaces of general type with p_g=0 and K^2=7Apr 17 2014The aim of this article is to classify the pairs (S, G), where S is a smooth minimal surface of general type with p_g=0 and K^2=7, G is a subgroup of the automorphism group of S and G is isomorphic to the group $\mathbb{Z}_2^2$. The Inoue surfaces with ... More

Covers of the projective line and the moduli space of quadratic differentialsMay 18 2010Consider the 1-dimensional Hurwitz space parameterizing covers of P^1 branched at four points. We study its intersection with divisor classes on the moduli space of curves. As an application, we calculate the slope of the Teichmuller curve parameterizing ... More

Degenerations of Abelian DifferentialsApr 08 2015Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, ... More

On the Upsilon invariant of cable knotsApr 16 2016Nov 28 2016In this paper, we study the behavior of $\Upsilon_K(t)$ under the cabling operation, where $\Upsilon_K(t)$ is the knot concordance invariant defined by Ozsv\'ath, Stipsicz, and Szab\'o, associated to a knot $K\subset S^3$. The main result is an inequality ... More

Twisted cohomology of configuration spaces and spaces of maximal tori via point-countingMar 12 2016We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in $\mathbb{C}^n$. ... More

Orientations, lattice polytopes, and group arrangements II: Modular and integral flow polynomials of graphsMay 13 2011We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart ... More

Dual complementary polynomials of graphs and combinatorial interpretation on the values of the Tutte polynomial at positive integersMay 13 2011Jun 08 2013We introduce a modular (integral) complementary polynomial $\kappa(G;x,y)$ ($\kappa_{\mathbbm z}(G;x,y)$) of two variables of a graph $G$ by counting the number of modular (integral) complementary tension-flows (CTF) of $G$ with an orientation $\epsilon$. ... More

Charmonium Production with QGP and Hadron Gas Effects at SPS and FAIROct 27 2015Nov 02 2015The production of charmonium in heavy-ion collisions is investigated based on Boltzmann-type transport model for charmonium evolution and langevin equation for charm quark evolution. Charmonium suppression and regeneration in both quark-gluon plasma (QGP) ... More

Colliding Plane Wave Solutions in String theory RevisitedSep 02 2004Dec 06 2004We construct the colliding plane wave solutions in the higher-dimensional gravity theory with fluxes and dilaton, with a more general ansatz on the metric. We consider two classes of solutions to the equations of motions and after imposing the junction ... More

A Smooth Compactification of the Moduli Space of Instantons and Its ApplicationApr 23 2002A smooth compactification of Donaldson moduli spaces is given. As an application, we use this new space to study the wall-crossing formula and prove the Kotschick-Morgan conjecture.

$G$-minimality and invariant negative spheres in $G$-Hirzebruch surfacesDec 03 2013Mar 08 2015In this paper a study of $G$-minimality, i.e., minimality of four-manifolds equipped with an action of a finite group $G$, is initiated. We focus on cyclic actions on $CP^2\# \overline{CP^2}$, and our work shows that even in this simple setting, the comparison ... More

On a notion of maps between orbifolds, II. homotopy and CW-complexOct 02 2006This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set ... More

Time-space fabric underlying anomalous diffusionMay 08 2005This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive fractional quantum ... More

A note on the Manin-Mumford conjectureMay 23 2014In this paper we prove a special case of the Andr\'e-Oort conjecture for Kuga varieties. If $M$ is a Kuga variety fibred over a pure Shimura variety $S$ as an abelian scheme, and $(M_n)$ is a sequence of special subvarieties in $M$ which are faithfully ... More

Bounded equidistribution of special subvarieties IIMar 21 2014In this paper, we prove a lower bound for the Galois orbits of a pure special subvariety in a general mixed Shimura variety. For special subvarieties that are not pure, we propose the notion of test invariants as a substitute for the lower bound estimation, ... More

On special subvarieties of Kuga varieties IIDec 12 2011In this paper we prove the equidistribution of $\Cbf$-special subvarieties in certain Kuga varieties, which implies a special case of the general Andr\'e-Oort conjecture formulated for mixed Shimura varieties proposed by R.Pink. The main idea is to reduce ... More

von Neumann-Landau equation for wave functions, wave-particle duality and collapses of wave functionsMar 22 2007Sep 29 2007It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the associated Schr\"{o}dinger's ... More

Variants of Bell inequalitiesNov 13 2006A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger ... More

Deeply Virtual Compton Scattering and Skewed Parton DistributionAug 02 2000An overview of the current status of and possible future theoretical, phenomenological and experimental studies of DVCS and SPD's is presented.

Strong laws of large numbers for capacitiesJun 03 2010In this paper, with the notion of independent identically distributed random variables under sub-linear expectations initiated by Peng, we derive three kinds of strong laws of large numbers for capacities. Moreover, these theorems are natural and fairly ... More

Algebras associated with Pseudo Reflection Groups: A Generalization of Brauer AlgebrasMar 27 2010We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra of simply-laced type introduced ... More

Mechanical Properties of La0.6Sr0.4Co0.2Fe0.8O3-d Fuel Cell ElectrodesFeb 07 2015LSCF is a promising candidate for the cathode in SOFCs. Understanding the microstructural characteristics is crucial to its application because they predominately determine the performance and durability of the porous cathodes and hence of the SOFCs. ... More

Boundedness of threefolds of Fano type with Mori fibration structuresJan 10 2016We show boundedness of $3$-folds of $\epsilon$-Fano type with Mori fibration structures. The proof is based on the birational boundedness result in our previous work arXiv:1509.08722 combining with arguments in Kawamata \cite{K} and Koll\'ar--Miyaoka--Mori--Takagi ... More

Machine Translation Model based on Non-parallel Corpus and Semi-supervised Transductive LearningMay 22 2014Although the parallel corpus has an irreplaceable role in machine translation, its scale and coverage is still beyond the actual needs. Non-parallel corpus resources on the web have an inestimable potential value in machine translation and other natural ... More

Sub-Gaussian heat kernel estimates and quasi Riesz transforms for $1\leq p\leq 2$Jan 10 2014On a complete non-compact Riemannian manifold $M$, we prove that a so-called quasi Riesz transform is always $L^p$ bounded for $1<p\leq 2$. If $M$ satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi ... More

Electron and phonon correlations in systems of one-dimensional electrons coupled to phononsJun 02 2008Aug 16 2008Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron ... More

Hsiao-Code Check Matrices and Recursively Balanced MatricesMar 08 2008The key step of generating the well-known Hsiao code is to construct a {0,1}-check-matrix in which each column contains the same odd-number of 1's and each row contains the same number of 1's or differs at most by one for the number of 1's. We also require ... More

The curvature of spectral energy distribution of blazarsMay 06 2014The SED of blazars show significant curvature. In this paper, we study the curvature properties for a large sample of Fermi/LAT bright blazars based on quasi-simultaneous SED. Both SEDs of synchrotron and inverse Compton (IC) components are fitted by ... More

GKM theory, characteristic classes and the equivariant cohomology ring of real GrassmannianSep 20 2016Oct 07 2016We use GKM theory to understand equivariant cohomology of real Grassmannian and oriented Grassmannian, then relate this to the Borel description which says the ring generators are equivariant Pontryagin classes, Euler classes in even dimension, and one ... More

On The Hardness of Approximate and Exact (Bichromatic) Maximum Inner ProductFeb 07 2018In this paper we study the (Bichromatic) Maximum Inner Product Problem (Max-IP), in which we are given sets $A$ and $B$ of vectors, and the goal is to find $a \in A$ and $b \in B$ maximizing inner product $a \cdot b$. Max-IP is very basic and serves as ... More

Real hypersurfaces with Miao-Tam critical metrics of complex space formsOct 18 2017Let $M$ be a real hypersurface of a complex space form with constant curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam critical metric, i.e. the induced metric $g$ on $M$ satisfies the equation:$-(\Delta_g\lambda)g+\nabla^2_g\lambda-\lambda ... More

Notes on Ricci solitons in $f$-cosymplectic manifoldsJan 17 2018The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class ... More

A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ MethodNov 13 2012By using the related results in the WZ theory, a new (as far as I know) formula for the values of Dirichlet beta function $\beta (s) = \sum\limits_{n = 1}^{+ \infty} {\frac{(-1)^{n - 1}}{(2n - 1)^s}} $ (where $Re(s) > 0$) at odd positive integers was ... More

Evaluations for zeta(2),zeta(4),...,zeta(2k)based on the WZ methodApr 18 2012Jul 30 2012Based on the framework of the WZ theory, a new evaluation for $\varsigma (2) = \frac{\pi ^2}{6}$ and $\varsigma (4) = \frac{\pi ^4}{90}$ was given respectively, finally, a new recurrence formula for $\varsigma (2k)$ was given.

The Analysis to Quasi-Local Energy and Hamiltonian Constraint based on VariationNov 07 2013Nov 14 2013In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic curvature dependent ... More

Zero density limit extrapolation of the superfluid transition temperature in a unitary atomic Fermi gas on a latticeSep 25 2011Feb 23 2012The superfluid transition temperature $T_c$ of a unitary Fermi gas on a three-dimensional isotropic lattice with an attractive on-site interaction is investigated as a function of density $n$, from half filling down to $5.0\times 10^{-7}$ per unit cell, ... More

Stable logarithmic maps to Deligne-Faltings pairs IAug 18 2010Feb 23 2011We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps is stable ... More

The degeneration formula for logarithmic expanded degenerationsSep 22 2010We define a notion of logarithmic stable maps based on Bumsig Kim's construction. Then we prove a degeneration formula under this setting by applying the method develeoped by Dan Abramovich and Barbara Fantechi for transversal maps.

On Algebraic Hyperbolicity of Log VarietiesNov 05 2001Dec 15 2001Fix a very general hypersurface D in P^n of degree at least 2n + 1 and we show that the complement P^n - D does not contain any algebraic torus C^*.

Minimal Twin SurfacesOct 25 2016Oct 16 2017We report some minimal surfaces that can be seen as copies of a triply periodic minimal surface (TPMS) related by reflections in parallel mirrors. We call them minimal twin surfaces for the resemblance with twin crystal. Brakke's Surface Evolver is employed ... More

Non-holonomy, critical manifolds and stability in constrained Hamiltonian systemsNov 10 2000Nov 12 2000We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it comprises the mechanical ... More

Typesafe Abstractions for Tensor OperationsOct 18 2017We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural ... More

On some determinant and matrix inequalities with a geometrical flavourJun 16 2016In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of Gressman [8]. ... More

On a theorem of Peters on automorphisms of Kahler surfacesDec 01 2004Dec 07 2004For any Kahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points and fixed ... More

On the $\pd$- and $\barpd$-Operators of a Generalized Complex StructureDec 02 2008Jan 16 2009In this note, we prove that the $\pd$- and $\barpd$-operators introduced by Gualtieri for a generalized complex structure coincide with the $\bdees$- and $\bdel$-operators introduced by Alekseev-Xu for Evens-Lu-Weinstein modules of a Lie bialgebroid.

Simply branched covers of an elliptic curve and the moduli space of curvesJun 04 2008Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g-2 points. Vary a branch point and the locus of such covers forms a one-parameter family W. We investigate the geometry of W by using admissible covers to study ... More

On Vojta's $1+ε$ ConjectureMay 11 2007Jun 01 2012I gave a geometric proof of Vojta's 1 + epsilon conjecture. Some gaps in the published paper were spotted and kindly pointed out to me by Paul Vojta. These were addressed in "Erratum".

Generalized Bloch spaces, Integral means of hyperbolic harmonic mappings in the unit ballDec 20 2016Nov 18 2017In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball $\mathbb{B}^{n}$ in $\IR^n$ $(n\geq 2)$. Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the Bloch space ... More

Mod r Vanishing Theorem of Seiberg-Witten Invariant for 4-Manifolds acted by Cyclic Group Z_rApr 07 2012Apr 11 2012In this paper, a vanishing theorem is stated and proved. If a 4-manifold $M$ admits a smooth action by a cyclic group $\mathbb{Z}_r$, then given an $\mathbb{Z}_r$-equivariant $Spin^c$-structure $\mathcal{C}$ on $M$, the Seiberg-Witten invariant $SW\mathcal{(C)}$ ... More

On the Alexander polynomial and the signature invariant of two-bridge knotsDec 13 2017Jan 10 2018Fox conjectured the Alexander polynomial of an alternating knot is trapezoidal, i.e. the coefficients first increase, then stabilize and finally decrease in a symmetric way. Recently, Hirasawa and Murasugi further conjectured a relation between the number ... More

A lower bound for the double slice genusJan 12 2018In this paper, we develop a lower bound for the double slice genus of a knot in the 3-sphere using Casson-Gordon invariants. As an application, we show that the difference between the slice genus and the double slice genus can be arbitrarily large. As ... More

Computing twisted Alexander polynomials for Montesinos linksSep 10 2017Oct 25 2018In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For a class of links, namely Montesinos links, we present an efficient method to compute the twisted Alexander polynomial associated to any linear ... More

On total flexibility of local structures of Finsler tori without conjugate pointsOct 28 2013Mar 09 2015We show that given a point on a Finsler surface, one can always find a neighborhood of the point and isometrically embed this neighborhood into a Finsler torus without conjugate points.