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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

Angora: Efficient Fuzzing by Principled SearchMar 04 2018Mar 27 2018Fuzzing is a popular technique for finding software bugs. However, the performance of the state-of-the-art fuzzers leaves a lot to be desired. Fuzzers based on symbolic execution produce quality inputs but run slow, while fuzzers based on random mutation ... More

Notes on "Einstein metrics on compact simple Lie groups attached to standard triples"Jan 06 2017In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant ... More

Modeling the Annual Growth Rate of Electricity Consumption of China in the 21st Century: Trends and PredictionOct 21 2017In this paper, the annual growth rate of electricity consumption in China in the first 15 years of the 21st century is modeled using multiple linear regression. Historical data and trends of gross domestic product, fixed assets investment and share of ... 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

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

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.

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, IIAug 16 2017By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano ... 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

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

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

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

Estimates of Dirichlet Eigenvalues for a Class of Sub-elliptic OperatorsMay 31 2019Let $\Omega$ be a bounded connected open subset in $\mathbb{R}^n$ with smooth boundary $\partial\Omega$. Suppose that we have a system of real smooth vector fields $X=(X_{1},X_{2},$ $\cdots,X_{m})$ defined on a neighborhood of $\overline{\Omega}$ that ... More

Spin and hyperelliptic structures of log twisted differentialsOct 17 2016Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian ... More

On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative EigenvaluesSep 11 2010For an indecomposable $3\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means ... 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

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

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

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

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)Mar 15 2018Jul 19 2018We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq ... More

Fine Residual Carrier Frequency and Sampling Frequency Estimation in Wireless OFDM SystemsNov 08 2012This paper presents a novel algorithm for residual phase estimation in wireless OFDM systems, including the carrier frequency offset (CFO) and the sampling frequency offset (SFO). The subcarriers are partitioned into several regions which exhibit pairwise ... More

CrowdFusion: A Crowdsourced Approach on Data Fusion RefinementFeb 02 2017Data fusion has played an important role in data mining because high-quality data is required in a lot of applications. As on-line data may be out-of-date and errors in the data may propagate with copying and referring between sources, it is hard to achieve ... 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

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

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

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

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

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

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

The Value of Interaction in Data IntelligenceDec 14 2018In human computer interaction (HCI), it is common to evaluate the value of HCI designs, techniques, devices, and systems in terms of their benefit to users. It is less common to discuss the benefit of HCI to computers. Every HCI task allows a computer ... 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

A Concise Proof of Discrete Jordan Curve TheoremNov 17 2014Nov 26 2014This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note on the discrete ... More

Secure Communication over Interference Channel: To Jam or Not to Jam?Oct 30 2018We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap ... More

Convergence of Krasulina SchemeAug 28 2018Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points $X_1, X_2,..., X_n$ are vectors drawn i.i.d. from a distribution with mean zero and covariance $\Sigma$, ... More

A Novel Radiation to Test Foundations of Quantum MechanicsMar 05 2014We point out that a new mechanism for radiation should exist if the Bohm theory of quantum mechanics is taken seriously. By traversing a quantum potential, an electron will necessarily be accelerated and radiate. For an illustration, we show that in the ... More

Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groupsApr 06 2018In this paper we show that the leading coefficients $\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in the affine Weyl group of type $\widetilde{B_n}$ can be $n$; in the cases of types $\widetilde{C_n}$ and $\widetilde{D_n}$ they can ... More

Thermodynamics and weak cosmic censorship conjecture in extended phase spaces of anti-de Sitter black holes with fermions' absorptionFeb 18 2019The thermodynamics and weak cosmic censorship conjecture in extended phase spaces of anti-de Sitter black holes where the cosmological constant is seen as a pressure with a conjugate volume are investigated by fermions' absorption. The first law of thermodynamics ... More

A gap theorem for minimal log discrepancies of non-canonical singularities in dimension threeApr 21 2019We show that there exists a positive real number $\delta>0$ such that for any normal quasi-projective $3$-fold $X$, if $X$ has worse than canonical singularities, that is, the minimal log discrepancy of $X$ is less than $1$, then the minimal log discrepancy ... More

Optimal density lower bound on nonisentropic gas dynamicsDec 14 2018In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations.

Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classificationJun 14 2017Nov 16 2017We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains ... More

An example of cobordism map on PFHJan 08 2019In this note, we compute the cobordism map on periodic Floer homology induced by elementary Lefschetz fibration

On Multiplicity Formula for Spherical VarietiesMay 16 2019May 24 2019In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois model and Shalika ... More

Morse-Novikov cohomology of almost nonnegatively curved manifoldsApr 22 2019Let $M^n$ be a closed manifold of almost nonnegative sectional curvature and nonzero first de Rham cohomology group. For any $[\theta] \in H^1_{dR}(M^n), [\theta] \neq 0$, we show that the Morse- Novikov cohomology group $H^p(M^n, \theta)$ vanishes 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

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

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

Discretized sum-product for large setsJan 27 2019Let $A\subset [1, 2]$ be a $(\delta, \sigma)$-set with measure $|A|=\delta^{1-\sigma}$ in the sense of Katz and Tao. For $\sigma\in (1/2, 1)$ we show that $$ |A+A|+|AA|\gtrapprox \delta^{-c}|A|, $$ for $c=\frac{(1-\sigma)(2\sigma-1)}{6\sigma+4}$. This ... 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

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.

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.

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.

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

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.

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

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

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

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

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

Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (III)Oct 26 2017Mar 05 2019In a recent paper, {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)}, we discussed two algorithms for deforming and contracting a simply connected discrete closed manifold into a discrete sphere. The first ... More

The universal surface bundle over the Torelli space has no sectionsOct 02 2017Oct 09 2017For $g>3$, we give two proofs of the fact that the \emph{Birman exact sequence} for the Torelli group \[ 1\to \pi_1(S_g)\to {\cal I}_{g,1}\to {\cal I}_g\to 1 \] does not split. This result was claimed by G. Mess in \cite{mess1990unit}, but his proof has ... More

Section problems for configuration spaces of surfacesAug 26 2017May 20 2019In this paper we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of $n$ ordered points on a surface $S$ of finite type so that all the points are still distinct? When this is possible, ... More

Surjective homomorphisms between surface braid groupsApr 17 2017Apr 26 2019Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then compute the automorphism ... More

Programming of Finite Element Methods in MATLABApr 14 2018We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. ... More

On the jet properties of the gamma-ray loud active galactic nucleiMar 14 2018Apr 12 2018Based on broadband spectral energy distribution (SEDs), we estimate the jet physical parameters of 1392 $\gamma$-ray-loud active galactic nuclei (AGNs), the largest sample so far. The (SED) jet power and magnetization parameter are derived for these AGNs. ... More

Steep Points of Gaussian Free Fields in Any DimensionFeb 08 2018This work aims to extend the existing results on the Hausdorff dimension of the classical thick point sets of a Gaussian free field (GFF) to a more general class of exceptional sets. We adopt the circle or sphere averaging regularization to treat a singular ... More

The universal $n$-pointed surface bundle only has $n$ sectionsNov 14 2016Sep 02 2018The classifying space BDiff$(S_{g,n})$ of the orientation-preserving diffeomorphism group of the surface $S_{g,n}$ of genus $g>1$ with $n$ ordered marked points has a universal bundle \[ S_g \to \text{UDiff}(S_{g,n})\xrightarrow{\pi}\text{BDiff}(S_{g,n}). ... More

Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)Jul 26 2015In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to assume an ambient ... More

A note on Sobolev type inequalities on graphs with polynomial volume growthFeb 07 2019We prove a scale of generalized $L^p$-Poincar\'e inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.

On minimal 3-folds of general type with maximal pluricanonical section indexApr 17 2016Jun 05 2017Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or $\delta(X)=18$. ... 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

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