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Scale Invariant Fully Convolutional Network: Detecting Hands EfficientlyJun 11 2019Existing hand detection methods usually follow the pipeline of multiple stages with high computation cost, i.e., feature extraction, region proposal, bounding box regression, and additional layers for rotated region detection. In this paper, we propose ... More

Data Priming Network for Automatic Check-OutApr 10 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognize the categories and counts of the items chosen by the customers. However, the training of such ... More

Representation for bounded linear operator on Hilbert spacesNov 07 2016In this paper we construct some $C^{*}$-algebra induced by polar decomposition $T=U|T|$. We get that $T$ is unitary equivalent to $\sqrt{|\eta|}M_{z\phi}$ on $\mathcal{L}^{2}(\sigma(|T|),\mu_{|T|})$, where $\phi\in\mathcal{L}^{\infty}(\sigma(|T|),\mu_{|T|})$ ... More

Protein Photo-folding and Quantum Folding TheoryMay 12 2011The rates of protein folding with photon absorption or emission and the cross section of photon -protein inelastic scattering are calculated from the quantum folding theory by use of standard field-theoretical method. All these protein photo-folding processes ... More

Law of Genome Evolution Direction : Coding Information Quantity GrowsAug 25 2008The problem of the directionality of genome evolution is studied. Based on the analysis of C-value paradox and the evolution of genome size we propose that the function-coding information quantity of a genome always grows in the course of evolution through ... More

Cohomology of Oriented Tree Diagram Lie AlgebrasApr 08 2008Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues ... More

On polynomial representations of classical strange Lie superalgebrasJan 20 2010In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the underlying modules. ... More

X-ray emission from magnetic dissipation in the magnetar magnetosphereMay 14 2007Magnetic dissipation through decay of Alfven waves in the magnetar magnetosphere is discussed. Transport of magnetic fields in the star leads to dissipation of the magnetic energy through either direct internal heating or transferring of the energy in ... More

A New Approach to Abstract Machines - Introduction to the Theory of Configuration MachinesJul 19 2010An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these notions as a ... More

Z decays into light gluinos: a calculation based on unitarityJan 08 2003May 11 2003The Z boson can decay to a pair of light gluinos through loop-mediated processes. Based on unitarity of the S-matrix, the imaginary part of the decay amplitude is computed in the presence of a light bottom squark. This imaginary part can provide useful ... More

Role of electrical field in quantum Hall effect of grapheneJul 19 2012The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation ... More

On Low Complexity Maximum Likelihood Decoding of Convolutional CodesNov 20 2007Jul 31 2008This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA), complexity reduction ... More

SNAP: SNowbAll multi-tree Pushing for Peer-to-Peer Media StreamingSep 13 2010Given the respective advantages of the two complimentary techniques for peer-to-peer media streaming (namely tree-based push and mesh-based pull), there is a strong trend of combining them into a hybrid streaming system. Backed by recently proposed mechanisms ... More

Damping Effect of Electromagnetic Radiation and Time-Dependent Schrodinger EquationFeb 05 2010Jun 06 2011The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term representing this effect ... More

Nonlinear Schrodinger equation containing the time derivative of the probability density: A numerical studyDec 29 2009May 11 2014The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of the corresponding ... More

Architectural Techniques for Improving NAND Flash Memory ReliabilityAug 12 2018Raw bit errors are common in NAND flash memory and will increase in the future. These errors reduce flash reliability and limit the lifetime of a flash memory device. We aim to improve flash reliability with a multitude of low-cost architectural techniques. ... More

On Generalization of Lax Equivalence Theorem into Unbounded Self-adjoint Operators with Nontrivial KernelAug 15 2017Apr 28 2019For an unbounded self-adjoint operator $ A $ and its resolvent approximation sequence $ \{ A_n \} $, the Moore-Penrose inverse sequence $ \{ A^\dagger_n \}$ is a natural computational scheme of the Moore-Penrose inverse $ A^\dagger $. This paper shows ... More

Remarks on the nonexistence of biharmonic mapsNov 23 2015Apr 04 2016In this short note we study nonexistence result of biharmonic maps from a complete Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. Assume that $\phi:(M,g)\to (N, h)$ is a biharmonic map, where $(M, g)$ is a complete ... More

Variable stars in the open cluster NGC 2141Oct 08 2014Oct 09 2014We report the results of a search for variable stars in the open cluster NGC 2141. Ten variable stars are detected, among which nine are new variable stars and they are classified as three short period W UMa type eclipsing binaries, two EA type eclipsing ... More

Zeros of exceptional orthogonal polynomials and the maximum of the modulus of an energy functionJun 24 2017We propose a new property of the zeros of exceptional orthogonal polynomials. It has been known that exceptional orthogonal polynomials (XOP) have both real and complex zeros. By fixing m variables at the imaginary parts of the complex zeros of XOP, we ... More

On-shell improved lattice QCD with staggered fermionsFeb 13 1997May 23 1997By using Symanzik's improvement program, we study on-shell improved lattice QCD with staggered fermions. We find that there are as many as 15 independent lattice operators of dimension of six~(including both gauge and fermion operators) which must be ... More

On conformal surfaces of annulus typeOct 24 2011Dec 07 2011Let $a>b>0$ and $f$ be a conformal map from $B_a\setminus B_b\subseteq R^2$ into $\R^n$, with $|\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\frac{\partial f}{\partial r},$ and $e_2=r^{-1}e^{-u}\frac{\partial f}{\partial\theta}$ is a moving ... More

Yet another normalisation proof for Martin-Lof's logical framework--Terms with correct arities are strongly normalisingJun 14 2005Jun 15 2005In this paper, we prove the strong normalisation for Martin-L\"{o}f's Logical Framework, and suggest that {}``correct arity'', a condition weaker than well-typedness, will also guarantee the strong normalisation.

Minima distribution for global optimizationDec 09 2018May 13 2019This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By introducing a class ... More

Stable Numerical Differentiation and Generalized Termwise Differentiation on Fourier SeriesMar 10 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on Fourier basis ... More

A note on Muller's irreducibility criterion for generalized principal seriesMar 18 2019In this paper, via Casselman--Tadic's Jacquet module machine, we reprove I. Muller's irreducibility criterion for principal series, and extend it to generalized principal series. An analogous criterion for covering groups is readily obtained. At last, ... More

Rodier type theorem for generalized principal seriesMar 16 2019In this paper, we extend Rodier's structural theorem for regular principal series to regular generalized principal series of split groups of classical types, which can be viewed as a first step to understand the internal structure of the singular case. ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019Apr 10 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of the first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric ... More

Variational bounds on the ground-state energy of three electrons and one hole in two-dimensionDec 31 2000Jan 09 2001We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon ^2 \hbar ^2 ... More

An Alternative Explanation on the Two Relaxation Rates in Cuprate SuperconductorsNov 22 2000Dec 05 2000Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. ... More

Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$Sep 17 2009Jan 22 2010The character formula of any finite dimensional irreducible module $L_\lambda$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module $L_\lambda\otimes \mathbb{C}^{n|2}$, where $\mathbb{C}^{n|2}$ is ... More

On the barycentric extensionMay 02 2019In this paper, we will study the Douady-Earle / barycentric extension of maps on $S^{n-1}$. We will show the extension is uniformly Lipschitz if the map is quasiregular. In particular, we will show the barycentric extension for a rational map $f$ on $S^2$ ... More

Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary ConditionsApr 07 2009In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied ... More

Reducing subspaces of multiplication operators on the Dirichlet spaceJun 28 2018In this paper, we study the reducing subspaces for the multiplication operator by a finite Blaschke product $\phi$ on the Dirichlet space $D$. We prove that any two distinct nontrivial minimal reducing subspaces of $M_\phi$ are orthogonal. When the order ... More

A Counting Lemma for Binary Matroids and Applications to Extremal ProblemsOct 30 2016Nov 20 2018In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that guarantees many ... More

Discussion on the origin of magic numbers in clustersNov 01 2014The distribution of the sizes of clusters is not continuous, but rather has local maxima. The numbers of atoms of those maxima distribution is called magic numbers. Two methods of determining magic numbers are firstly introduced, followed by three different ... More

Exploration on Grounded Word Embedding: Matching Words and Images with Image-Enhanced Skip-Gram ModelSep 08 2018Word embedding is designed to represent the semantic meaning of a word with low dimensional vectors. The state-of-the-art methods of learning word embeddings (word2vec and GloVe) only use the word co-occurrence information. The learned embeddings are ... More

Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheresDec 09 2013Dec 04 2014We consider stochastic differential equations on the group of volume-preserving homeomorphisms of the sphere $S^d\,(d\geq 2)$. The diffusion part is given by the divergence free eigenvector fields of the Laplacian acting on $L^2$-vector fields, while ... More

A note on complete hyperbolic structures on ideal triangulated 3-manifoldsOct 18 2010It is a theorem of Casson and Rivin that the complete hyperbolic metric on a cusp end ideal triangulated 3-manifold maximizes volume in the space of all positive angle structures. We show that the conclusion still holds if some of the tetrahedra in the ... More

Automorphisms of Thurston's Space of Measured LaminationsMay 21 1999We give a characterization of the action of the mapping class group on Thurston's space of measured laminations.

Solving a Mathematical Problem in Square War: a Go-like Board GameJul 26 2015Nov 29 2015In this paper, we present a board game: Square War. The game definition of Square War is similar to the classic Chinese board game Go. Then we propose a mathematical problem of the game Square War. Finally, we show that the problem can be solved by using ... More

Solving Thurston Equation in a Commutative RingJan 11 2012We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.

Unified Description of Efficiency Correction and Error Estimation for Moments of Conserved Quantities in Heavy-Ion CollisionsOct 15 2014Apr 05 2015I provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected for the efficiency ... More

A Framework for Solving Turing Kernel (Compression) Lower Bound Problem and Finding Natural Candidate Problems in NP-intermediateSep 18 2016Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. For kernelization, It has been established a nice hardness theory [Bodlaender etc. (ICALP 2008, JCSS2009), Fortnow and Santhanam ... More

Weak contraction map and topological non-convex optimizationJul 08 2018Nov 11 2018The definition of weak contraction map and the existence and uniqueness of the fixed-point of weak contraction map is discussed. A stochastic contour-based optimization method based on weak contraction map is proposed to achieve global minimum convergence. ... More

Intrinsic Awareness, the Fundamental State of ConsciousnessJan 12 2011Oct 31 2013In an effort to simplify the complexity in the studies of consciousness, the author suggests to divide the conscious experiences into a fundamental state, the intrinsic awareness (IA), and functions of this fundamental state. IA does not depend on external ... More

Improvement of the Staggered Fermion OperatorsApr 30 1996We present a complete and detailed derivation of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order ... More

Quantum Theory on Glucose Transport Across MembraneJul 27 2014Nov 26 2014After a brief review of the protein folding quantum theory and a short discussion on its experimental evidences the mechanism of glucose transport across membrane is studied from the point of quantum conformational transition. The structural variations ... More

Abelian Ideals and Cohomology of Symplectic TypeApr 08 2008For symplectic Lie algebras $\mathfrak{sp}(2n,\mathbb{C})$, denote by $\mathfrak{b}$ and $\mathfrak{n}$ its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of $\mathfrak{b}$ and the ... More

A Unified Theory on Construction and Evolution of the Genetic CodeAug 21 2009A quantitative theory on the construction and the evolution of the genetic code is proposed. Through introducing the concept of mutational deterioration (MD) and developing a theoretical formalism on MD minimization we have proved: 1, the redundancy distribution ... More

On the Law of Directionality of Genome EvolutionMay 08 2008Aug 04 2011The problem of the directionality of genome evolution is studied from the information-theoretic view. We propose that the function-coding information quantity of a genome always grows in the course of evolution through sequence duplication, expansion ... More

Entropy Production in a Cell and Reversal of Entropy Flow as an Anticancer TherapyFeb 01 2008The entropy production rate of cancer cell is always higher than healthy cell under the case of no external field applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is ... More

Sub-picosecond proton tunnelling in deformed DNA hydrogen bonds under an asymmetric double-oscillator modelMar 21 2018Jul 03 2018We present a model of proton tunnelling across DNA hydrogen bonds, compute the characteristic tunnelling time (CTT) from donor to acceptor and discuss its biological implications. The model is a double oscillator characterised by three geometry parameters ... More

Loops and autonomy promote evolvability of ecosystem networksJul 10 2015The structure of ecological networks, in particular food webs, determines their ability to evolve further, i.e. evolvability. The knowledge about how food web evolvability is determined by the structures of diverse ecological networks can guide human ... More

Coherent synchrotron emission from cosmic ray air showersJun 01 2006Coherent synchrotron emission by particles moving along semi-infinite tracks is discussed, with a specific application to radio emission from air showers induced by high-energy cosmic rays. It is shown that in general, radiation from a particle moving ... More

Structure of polynomial representations for orthosymplectic Lie superalgebrasJan 20 2010Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the structure of their ... More

On the Braverman-Kazhdan Proposal for Local Factors: Spherical CaseSep 15 2018In this paper, we study the Braverman-Kazhdan proposal for the local spherical situation. In the $p$-adic case, we give a definition of the spherical component of conjectural space $S_{\rho}(G,K)$ and the $\rho$-Fourier transform kernel $\Phi^{K}_{\rho}$, ... More

On Maximum Norm of Exterior Product and A Conjecture of C.N. YangSep 13 2014Jan 08 2015Let $V$ be a finite dimensional inner product space over $\mathbb{R}$ with dimension $n$, where $n\in \mathbb{N}$, $\wedge^{r}V$ be the exterior algebra of $V$, the problem is to find $\max_{\| \xi \| = 1, \| \eta \| = 1}\| \xi \wedge \eta \|$ where $k,l$ ... More

Quantum error correcting codes based on privacy amplificationAug 10 2008Calderbank-Shor-Steane (CSS) quantum error-correcting codes are based on pairs of classical codes which are mutually dual containing. Explicit constructions of such codes for large blocklengths and with good error correcting properties are not easy to ... More

Clone Theory: Its Syntax and Semantics, Applications to Universal Algebra, Lambda Calculus and Algebraic LogicOct 17 2008The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various ... More

0-Calabi-Yau Configurations and Finite Auslander-Reiten Quivers of Gorenstein OrdersJun 02 2014Oct 07 2014We will revisit Wiedemann's classification of Auslander-Reiten quivers of representation-finite Gorenstein orders in this paper. We give a simpler proof of his result in which he described the Auslander-Reiten quiver of a representation-finite Gorenstein ... More

Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptionsJul 13 2012In this paper we study the rank of planar rigidity matrix of 4-valent graphs, both in case of generic realizations and configurations in general position, under various connectivity assumptions on the graphs. For each case considered, we prove a lower ... More

Non-unitary deviation from the tri-bimaximal lepton mixing and its implications on neutrino oscillationsApr 30 2008Jul 05 2008We propose a new pattern of the neutrino mixing matrix which can be parametrized as the product of an arbitrary Hermitian matrix and the well-known tri-bimaximal mixing matrix. In this scenario, nontrivial values of the smallest neutrino mixing angle ... More

On Graph Cohomology and Betti Numbers of Hamiltonian GKM ManifoldsJun 26 2012In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then use this concept ... More

Minima distribution for global optimizationDec 09 2018May 24 2019This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By introducing a class ... More

Noncommutative functional calculate and its applicationNov 07 2016Dec 09 2017In this paper we construct an unitary operator $F_{xx*}$ such that $(F_{xx^{*}})^2=identity$ and $Fix(F_{xx^*})\neq\emptyset$. We get the unitary equivalent representations $F_{xx*}(M_{z\psi(z)}-a)$ on $\mathcal{L}^{2}(\sigma(|T+a|),\mu_{|T+a|})$ for ... More

Triangulated 3-Manifolds: from Haken's normal surfaces to Thurston's algebraic equationMar 23 2010Jul 23 2010We give a brief summary of some of our work and our joint work with Stephan Tillmann on solving Thurston's equation and Haken equation on triangulated 3-manifolds in this paper. Several conjectures on the existence of solutions to Thurston's equation ... More

Volume Optimization, Normal Surfaces and Thurston's Equation on Triangulated 3-ManifoldsMar 06 2009Jun 19 2010We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume. This is a generalization ... More

3-Dimensional Schlaefli Formula and Its GeneralizationFeb 19 2008Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

Automorphisms of the Complex of CurvesApr 04 1999This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.

Geodesic Length Functions and Teichmüller SpacesJan 07 1998Given a compact orientable surface with finitely many punctures $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential unoriented simple closed curves in $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ ... More

Simple Loops on Surfaces and Their Intersection NumbersJan 06 1998Given a compact orientable surface $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential simple loops on $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ to $\bold Z$ to be a geometric intersection ... More

Topological Entropy ConjectureSep 18 2012Mar 11 2018In 1974, M. Shub stated Topological Entropy Conjecture, that is, the inequality $\log\rho\leq ent(f)$ is valid or not, where $f$ is a continuous self-map on a compact manifold $M$, $ent(f)$ is the topological entropy of $f$ and $\rho$ is the maximum absolute ... More

Spreading of cooperative behaviour across interdependent groupsOct 15 2013Recent empirical research has shown that links between groups reinforce individuals within groups to adopt cooperative behaviour. Moreover, links between networks may induce cascading failures, competitive percolation, or contribute to efficient transportation. ... More

Spectral Viscosity Method with Generalized Hermite Functions for Nonlinear Conservation LawsFeb 16 2014Aug 10 2015In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution ... More

Topological entropy conjectureSep 18 2012Sep 22 20121974,Shub stated a conjecture,named Topological Entropy Conjecture,The inequality is so simple connected in the first place with the work of Smale,Shub,and Sullivan,that one attempts to prove it have been very fruitful. But unlike the equality of Gauss-Bonet ... More

Floquet states of Valley-Polarized Metal with One-way Spin or Charge Transport in Zigzag NanoribbonsAug 17 2018Jan 24 2019Two-dimensional Floquet systems consisting of irradiated valley-polarized metal are investigated. For the corresponding static systems, we consider two graphene models of valley-polarized metal with either a staggered sublattice or uniform intrinsic spin-orbital ... More

Proof of Clozel's finiteness conjecture of special exponents: A Reduction StepMar 23 2019In this paper, via Casselman--Tadic's Jacquet module machine, we establish a ``product formula'' of the cardinality of the Jordan--Holder series of generalized principal series. As a byproduct, we prove Clozel's finiteness conjecture of the exponents ... More

Frameworks for Solving Turing Kernel Lower Bound Problem and Finding Natural Candidate Problems in NP-intermediateSep 18 2016Nov 20 2016Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. In the aspect of kernelization, an impressive hardness theory has been established [Bodlaender etc. (ICALP 2008, JCSS2009), Fortnow ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019Apr 02 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of the first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric ... More

Absolute continuity under flows generated by SDE with measurable drift coefficientSep 28 2010We consider the It\^{o} SDE with non-degenerate diffusion coefficient and measurable drift coefficient. Under the condition that the gradient of the diffusion coefficient and the divergences of the diffusion and drift coefficients are exponentially integrable ... More

On the inhomogeneity of the Mandelbrot setAug 30 2018We will show the Mandelbrot set $M$ is locally conformally inhomogeneous: the only conformal map $f$ defined in an open set $U$ intersecting $\partial M$ and satisfying $f(U\cap\partial M)\subset \partial M$ is the identity map. The proof uses the study ... More

Witten Deformation And Some Topics Relating To ItNov 13 2017Nov 17 2017This is a simple reading report of professor Weiping Zhang's lectures. In this article we will mainly introduce the basic ideas of Witten deformation, which were first introduced by Edward Witten on, and some applications of it. The first part of this ... More

Hodge-type decomposition for de Rham cohomology of $ p $-adically uniformized varietiesNov 03 2018We prove a Hodge-type decomposition for the de-Rham cohomology of $ p$-adically uniformized varieties by the product of Drinfeld's symmetric spaces. It is based on work of Schneider, Stuhler, Iovita and Spiess on the cohomology of Drinfeld's symmetric ... More

The maximal principle for properly immersed submanifolds and its applicationsMay 25 2015In this note we consider the Liouville type theorem for a properly immersed submanifold $M$ in a complete Riemmanian manifold $N$. Assume that the sectional curvature $K^N$ of $N$ satisfies $K^N\geq-L(1+dist_N(\cdot,q_0)^2)^\frac{\alpha}{2}$ for some ... More

A Bernstein type theorem for graphic self-shrinkers with flat normal bundleApr 18 2012In this note we will prove that an $n$ dimensional graphic self-shrinker in $R^{n+m}$ with flat normal bundle is a linear subspace. This result is a generalization of the corresponding result of Lu Wang in codimension one case.

Tropical Convexity and Canonical ProjectionsApr 30 2013Using a potential theory on metric graphs "Gamma", we introduce the notion of tropical convexity to the space "RDiv^d(Gamma)" of effective R-divisors of degree d on "Gamma" and show that a natural metric can be defined on "RDiv^d(Gamma)". In addition, ... More

A Proposal on Quantum Histone Modification in Gene ExpressionJun 11 2012A quantum mechanical model on histone modification is proposed. Along with the methyl / acetate or other groups bound to the modified residues the torsion angles of the nearby histone chain are supposed to participate in the quantum transition cooperatively. ... More

Abelian ideals with given dimension in Borel subalgebrasAug 15 2008A well-known Peterson's theorem says that the number of abelian ideals in a Borel subalgebra of a rank-$r$ finite dimensional simple Lie algebra is exactly $2^r$. In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra ... More

A Model on Genome EvolutionNov 09 2014A model of genome evolution is proposed. Based on three assumptions the evolutionary theory of a genome is formulated. The general law on the direction of genome evolution is given. Both the deterministic classical equation and the stochastic quantum ... More

A Quantum Model on Chemically-Physically Induced Pluripotency in Stem CellsSep 29 2013Jan 06 2015A quantum model on the chemically and physically induced pluripotency in stem cells is proposed. Based on the conformational Hamiltonian and the idea of slow variables (molecular torsions) slaving fast ones the conversion from the differentiate state ... More

Quantum conformational transition in biological macromoleculeJan 11 2013Aug 05 2013The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending ... More

On Binary Cyclic Codes with Five Nonzero WeightsApr 15 2009Let $q=2^n$, $0\leq k\leq n-1$, $n/\gcd(n,k)$ be odd and $k\neq n/3, 2n/3$. In this paper the value distribution of following exponential sums \[\sum\limits_{x\in \bF_q}(-1)^{\mathrm{Tr}_1^n(\alpha x^{2^{2k}+1}+\beta x^{2^k+1}+\ga x)}\quad(\alpha,\beta,\ga\in ... More

Spatially Differential Forms of Lenz LawSep 15 2003Two sets of spatially differential formulas of Lenz law on electromagnetic inductance are presented. They are a cut-magnetic flux induced voltage, which instantaneously results from cutting magnetic flux as a conductor moving with respect to an external ... More

Phase Difference Function in Coherent Temporal-spatial Region and Unified Equations of Steady, Non-steady InterferenceApr 08 2003Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency and measured ... More

The morphology and dynamics of polymerization-induced phase separationFeb 21 2006The morphology and dynamics of polymerization-induced phase separation in the initially homogeneous solution of a non-reactive component in reactive monomers are investigated by incorporating the reaction kinetics into the time-dependent Ginzburg Landau ... More

Contou-Carrere symbol via iterated integrals and its reciprocity lawMar 07 2010This paper gives a new definition of the Contou-Carrere symbol in terms of an exponential of a Chen iterated integral and proves the corresponding reciprocity law.

Algebraic Logic, I Quantifier Theories and Completeness TheoremsJan 04 2013Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the category of a ... More

An Invariant of Algebraic Curves from the Pascal TheoremJan 06 2012In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a different comprehension ... More

On Channel State Feedback Model and Overhead in Theoretical and Practical ViewsMay 15 2017Channel state feedback plays an important role to the improvement of link performance in current wireless communication systems, and even more in the next generation. The feedback information, however, consumes the uplink bandwidth and thus generates ... More