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Analytical Gradients for Projection-Based Wavefunction-in-DFT EmbeddingMar 14 2019Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of density functional ... More

Hassle-free Approach to Thermal Transport Measurements Using Spatial-Temporal Temperature DataMar 07 2019Nanoscale engineering and novel materials have created interesting effects in thermal transport. Thermal conductivity can now be different due to physical and heating sizes. Also, highly anisotropic thermal conductivity can result from unique material ... More

Theoretical study of position-dependent defect formation in a single-walled carbon nanotube: Stability towards an open endJul 30 2006Point defects, including atom vacancy, add atom and Stone-Wale defect, close to a (5, 5) single-walled carbon nanotube (SWNT) end were studied by DFT, semi-empirical PM3 method and empirical Brenner Potential. It is found that closer to the SWNT opening ... More

Companion points and locally analytic socle for $\mathrm{GL}_2(L)$Feb 29 2016Let $p>2$ be a prime number, and $L$ be a finite extension of $\mathbb{Q}_p$, we prove Breuil's locally analytic socle conjecture for $\mathrm{GL}_2(L)$, showing the existence of all the companion points on the definite (patched) eigenvariety. This work ... More

$\mathcal{L}$-invariants, partially de Rham families and local-global compatibilityAug 29 2015Feb 22 2016Let $F_{\wp}$ be a finite extension of $\mathbb{Q}_p$. By considering partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on Fontaine-Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional semi-stable non-crystalline $\mathrm{Gal}(\overline{\mathbb{Q}_p}/F_{\wp})$-representations. ... More

Minimal cones and self-expanding solutions for mean curvature flowsMar 09 2015In this paper, we study self-expanding solutions for mean curvature flows and applications to minimal cones in Euclidean space. For an embedded mean convex (but not area-minimizing) cone $C$ pointing into a domain $\Omega$ with $\partial\Omega=C$, there ... More

A Construction of Binary Linear Codes from Boolean FunctionsNov 01 2015Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on the study of ... More

Cyclic Codes from APN and Planar FunctionsJun 20 2012Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear functions and planar ... More

A Sequence Construction of Cyclic Codes over Finite FieldsNov 20 2016Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer electronics, and data storage systems. There are several approaches to constructing all cyclic codes ... More

The Application of Bayesian Technique for Particle IdentificationFeb 24 2006Oct 26 2006The PID problem in high energy physics experiments is analysed with Bayesian technique. The corresponding applicable method is presented.

Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general treesMar 22 2011Feb 25 2014In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, ... More

Hopf algebra extension of a Zamolochikov algebra and its doubleDec 04 1996Dec 05 1996The particles with a scattering matrix R(x) are defined as operators $\Phi_i(z)$ satisfying the relation $ R_{i,j}^{j',i'}(x_1/x_2) \Phi_{i'}(x_1)\Phi_{j'}(x_2)= \Phi_i(x_2)\Phi_j(x_1)$. The algebra generated by those operators is called a Zamolochikov ... More

Partial Gauss decomposition, \bf $U_q(\widehat{\frak{gl}(n-1)})\in U_q(\widehat{\frak{gl}(n)}) $ and Zamolodchikov algebraJan 19 1998We use the idea of partial Gauss decomposition to study structures related to $U_q(\widehat{{{\frak{gl}}}(n-1)})$ inside $U_q(\widehat{{{\frak{gl}}}(n)}) $. This gives a description of $U_q(\widehat{{{\frak{gl}}}(n)})$ as an extension of $U_q(\widehat{{{\frak{gl}}}(n-1)})$ ... More

Three Occurrences of the Hyperbolic-Secant DistributionJan 07 2014Although it is the generator distribution of the sixth natural exponential family with quadratic variance function, the Hyperbolic-Secant distribution is much less known than other distributions in the exponential families. Its lack of familiarity is ... More

On equivalence relations generated by Schauder basesApr 01 2015In this paper, a notion of Schauder equivalence relation $\mathbb R^\mathbb N/L$ is introduced, where $L$ is a linear subspace of $\mathbb R^\mathbb N$ and the unit vectors form a Schauder basis of $L$. The main theorem is to show that the following conditions ... More

Variational Analysis of the Ky Fan $k$-normJan 27 2016In this paper, we will study some variational properties of the Ky Fan $k$-norm $\theta=\|\cdot\|_{(k)}$ of matrices, which are closed related to a class of basic nonlinear optimization problems involving the Ky Fan $k$-norm. In particular, for the basic ... More

A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret SharingMar 23 2015In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear ... More

Selective Radiative Heating of Nanostructures Using Hyperbolic MetamaterialsDec 16 2014Hyperbolic metamaterials (HMM) are of great interest due to their ability to break the diffraction limit for imaging and enhance near-field radiative heat transfer. Here we demonstrate that an annular, transparent HMM enables selective heating of a sub-wavelength ... More

Spinor representations of $U_q(\hat{\frak o}(N))$Feb 12 1996This is an extension of quantum spinor construction of $U_q(\hat {\frak gl}(n))$. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of $U_q(\hat{\frak ... More

Applying weighted PageRank to author citation networksFeb 09 2011This paper aims to identify whether different weighted PageRank algorithms can be applied to author citation networks to measure the popularity and prestige of a scholar from a citation perspective. Information Retrieval (IR) was selected as a test field ... More

Singular vector distribution of covariance matricesNov 06 2016We consider a class of covariance matrices of the form $Q=\Sigma^{\frac{1}{2}}XX^{*} \Sigma^{\frac{1}{2}},$ where $X=(x_{ij})$ is an $M \times N$ rectangle matrix consisting of i.i.d entries and $\Sigma$ is a diagonal positive definite matrix satisfying ... More

The Exploratory Research of the Effect Communication Model and Effect Improving Strategy of Interactive AdvertisingMar 08 2016Interactive advertising which characterized by interactivity has become the mainstream of advertising by gradually replacing traditional one-way advertising during the new media era. This paper has obeyed the research outline below, literature review, ... More

Entanglement Entropy in Many-Fermion SystemAug 17 2009In this four-part prospectus, we first give a brief introduction to the motivation for studying entanglement entropy and some recent development. Then follows a summary of our recent work about entanglement entropy in states with traditional long-range ... More

On the Schrödinger flowsApr 18 2003We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.

Cyclotomic Constructions of Cyclic Codes with Length Being the Product of Two PrimesNov 13 2011Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made. In this paper, ... More

Cyclic Codes from Dickson PolynomialsJun 20 2012Nov 17 2016Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first and second kind ... More

Asymptotic Bound on Binary Self-Orthogonal CodesApr 26 2008We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R=1/2, by our constructive lower bound, the relative ... More

Learning Undirected Graphical Models with Structure PenaltyApr 27 2011In undirected graphical models, learning the graph structure and learning the functions that relate the predictive variables (features) to the responses given the structure are two topics that have been widely investigated in machine learning and statistics. ... More

Comment on "Quantum Strategy Without Entanglement"Jun 01 2006Sep 15 2006We make remarks on the paper of Du et al (quant-ph/0011078) by pointing out that the quantum strategy proposed by the paper is trivial to the card game and proposing a simple classical strategy to make the game in classical sense fair too.

Connections between Double Zeta Values relative to $μ_N$, Hecke Operators $T_N$, and Newforms of Level $Γ_0(N)$ for $N=2,3$Nov 19 2015In this paper, we will study various connections between double zeta values relative to $\mu_N$, Hecke operators $T_N$, and newforms of level $\Gamma_0(N)$ for $N=2,3$. Those various connections generalize the well-known of Baumard and Schneps. We also ... More

On The 1+2 Dimensional Landau-Lifshitz EquationApr 14 2005By using the geometric concept of PDEs with prescribed curvature representations, we show that the 1+2 dimensional Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schr\"odinger-type system. From the nonlinear Schr\"odinger-type ... More

A Bernstein type theorem for minimal hypersurfaces via Gauss mapsMar 19 2018Let $M$ be an $n$-dimensional smooth oriented complete minimal hypersurface in $\mathbb{R}^{n+1}$ with Euclidean volume growth. We show that if the image under the Gauss map of $M$ avoids some neighborhood of a half-equator, then $M$ must be an affine ... More

Entire spacelike translating solitons in Minkowski spaceApr 09 2012In this paper, we study entire spacelike translating solitons in Minkowski space. By constructing convex spacelike solutions to (1.3) in bounded convex domains, we obtain many entire smooth convex strictly spacelike translating solitons by prescribing ... More

Greedy Strategy Works for Clustering with Outliers and Coresets ConstructionJan 24 2019We study the problems of clustering with outliers in high dimension. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithms with low complexities for the problems. Our ... More

Borel reducibility and Holder($α$) embeddability between Banach spacesDec 10 2009We investigate Borel reducibility between equivalence relations $E(X,p)=X^{\Bbb N}/\ell_p(X)$'s where $X$ is a separable Banach space. We show that this reducibility is related to the so called H\"older$(\alpha)$ embeddability between Banach spaces. By ... More

Scaling window for mean-field percolation of averagesOct 14 2011Feb 15 2013For a complete graph of size $n$, assign each edge an i.i.d. exponential variable with mean $n$. For $\lambda>0$, consider the length of the longest path whose average weight is at most $\lambda$. It was shown by Aldous (1998) that the length is of order ... More

Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free fieldMay 29 2011Sep 25 2012We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay ... More

A remark on Gromov-Witten-Welschinger invariants of $\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$Feb 20 2019We generalize the formula of Gromov-Witten-Welschinger invariants of $\mathbb{C} P^3$ established by E. Brugall\'e and P. Georgieva in [BG16b] to $\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$. Using pencils of quadrics, some real and complex enumerative ... More

Period polynomial relations between formal double zeta values of odd weightSep 26 2014Oct 21 2015For odd $k$, we give a formula for the relations between double zeta values $\zeta(r,k-r)$ with $r$ even. This formula provides a connection with the space of cusp forms on $\mathrm{SL}_2(\mathbb{Z})$. This is the odd weight analogue of a result by Gangl, ... More

On quantum cluster algebras of finite typeNov 07 2010Feb 24 2011We extend the definition of a quantum analogue of the Caldero-Chapoton map defined in \cite{rupel}. When $Q$ is a quiver of finite type, we prove that the algebra $\mathcal{AH}_{|k|}(Q)$ generated by all cluster characters (see Definition \ref{def}) is ... More

On surjectively universal Polish groupsSep 11 2011A Polish group is surjectively universal if it can be continuously homomorphically mapped onto every Polish group. Making use of a type of new metrics on free groups \cite{DG}, we prove the existence of surjectively universal Polish groups, answering ... More

On the Conditional Distribution of the Multivariate $t$ DistributionApr 02 2016As alternatives to the normal distributions, $t$ distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate $t$ distribution are well documented in Kotz and Nadarajah's book, which, however, ... More

Spinor Representations of $U_q(\hat{\frak gl}(n))$ and Quantum Boson-Fermion CorrespondenceOct 17 1995Nov 20 1995This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak gl}(n))$ and explain ... More

A Remark On the FRTS realization and Drinfeld Realization of Quantum Affine Superalgebra $U_q(\hat {osp}(1,2))$May 13 1999May 14 1999In this paper, we present the hidden symmetry behind the Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky realization of quantum affine superalgebras $U_q(\hat {osp}(1,2))$ and add the q-Serre relation to the Drinfeld realization of $U_q(\hat {osp}(1,2))$ ... More

$\mathcal{L}$-invariants and local-global compatibility for the group $\mathrm{GL}_2/F$Jan 27 2015Feb 18 2016Let $F$ be a totally real number field, $\wp$ a place of $F$ above $p$. Let $\rho$ be a $2$-dimensional $p$-adic representation of $\mathrm{Gal}(\bar{F}/F)$ which appears in the \'etale cohomology of quaternion Shimura curves (thus $\rho$ is associated ... More

Analysis of Massive Heterogeneous Temporal-Spatial Data with 3D Self-Organizing Map and Time VectorSep 27 2016Self-organizing map(SOM) have been widely applied in clustering, this paper focused on centroids of clusters and what they reveal. When the input vectors consists of time, latitude and longitude, the map can be strongly linked to physical world, providing ... More

Some results on locally analytic socle for $\mathrm{GL}_n(\mathbb{Q}_p)$Nov 21 2015We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuil's locally analytic socle conjecture ... More

An ExpTime Procedure for Description Logic $\mathcal{ALCQI}$ (Draft)Mar 12 2007Mar 18 2007A worst-case ExpTime tableau-based decision procedure is outlined for the satisfiability problem in $\mathcal{ALCQI}$ w.r.t. general axioms.

Testing Lorentz and CPT Symmetries in Penning TrapsOct 28 2016A modified Dirac equation with general Lorentz- and CPT-violating operators in the electromagnetic field is studied. Constraints on and possible sensitivities to Lorentz-violating coefficients in the nonminimal sector up to mass-dimension six can be obtained ... More

Cyclic Codes from Cyclotomic Sequences of Order FourJul 11 2012Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In this paper, three ... More

Linear Codes from Some 2-DesignsMar 23 2015A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the literature. In this ... More

Causally neutral quantum physicsFeb 15 2019In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present an algebraic ... More

Henri Lebesgue and the End of Classical Theories on CalculusJan 11 2012In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the theories on current ... More

The Radical Mistakes in the Theories on Calculus of Cauchy-Lebesgue SystemDec 10 2011The misunderstanding of the concept of differentials in the theories on calculus of Cauchy-Lebesgue system was exposed in this paper. The defects of the definition of differentials and the associated mistakes in the differentiation of composite functions ... More

Explicit Blowing-up Solutions to the Schrödinger Maps from ${\bf R}^2$ to the Hyperbolic 2-Space ${\bf H}^2$Dec 01 2003Jun 01 2009In this article, we prove that the equation of the Schr\"odinger maps from ${\bf R}^2$ to the hyperbolic 2-space ${\bf H}^2$ is SU(1,1)-gauge equivalent to the following 1+2 dimensional nonlinear Schr\"odinger-type system of unknown three complex functions ... More

A paradox from randomization-based causal inferenceFeb 02 2014Jun 23 2016Under the potential outcomes framework, causal effects are defined as comparisons between potential outcomes under treatment and control. To infer causal effects from randomized experiments, Neyman proposed to test the null hypothesis of zero average ... More

Dynamics of Yang-Mills Cosmology Bubbles in Bartnik-McKinnon SpacetimesApr 20 1995May 01 1995We investigate the dynamics of a Yang-Mills cosmology (YMC, the FRW type spacetime) bubble in the Bartnik-McKinnon (BK) spacetimes. Because a BK spacetime can be identified to a YMC spacetime with a finite scale factor in the neighborhood of the origin, ... More

Tensor Powers of the Defining Representation of $S_n$Aug 21 2015Feb 05 2016We give a decomposition formula for tensor powers of the defining representation of $S_n$ and apply it to bound the mixing time of a Markov chain on $S_n$.

Two paradoxical results in linear models: the variance inflation factor and the analysis of covarianceMar 09 2019A result from a standard linear model course is that the variance of the ordinary least squares (OLS) coefficient of a variable will never decrease if we add additional covariates. The variance inflation factor (VIF) measures the increase of the variance. ... More

A toy model of shtukasFeb 13 2018Nov 02 2018Motivated by the question of constructing certain rational functions (modular units) on the moduli stack of Drinfeld shtukas, we introduce the notion of toy shtukas. We prove basic properties of the moduli scheme of toy shtukas. Analogously to horospherical ... More

Construction of certain rational functions on the moduli stack of Drinfeld shtukasOct 20 2018We construct certain rational functions (modular units) on the moduli stack of Drinfeld shtukas. The divisors of these rational functions are supported on horospherical divisors of the moduli stack. The key to our construction is a vanishing theorem for ... More

On some partially de Rham Galois representationsOct 16 2014Sep 01 2015We study some partially de Rham representations of $\mathrm{Gal}(\bar{L}/L)$ for a finite unramified extension $L$ of $\mathbb{Q}_p$. We study some related subspaces of Galois cohomology and of cohomology of $B$-pairs. As an application, we associate ... More

Two Propositions Involving the Standard Representation of $S_n$Feb 10 2013We present here two standalone results from a forthcoming work on the analysis of Markov chains using the representation theory of $S_n$. First, we give explicit formulas for the decompositions of tensor powers of the defining and standard representations ... More

On the Gradient of Harmonic FunctionsNov 10 2018Dec 05 2018For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined by ... More

Active Thermal Extraction of Near-field Thermal RadiationApr 08 2015Radiative heat transport between materials supporting surface-phonon polaritons is greatly enhanced when the materials are placed at sub-wavelength separation as a result of the contribution of near-field surface modes. However, the enhancement is limited ... More

High Resolution Ultraviolet Quasar Absorption Line Spectroscopy of z~1 Galaxy GroupJul 18 2002We used ultraviolet spectra from HST/STIS (R=30,000), together with optical spectra from Keck/HIRES (R=45,000), to study the three MgII-selected absorption systems at z=0.9254, 0.9276, and 0.9342 toward the quasar PG 1206+459. A multi-phase gaseous structure, ... More

A restriction for singularities on collapsing orbifoldsJan 24 2011Jul 07 2011An orbifold $X$ is locally homeomorphic to $G_x\backslash B_r(0)$, where $G_x$ is a finite group acting on $B_r(0)\subset{\mathbb R}^n$, so that $G_x(0)=0$. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in $|G_x|$. ... More

Semantic Web: Who is who in the field - A bibliometric analysisDec 21 2010The Semantic Web is one of the main efforts aiming to enhance human and machine interaction by representing data in an understandable way for machines to mediate data and services. It is a fast-moving and multidisciplinary field. This study conducts a ... More

On List-decodability of Random Rank Metric CodesJan 13 2014Jan 23 2014In the present paper, we consider list decoding for both random rank metric codes and random linear rank metric codes. Firstly, we show that, for arbitrary $0<R<1$ and $\epsilon>0$ ($\epsilon$ and $R$ are independent), if $0<\frac{n}{m}\leq \epsilon$, ... More

A Construction for Constant-Composition CodesFeb 13 2008By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving ... More

Axiomatization and complexity of modal logic with knowing-what operator on model class KSep 25 2016Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In "Conditionally Knowing ... More

Cosmological Sphaleron from Real Tunneling and Its FateJul 25 1994Aug 05 1994We show that the cosmological sphaleron of Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the Lorentzian signature ... More

Borel reducibility and finitely Holder(α) embeddabilityJul 02 2010Let $(X_n,d_n),\,n\in\Bbb N$ be a sequence of pseudo-metric spaces, $p\ge 1$. For $x,y\in\prod_{n\in\Bbb N}X_n$, let $(x,y)\in E((X_n)_{n\in\Bbb N};p)\Leftrightarrow\sum_{n\in\Bbb N}d_n(x(n),y(n))^p<+\infty$. For Borel reducibility between equivalence ... More

Characterization of $\ell_p$-like and $c_0$-like equivalence relationsJun 23 2010Let $X$ be a Polish space, $d$ a pseudo-metric on $X$. If $\{(u,v):d(u,v)<\delta\}$ is ${\bf\Pi}^1_1$ for each $\delta>0$, we show that either $(X,d)$ is separable or there are $\delta>0$ and a perfect set $C\subseteq X$ such that $d(u,v)\ge\delta$ for ... More

Certain Metric Properties of Level HypersurfacesApr 21 2018This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

Higher genus Welschinger invariants under real surgeriesOct 09 2017Jan 14 2018According to [3], a real surgery of a real del Pezzo surface $X_\mathbb{R}$ along a real sphere $S$ is a modification of the real structure on $X_\mathbb{R}$ in a neighborhood of $S$. In this paper, we study the behavior of higher genus Welschinger invariants ... More

Hawking radiation and total entropy change as tunnelingFeb 02 2013Oct 21 2013In the frame of Hamilton-Jacobi method, the back-reactions of the radiating particles together with the total entropy change of the whole system are investigated. The emission probability from this process is found to be equivalent to the null geodesic ... More

Axiomatization and complexity of modal logic with knowing-what operator on model class KSep 25 2016Nov 25 2016Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In "Conditionally Knowing ... More

Cyclic Codes from Dickson PolynomialsJun 20 2012Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first and second kind ... More

Probabilistic Inferences in Bayesian NetworksNov 03 2010Nov 05 2010Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to complex problems. ... More

Graphs without large $K_{2,n}$-minorsFeb 05 2017The purpose of this paper is to characterize graphs that do not have a large $K_{2,n}$-minor. As corollaries, it is proved that, for any given positive integer $n$, every sufficiently large 3-connected graph with minimum degree at least six, every 4-connected ... More

A rigidity theorem on the second fundamental form for self-shrinkersJan 27 2017In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).

Minimal cones and self-expanding solutions for mean curvature flowsMar 09 2015Jun 05 2017In this paper, we study self-expanding solutions for mean curvature flows and their relationship to minimal cones in Euclidean space. In [17], Ilmanen proved the existence of self-expanding hypersurfaces with prescribed tangent cones at infinity. If the ... More

Subsequent singularities of mean convex mean curvature flows in smooth manifoldsFeb 09 2015Jan 05 2016For any $n$-dimensional smooth manifold $\Sigma$, we show that all the singularities of the mean curvature flow with any initial mean convex hypersurface in $\Sigma$ are cylindrical (of convex type) if the flow converges to a smooth hypersurface $M_{\infty}$ ... More

Infinite families of $t$-designs from a type of five-weight codesJul 17 2016It has been known for a long time that $t$-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a $t$-design. While a lot of progress in the direction of constructing codes from ... More

Renormalization and alpha-limit set for expanding Lorenz mapsMar 27 2007Jun 17 2009We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of periodic orbit of ... More

Inverse of a matrix related to double zeta values of odd weightOct 21 2015In this paper, we give a proof of a conjecture made by Zagier about the inverse of some matrix related to double zeta values of parity $(\mathrm{even},\mathrm{odd})$. As a result, we obtain a family of Bernoulli number identities. We further generalize ... More

A trichotomy for a class of equivalence relationsJan 06 2010Let $X_n, n\in\Bbb N$ be a sequence of non-empty sets, $\psi_n:X_n^2\to\Bbb R^+$. We consider the relation $E((X_n,\psi_n)_{n\in\Bbb N})$ on $\prod_{n\in\Bbb N}X_n$ by $(x,y)\in E((X_n,\psi_n)_{n\in\Bbb N})\Leftrightarrow\sum_{n\in\Bbb N}\psi_n(x(n),y(n))<+\infty$. ... More

Several Metric Properties of Level CurvesApr 21 2018This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of the function. ... More

On cover times for 2D latticesOct 15 2011Jun 05 2012We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2}[\sqrt{2/\pi} ... More

Smallest Irreducible of the Form $x^2-dy^2$Mar 01 2016It is a classical result that prime numbers of the form $x^2+ny^2$ can be characterized via class field theory for an infinite set of $n$. In this paper we derive the function field analogue of the classical result. Then we apply an effective version ... More

Faster Balanced Clusterings in High DimensionSep 04 2018Sep 10 2018The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by the given lower ... More

Balanced $k$-Center Clustering When $k$ Is A ConstantApr 08 2017The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds. The problem ... More

Bayesian Robust Inference of Sample Selection Using Selection-t ModelsJan 07 2014Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection-t ... More

A remark on degenerate singularity in three dimensional Ricci flowSep 05 2007We show that a rescale limit at any degenerate singularity of Ricci flow in dimension 3 is a steady gradient soliton. In particular, we give a geometric description of type I and type II singularities.

Characterizing Level-set Families of Harmonic FunctionsDec 05 2018Families of hypersurfaces that are level-set families of harmonic functions are characterized by a simple analytic condition. Harmonic functions with a specified level-set family are constructed from geometric data. Emphasis is placed on the two-variable ... More

Phonon Coherence and Its Effect on Thermal Conductivity of NanostructuresJun 09 2018Aug 31 2018The concept of coherence is one of the fundamental phenomena in electronics and optics. In addition to electron and photon, phonon, is another important energy and information carrier in nature. Without any doubt, exploration of the phonon coherence and ... More

A Legendrian surgery presentation of contact 3-manifoldsJul 06 2001Jun 01 2003We prove that every closed, connected contact 3-manifold can be obtained from the 3-sphere with its standard contact structure by contact surgery of coefficient plus or minus 1 along a Legendrian link. As a corollary, we derive a result of Etnyre and ... More

Symplectic fillability of tight contact structures on torus bundlesApr 10 2001We study weak versus strong symplectic fillability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically fillable. For the ... More

A unique decomposition theorem for tight contact 3-manifoldsOct 09 2006It has been shown by V. Colin that every tight contact 3-manifold can be written as a connected sum of prime manifolds. Here we prove that the summands in this decomposition are unique up to order and contactomorphism.