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Distribution of velocity gradient orientations: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Aug 01 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity gradients provide a reliable tracing of magnetic field direction in turbulent plasmas. In this paper, we explore the ability of velocity gradients to measure the magnetization ... More

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

Statistical tracing of magnetic fields: comparing and improving the techniquesApr 08 2018Aug 14 2018Magnetohydrodynamic(MHD) turbulence displays velocity anisotropies which reflect the direction of the magnetic field. This anisotropy has led to the development of a number of statistical techniques for studying magnetic fields in the interstellar medium. ... More

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

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

Celer Network: Bring Internet Scale to Every BlockchainSep 28 2018Off-chain scaling techniques allow mutually distrustful parties to execute a contract locally among themselves instead of on the global blockchain. Parties involved in the transaction maintain a multi-signature fraud-proof off-chain replicated state machine, ... 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 (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

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

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

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.

Urbanization, Ikization, and Replacement DynamicsNov 04 2015The phenomenon of Iks was first found by anthropologists and biologists, but it is actually a problem of human geography. However, it has not yet drawn extensive attention of geographers. In this paper, a hypothesis of ikization is presented that sudden ... More

The Tractability Frontier of Graph-Like First-Order Query SetsJul 13 2014We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this problem is tractable, ... More

Regular balanced Cayley maps on ${\rm PSL}(2,p)$Jan 20 2016Jul 05 2016A {\it regular balanced Cayley map} (RBCM for short) on a finite group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface, with some special symmetric property. People have classified RBCM's for cyclic, dihedral, generalized quaternion, ... More

Cellular Automata to More Efficiently Compute the Collatz MapJan 14 2013The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the Collatz map in bases ... More

Basis Collapse for Holographic Algorithms Over All Domain SizesNov 03 2015The theory of holographic algorithms introduced by Valiant represents a novel approach to achieving polynomial-time algorithms for seemingly intractable counting problems via a reduction to counting planar perfect matchings and a linear change of basis. ... More

Pseudo-holomorphic curves and the Weinstein conjectureAug 10 1997Feb 02 2000We established existence of periodic Reeb orbits for a large class of tight contact structures on closed 3-manifolds, notably the Stein fillable structures, based on a fundamental theorem of Cliff Taubes on symplectic 4-manifolds.

CRT-Based High Speed Parallel Architecture for Long BCH EncodingApr 21 2009BCH (Bose-Chaudhuri-Hocquenghen) error correcting codes ([1]-[2]) are now widely used in communication systems and digital technology. Direct LFSR(linear feedback shifted register)-based encoding of a long BCH code suffers from serial-in and serial-out ... More

Technical Report: Representing SES Cases Using OntologyJan 31 2016Socio-ecological System (SES) research studies the interaction between environment, users, and governance of environment resources. Data produced during the research cycle can be both long-tail (e.g. heterogeneous) and longitudinal data. For example, ... More

The evolution of Zipf's law indicative of city developmentApr 16 2015Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban scientists. However, ... More

Basis entropy: A useful physical quantity about projective measurementJun 05 2016Sep 30 2016Projective measurement can increase the entropy of a state $\rho$, the increased entropy is not only up to the basis of projective measurement, but also has something to do with the properties of the state itself. In this paper we define this increased ... More

A Gentle Tutorial of Recurrent Neural Network with Error BackpropagationOct 08 2016We describe recurrent neural networks (RNNs), which have attracted great attention on sequential tasks, such as handwriting recognition, speech recognition and image to text. However, compared to general feedforward neural networks, RNNs have feedback ... More

Approximating the Minimum Breakpoint Linearization Problem for Genetic Maps without Gene StrandednessFeb 25 2015The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint distance to a ... More

Xiao's Conjecture on Canonically Fibered SurfacesMay 20 2014A canonically fibered surface is a surface whose canonical series maps it to a curve. Using Miyaoka-Yau inequality, A. Beauville proved that a canonically fibered surface has relative genus at most 5 when its geometric genus is sufficiently large. G. ... More

Grand Challenges in Measuring and Characterizing Scholarly ImpactMar 02 2016The constantly growing body of scholarly knowledge of science, technology, and humanities is an asset of the mankind. While new discoveries expand the existing knowledge, they may simultaneously render some of it obsolete. It is crucial for scientists ... More

An ontology-based approach to the optimization of non-binary (2,v)-regular LDPC codesSep 06 2014A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected cycle patterns ... More

Revisit Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified ViewpointSep 20 2016In this paper, we revisit the topic "Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint". We also revisit the topic "New Approach to Synchronization Analysis of Linearly Coupled Ordinary Differential Systems" ... More

Smoothness and Smooth Extensions (I): Generalization of MWK Functions and Gradually Varied FunctionsMay 20 2010A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth surface in the ... More

Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic EquationsMar 16 2015We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas ... More

A quantum algorithm for solving the 3-SAT problemOct 16 2012Oct 18 2012The method in this paper is wrong.

Bouchard-Klemm-Marino-Pasquetti Conjecture for $\mathbb{C}^3$Oct 20 2009In this paper, we give a proof of the Bouchard-Klemm-Marino-Pasquetti conjecture for a framed vertex, by using the symmetrized Cut-Join Equation developed in a previous paper.

Existence of the rhombohedral and tetragonal deformation families of the gyroidJan 13 2019We provide an existence proof for two 1-parameter families of triply periodic minimal surfaces of genus three, namely the tG family with tetragonal symmetry that contains the gyroid, and the rGL family with rhombohedral symmetry that contains the gyroid ... More

Minimal rPD-Twin SurfacesOct 25 2016We study a $2$-parameter family of minimal surfaces with twin structure, namely the rPD-twin surfaces. A (polysynthetic) rPD-twin surface can be seen as copies of an rPD-surface that are symmetric about parallel mirrors. Candidates of rPD-twin surfaces ... More

The Ladder Theory of Behavioral Decision MakingSep 07 2018Sep 13 2018We study individual decision-making behavioral on generic view. Using a formal mathematical model, we investigate the action mechanism of decision behavioral under subjective perception changing of task attributes. Our model is built on work in two kinds ... More

Stability in the cohomology of the space of complex irreducible polynomials in several variablesFeb 05 2019We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology stabilizes as $n$ ... More

Singularities, geodesics and Green functions in the BTZ black holeNov 04 2006Jul 13 2007In the context of studying black hole singularities by the AdS/CFT correspondence, we study the BTZ black hole by a scalar field propagating on it and the corresponding two-point Green functions. We explore how positions inside the horizon are encoded ... More

Levy stable distribution and [0,2] power law dependence of acoustic absorption on frequencyMay 09 2005The absorption of acoustic wave propagation in a broad variety of lossy media is characterized by an empirical power law function of frequency, w^y. It has long been noted that exponent y ranges from 0 to 2 for diverse media. Recently, the present author ... More

Geometrical perspective on quantum states and quantum computationNov 20 2013We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge transformations ... More

On the Generative Power of Omega-Grammars and Omega-AutomataAug 21 2013An \omega-grammar is a formal grammar used to generate \omega-words (i.e. infinite length words), while an \omega-automaton is an automaton used to recognize \omega-words. This paper gives clean and uniform definitions for \omega-grammars and \omega-automata, ... More

Characterization of maximally entangled two-qubit states via the Bell-Clauser-Horne-Shimony-Holt inequalityFeb 02 2004Jun 09 2004Maximally entangled states should maximally violate the Bell inequality. In this paper, it is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them ... More

Quantum Theory for the Binomial Model in Finance ThoeryDec 25 2001Feb 19 2010In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\bf R}^3,$ whose radius is a function of the risk-free interest rate with ... More

Necessary and sufficient condition for a realistic theory of quantum systemsNov 13 2009We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values, except for a simple ... More

Variant of the Clauser-Horne-Shimony-Holt inequalityNov 06 2007We construct a Bell inequality from the Clauser-Horne-Shimony-Holt inequality for two qubits that provides a stronger bound on the correlations of entangled states than allowed by the CHSH inequality. The argument involved here can be generalized to $n$ ... More

Maximal violation of Mermin's inequalitiesJul 05 2004In this paper, it is proved that the maximal violation of Mermin's inequalities of $n$ qubits occurs only for GHZ's states and the states obtained from them by local unitary transformations. The key point of our argument involved here is by using the ... More

Generic character sheaves on reductive groups over a finite ringApr 07 2016Here we consider a construction of generic character sheaves on reductive groups over a finite ring at even levels, as well as the relevant induction and restriction functors, and a variant of Frobenius reciprocity. This is motivated by an algebraisation ... More

The uniqueness in the de Rham-Wu decompositionApr 21 2011Jun 30 2015In this paper, we study the uniqueness in the de Rham-Wu decomposition for pseudo-Riemannian manifolds.

Analysis of beauty-full bb\bar{b}\bar{b} stateJan 31 2019Motivated by the searching for $bb\bar{b}\bar{b}$ states at LHC recently, we calculate the ground-state energies of $bb\bar{b}\bar{b}$ states with quantum numbers $IJ^P=00^+,01^+,02^+$ in a nonrelativistic chiral quark model using the Gaussian expansion ... More

On the Feynman Rules of Massive Gauge Theory in Physical GaugesFeb 15 2019For a massive gauge theory with Higgs mechanism in a physical gauge, the longitudinal polarization of gauge bosons can be naturally identified as mixture of the goldstone component and a remnant gauge component that vanishes at the limit of zero mass, ... More

Magnetically-driven orbital-selective insulator-metal transition in double perovskite oxidesNov 08 2018Interaction-driven metal-insulator transitions or Mott transitions are widely observed in condensed-matter systems. In multi-orbital systems, many-body physics is richer in which an orbital-selective metal-insulator transition is an intriguing and unique ... More

On a generalised Blaschke-Santalò inequalityAug 07 2018In this paper, we establish a generalised Blaschke-Santal\`o inequality for convex bodies in $\mathbb R^{n+1}$. This inequality gives an upper bound estimate for the product of dual quermassintegrals of convex body and its polar set. Our argument is based ... More

An analytic proof of the Borwein ConjectureJan 30 2019Feb 17 2019We provide a proof of the Borwein Conjecture using analytic methods.

Learning Orientation-Estimation Convolutional Neural Network for Building Detection in Optical Remote Sensing ImageMar 14 2019Benefiting from the great success of deep learning in computer vision, CNN-based object detection methods have drawn significant attentions. Various frameworks have been proposed which show awesome and robust performance for a large range of datasets. ... More

Lengths, area and modulus of continuity of some classes of complex-valued functionsMar 17 2019In this paper, we discuss the modulus of continuity of solutions to Poisson's equation, and give bounds of length and area distortion for some classes of $K$-quasiconformal mappings satisfying Poisson's equations. The obtained results are the extension ... More

On the Feynman Rules of Massive Gauge Theory in Physical GaugesFeb 15 2019Mar 27 2019For a massive gauge theory with Higgs mechanism in a physical gauge, the longitudinal polarization of gauge bosons can be naturally identified as mixture of the goldstone component and a remnant gauge component that vanishes at the limit of zero mass, ... More

Recent Progress in Cosmology and Particle AstrophysicsOct 03 2013Recent years have seen dramatic progress in cosmology and particle astrophysics. So much so that anyone who dares to offer an overview would certainly risk him- or herself for being incomplete and biased at best, and even incorrect due to the author's ... More

Applying TQFT to count regular coverings of Seifert 3-manifoldsOct 02 2011Aug 24 2012I give a formula for computing the number of regular $\Gamma$-coverings of closed orientable Seifert 3-manifolds, for a given finite group $\Gamma$. The number is computed using a 3d TQFT with finite gauge group, through a cut-and-glue process.

Surjective homomorphisms between surface braid groupsApr 17 2017Let $PB_n(S_{g,p})$ 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

Towards Global Optimization in Display Advertising by Integrating Multimedia Metrics with Real-Time BiddingMay 21 2018Real-time bidding (RTB) has become a new norm in display advertising where a publisher uses auction models to sell online user's page view to advertisers. In RTB, the ad with the highest bid price will be displayed to the user. This ad displaying process ... More

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression burstsJul 24 2017Aug 20 2017Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast ... More

Regularity properties of some perturbations of non-densely defined operators with applicationsApr 23 2019This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup such as norm ... More

On the well-posedness of the inviscid multi-layer quasi-geostrophic equationsJun 15 2018The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces. Using the barotropic ... More

The barotropic quasi-geostrophic equation under a free surfaceJul 18 2017Aug 05 2017The inviscid barotropic quasi-geostrophic equation with a free surface is considered. The free surface mandates a non-standard boundary condition. The global existence existence and uniqueness of a weak solution is established, thanks to the uniform in ... More

Effect of the particle-hole channel on BCS--Bose-Einstein condensation crossover in atomic Fermi gasesSep 11 2011Feb 23 2012BCS--Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel. Here we study the effect of the particle-hole channel on the zero $T$ gap $\Delta(0)$, superfluid ... More

On certain integral tensor categories and integral TQFTsAug 25 2004We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these categories.

On the total curvature of minimal annuli in $R^3$ and Nitsche's conjectureJan 16 1997We present a proof of the generalized Nitsche's conjecture proposed by W.H.Meeks III and H. Rosenberg: For $t\ge 0$, let $P_t$ denote the horizontal plane of height $t$ over the $x_1,x_2$ plane. Suppose that $M \subset R^3$ is a minimal annulus with the ... More

On a notion of maps between orbifolds, I. function spacesMar 29 2006This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological ... More

A modified BFGS quasi-Newton iterative formulaJul 14 1999The quasi-Newton equation is the very basis of a variety of the quasi-Newton methods. By using a relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix. presented recently by the present author, we established ... More

A new definition of nonlinear statistics mean and varianceJul 24 1999This note presents a new definition of nonlinear statistics mean and variance to simplify the nonlinear statistics computations. These concepts aim to provide a theoretical explanation of a novel nonlinear weighted residual methodology presented recently ... More

A Simple Proof that Rational Curves on K3 are NodalNov 23 2000Jul 16 2001We give a simple proof of the statement that every rational curve in the primitive class of a general K3 surface is nodal.

Equivariant localization and completion in cyclic homology and derived loop spacesAug 21 2017Nov 08 2018We prove an equivariant localization theorem for smooth quotient stacks by reductive groups $X/G$ in the setting of derived loop spaces and cyclic homology. This realizes a Jordan decomposition of loop spaces described by Ben-Zvi and Nadler where the ... More

Correction to Solution of Dirac EquationAug 29 2009Oct 13 2015Using the China unitary principle to test the Dirac theoryfor the hydrogen atomic spectrum shows that the standard Dirac function withthe Dirac energy levels is only one the formal solutions of theDirac-Coulomb equation, which conceals some pivotal mathematicalcontradictions. ... More

Historical pseudo simplified solution of the Dirac-Coulomb equationJul 02 2007Aug 21 2007One of the simplified solutions of the Dirac equations with the pure Coulomb potential given in a paper published in 1985 is pseudo. The original paper solved the Dirac equations by introducing a transformation of functions with two strange parameters ... More

Established pseudo solution of second-order Dirac-Coulomb equation with position-dependent massJun 28 2007Jul 13 2007We show that one of exact solutions of the second-order Dirac-Coulomb equation were pseudo. In the corresponding original literature, it was considered that the mass of the electron with a Coulomb potential was position-dependent, but the obtained eigenvalues ... More

$\ell$-torsion in class groups of certain families of $D_4$-quartic fieldsAug 06 2018We prove an upper bound for $\ell$-torsion in class groups of almost all fields in certain families of $D_4$-quartic fields. Our key tools are a new Chebotarev density theorem for these families of $D_4$-quartic fields and a lower bound for the number ... More

Schur-Concavity for Avoidance of Increasing Subsequences in Block-Ascending PermutationsAug 04 2017Oct 07 2017For integers $a_1, \dots, a_n \ge 0$ and $k \ge 1$, let $\mathcal L_{k+2}(a_1, \dots, a_n)$ denote the set of permutations of $\{1, \dots, a_1+\dots+a_n\}$ whose descent set is contained in $\{a_1, a_1+a_2, \dots, a_1+\dots+a_{n-1}\}$, and which avoids ... More

Synchronization, Consensus of Complex Networks and their relationshipsSep 20 2016Apr 27 2018In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li} can be obtained by the results in \cite{Lu2006}. ... More

The Associated Map of the Nonabelian Gauss-Manin ConnectionJul 11 2011Jul 13 2011The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. ... More

Critical manifolds and stability in Hamiltonian systems with non-holonomic constraintsFeb 09 2003Jun 11 2003We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained Hamiltonian system, ... More

Operator-theoretic infrared renormalization and construction of dressed 1-particle states in non-relativistic QEDAug 24 2001We consider the infrared problem in a model of a freely propagating, nonrelativistic charged particle of mass 1 in interaction with the quantized electromagnetic field. The hamiltonian of the system is regularized by an infrared cutoff $\ssig\ll 1$ and ... More

Large deviations and laws of the iterated logarithm for the local times of additive stable processesMar 07 2006Jul 25 2007We study the upper tail behaviors of the local times of the additive stable processes. Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\alpha\le 2$ and consider the additive stable process $\bar{X}(t_1,...,t_p)=X_1(t_1)+... ... More

Consistency of the MLE under mixture modelsJul 05 2016The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore ... More

Model simplification and loss of irreversibilityMay 11 2016In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we divide the ... More

Real hypersurfaces with $^{*}$-Ricci solitons of non-flat complex space formsNov 17 2017Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of $^*$-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a $^*$-Ricci soliton whose potential vector field is the structure vector field. In this ... More

An Improved EM algorithmMay 03 2013In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement ... More

Computational Complexity of Stable Marriage and Stable Roommates and Their VariantsApr 17 2019This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in the paper. If ... More

The LHC searches for heavy neutral Higgs bosons by jet substructure analysisNov 24 2016The two-Higgs-doublet model contains extra Higgs bosons, with mass ranges spanning from several hundred GeV to about 1 TeV. We study the possible experimental searches for the neutral Higgs bosons of $A$ and $H$ at the future high-luminosity LHC runs. ... More