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Spatial Imaging of Landé g Factor through Extended Kondo Effect in a Single Magnetic MoleculeOct 31 2013A methodology of atomically resolved Land\'{e} g factor mapping of a single molecule is reported. Mn(II)-phthalocyanine (MnPc) molecules on Au(111) surface can be dehydrogenated via atomic manipulation with manifestation of tailored extended Kondo effect, ... More

Evidence for Majorana bound state in an iron-based superconductorJun 19 2017Mar 19 2018The search for Majorana bound state (MBS) has recently emerged as one of the most active research areas in condensed matter physics, fueled by the prospect of using its non-Abelian statistics for robust quantum computation. A highly sought-after platform ... More

The design of two-dimensional topological insulator CuSe-X (X = Na, K) from monolayer CuSe via atomic decorationSep 19 2018Two-dimensional (2D) topological materials are promising for the realization of quantum spin Hall effect which is important for highly efficient and low consumption spintronics devices. Most research to date has proposed the decoration of either semiconducting ... More

Graphene-Silicon Layered Structures on Single-crystalline Ir(111) Thin FilmsMar 02 2015Single-crystalline transition metal films are ideal playing fields for the epitaxial growth of graphene and graphene-base materials. Graphene-silicon layered structures were successfully constructed on Ir(111) thin film on Si substrate with an yttria-stabilized ... More

A new Majorana platform in an Fe-As bilayer superconductorJul 01 2019Recently, iron-chalcogenide superconductors have emerged as a new and promising platform for studying and manipulating Majorana zero mode (MZM). By combining topological band structure and superconductivity in a multiband material, they provide significant ... More

Graphyne- and Graphdiyne-based Nanoribbons: Density Functional Theory Calculations of Electronic StructuresNov 19 2012We report on the configurations and electronic properties of graphyne and graphdiyne nanoribbons with armchair and zigzag edges investigated with first principles calculations. Our results show that all the nanoribbons are semiconductors with suitable ... More

Stacking-dependent electronic property of trilayer graphene epitaxially grown on Ru(0001)Feb 10 2017The growth, atomic structure, and electronic property of trilayer graphene (TLG) on Ru(0001) were studied by low temperature scanning tunneling microscopy and spectroscopy in combined with tight-binding approximation (TBA) calculations. TLG on Ru(0001) ... More

Orbital design of topological insulators from two-dimensional semiconductorsSep 19 2018Apr 27 2019Two-dimensional (2D) materials have attracted much recent attention because they exhibit various distinct intrinsic properties/functionalities, which are, however, usually not interchangeable. Interestingly, here we propose a generic approach to convert ... More

The Origin of Half-Metallicity in Conjugated Electron System -- a Study on Transition Metal Doped GraphyneOct 24 2013We studied the mechanism of half-metallicity (HM) formation in transition metal doped (TM) conjugated carbon based structures by first-principles electronic structure simulations. It is found that the HM is a rather complex phenomenon, determined by the ... More

There are infinitely many cousin primesOct 16 2005Oct 24 2005We proved that there are infinitely many cousin primes.

There are Infinitely Many Pairs of Twin PrimeOct 09 2005We proved that there are infinitely many pairs of twin prime.

Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUCMay 17 2008In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit ... More

There is at least one pair of double primes for any even numberOct 16 2005We proved that any even number not less than 6 can be expressed as the sum of two old primes, $2n=p_i+p_j$

On the two mutually independent factors that determine the convergence of least-squares projection methodJun 03 2014Aug 25 2014This paper investigates the least-squares projection method for bounded linear operators, which provides a natural regularization scheme by projection for many ill-posed problems. Yet, without additional assumptions, the convergence of this approximation ... More

Serious Game for Human Environmental Consciousness Education in Residents Daily LifeMar 20 2015It has been challenging to find ways to educate people to have better environmental consciousness. In some cases, people do not know what the right behaviors are to protect the environment. Game engine has been used in the AEC industry for visualization. ... More

Weak Siegel-Weil formula for M_2(Q) and arithmetic on quaternionsApr 14 2018May 17 2018In this paper, we prove the weak Siegel-Weil formula for the space M_2(Q) . We study the Hecke correspondence and representation numbers associated to Eichler orders, and give the explicit formula for degree of Hecke correspondence and average representation ... More

The Discrete Sell or Hold Problem with Constraints on Asset ValuesJul 23 2014The discrete sell or hold problem (DSHP), which is introduced in \cite{H12}, is studied under the constraint that each asset can only take a constant number of different values. We show that if each asset can take only two values, the problem becomes ... More

Ranking via Arrow-Debreu EquilibriumOct 03 2009In this paper, we establish a connection between ranking theory and general equilibrium theory. First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market. This gives a natural ... More

Enhanced Spin-Orbit Torques and Magnetization Switching through Interface EngineeringJun 13 2018The origin of spin-orbit torques generated from the conversion of charge-to-spin currents is of considerable debate. Solid understanding of the physics behind is key to the development of current and voltage controlled switching dynamics in ultrathin ... More

Transition state theory: a generalization to nonequilibrium systems with power-law distributionsFeb 17 2011Feb 18 2011Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the Langevin equations ... More

Recent progress in B physicsSep 10 2007Sep 12 2007We firstly address the recent efforts on calculations of the next-to-leading order corrections to the color-suppressed tree amplitude in QCD factorization method which may be essential to solve the puzzles in $B\to \pi\pi$ and $\pi K$ decays. Then we ... More

Global analysis of B-->PP, PV charmless decays with QCD factorizationNov 11 2003The global analysis of B-->PP, PV charmless decays with QCD factorization (QCDF) is presented. The predictions of QCDF are in good agreement with experiments. The best fitted CKM angel gamma is around 79 degree. The predicted branching ratios of B --> ... More

The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable SurfacesNov 12 2018Nov 19 2018Let $N_g$ be the non-orientable surface with genus $g$, $\text{MCG}(N_g)$ be the mapping class group of $N_g$, $\mathcal{T}(N_g)$ be the index 2 subgroup generated by all Dehn twists of $\text{MCG}(N_g)$. We prove that for odd genus, $\mathcal{T}(N_g)$ ... More

Silicon Layer Intercalation of Centimeter-Scale, Epitaxially-Grown Monolayer Graphene on Ru(0001)Dec 19 2011We develop a strategy for graphene growth on Ru(0001) followed by silicon-layer intercalation that not only weakens the interaction of graphene with the metal substrate but also retains its superlative properties. This G/Si/Ru architecture, produced by ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Aug 29 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Higher Groupoid Actions, Bibundles, and DifferentiationDec 14 2015In this thesis, we employ simplicial methods to study actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids, we use pairs of a Kan fibration and a special acyclic fibration to ... More

Random Walks on Dicyclic GroupMar 16 2009This paper works out the rate of convergence of two "natural" random walks on the dicyclic group.

Quantum-State Purity of Heralded Single Photons Produced from Frequency-Anti-Correlated BiphotonsJul 13 2015Sep 15 2015We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector ... More

A Polynomial time Algorithm for Hamilton Cycle and its detailed proofApr 12 2010Mar 21 2019Based on the famous Rotation-Extension technique, by creating the new concepts and methods: broad cycle, main segment, useful cut and insert, destroying edges for a main segment, main goal Hamilton cycle, depth-first search tree, we develop a polynomial ... More

Favard, Baxter, Geronimus, Rakhmanov, Szegö and the strong Szegö theorems for orthogonal trigonometric polynomialsJul 23 2008In this paper, we obtain some analogs of Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems appeared in the theory of orthogonal polynomials on the unit circle (OPUC) for orthogonal trigonometric polynomials (OTP). The key tool ... More

Application of Autoencoder-Assisted Recurrent Neural Networks to Prevent Cases of Sudden Infant Death SyndromeApr 28 2019This project develops and trains a Recurrent Neural Network (RNN) that monitors sleeping infants from an auxiliary microphone for cases of Sudden Infant Death Syndrome (SIDS), manifested in sudden or gradual respiratory arrest. To minimize invasiveness ... More

Two spectral methods for 2D quasi-periodic scattering problemsJul 06 2015Jul 12 2015We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product spectral method ... More

Test of Nonextensive Statistical Mechanics by Solar Sound SpeedsFeb 05 2006Jul 26 2006To check the validity of the theory of nonextensive statistical mechanics, we have investigated the nonextensive degree of the solar interior and have tried to find the experimental evidence by helioseismological measurements that q is different from ... More

On Graph Isomorphism ProblemOct 26 2017Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that $G = H$, we ... More

On the Automorphism Group of a GraphJul 02 2016An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$ from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by $\mathfrak{G}$ the group ... More

Observation of Majorana conductance plateau by scanning tunneling spectroscopyApr 12 2019Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits perfect ... More

Observation of half-integer level shift of vortex bound states in an iron-based superconductorJan 08 2019Vortices in topological superconductors host Majorana zero modes (MZMs), which are proposed to be building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform for realizing MZM has been discovered in iron-based ... More

Robust Mechanisms Under Common ValuationMar 20 2016Nov 19 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

Generating the mapping class groups with torsionsJun 14 2015Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

Negative frequency communicationDec 07 2010Sep 26 2011Spectrum is the most valuable resource in communication system, but unfortunately, so far, a half of the spectrum has been wasted. In this paper, we will see that the negative frequency not only has a physical meaning but also can be used in communication. ... More

On the canonical maps of nonsingular threefolds of general typeDec 21 2016Dec 28 2016Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ ... More

Smooth solution to higher dimensional complex Plateau problemDec 07 2017Dec 14 2017Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In ... More

Optimizing Multi-hop Mechanism for the Long Range Wide Area NetworkNov 13 2018Nov 20 2018Long Range (LoRa) is a modem technology for wireless communication in the Internet of Things (IoT), which trades off low data-rate for low power consumption. Long Range Wide Area Network (LoRaWAN) has an open specification that determines the Medium Access ... More

On well-conditioned spectral collocation and spectral methods by the integral reformulationNov 04 2015Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput. Phys.}, 229 ... More

Preconditioning rectangular spectral collocationOct 01 2015Oct 21 2015Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely ill-conditioned ... More

Surface plasmon resonance under conditions of electromagnetically induced transparencyDec 18 2011A scheme for a surface plasmon resonance system under conditions of electromagnetically induced transparency (EIT) is proposed. The system is composed of three layers: a prism, a thin metal film, and a hybrid dielectric consisting of EIT atoms and a background ... More

On Self-mapping Degrees of $S^3$-geometry manifoldsNov 26 2008In this paper we determined all of the possible self mapping degrees of the manifolds with $S^3$-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self mapping degrees ... More

Transport coefficients in Lorentz plasmas with the power-law kappa-distributionJul 15 2013Sep 07 2013Transport coefficients in Lorentz plasma with the power-law kappa-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient ... More

Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactionsMar 30 2006Nov 18 2007By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the ... More

What does the nonextensive parameter q stand for in self-gravitating systems ?Apr 21 2004Apr 06 2010It is natural important question for us to ask what the nonextensive parameter stands for when Tsallis statistics is applied to the self-gravitating systems. In this paper, some properties of the nonextensive parameter and Tsallis equilibrium distribution ... More

The nonextensive parameter and Tsallis distribution for self-gravitating systemsSep 18 2004The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized Maxwellian ... More

QCD Factorization and Rare B Meson DecaysAug 29 2005Aug 30 2005Some recent progress in China in the study of charmless B decays with QCD factorization is reviewed. Chirally enhanced power corrections and infrared divergence problem are stressed.

Contributions to Persistence TheoryOct 11 2012Apr 20 2014This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4. This paper is ... More

The Torsion Generating Set Of The Extended Mapping Class Groups In Low Genus CasesJan 05 2019We prove that for genus $g=3,4$, the extended mapping class group $\text{Mod}^{\pm}(S_g)$ can be generated by two elements of finite orders. But for $g=1$, $\text{Mod}^{\pm}(S_1)$ cannot be generated by two elements of finite orders.

Solvability conditions for indefinite linear quadratic optimal stochastic control problems and associated stochastic Riccati equationsFeb 06 2014Dec 18 2015A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward stochastic differential ... More

$W^{2,p}$-solutions of parabolic SPDEs in general domainsMay 17 2018The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of $L^{p}(\Omega\times(0,T),W^{2,p}(G))$-norms ... More

Higher order Poisson Kernels and $L^p$ polyharmonic boundary value problems in Lipschitz domainsMar 04 2015Mar 21 2015In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define multi-layer potentials ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Nov 10 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Opaque Response Generation Enabling Automatic Creation of Virtual Services for Service VirtualisationAug 17 2016Service virtualisation is a method to create virtual service models that can mimic interaction behaviors between a system under test and the target system. With service virtualisation, the development team can get access to the production-like conditions ... More

Trilateration-based Multi-hop for the Long Range Wide Area NetworkNov 15 2018Nov 20 2018Long Range Wide Area Network (LoRaWAN) has an open specification that defines the Medium Access Control (MAC) protocol for LoRa networks, mainly based on pure-Aloha with beacon option. The LoRaWAN has a star of star topology where end-devices are directly ... More

Long Range Wide Area Network: A Simulation Module for ns-3Nov 14 2018Nov 20 2018Long Range (LoRa) is a wireless communication technology for the Internet of Things (IoT), able to provide wide coverage networking to devices with low power consumption and low data-rate. This paper~proposes and describes a simulation module of LoRa ... More

Preconditioning fractional spectral collocationOct 20 2015Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely ill-conditioned as ... More

Improving LSTM Neural Networks for Better Short-Term Wind Power PredictionsJun 30 2019This paper introduces an improved method of wind power prediction via weather forecast-contextualized Long Short- Term Memory Neural Network (LSTM) models. Wind power and weather forecast data were acquired from open-source databases and combined. However, ... More

Refined upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithmsJan 10 2018The randomized extended Kaczmarz and Gauss-Seidel algorithms have attracted much attention because of their ability to treat all types of linear systems (consistent or inconsistent, full rank or rank-deficient). In this paper, we interpret the randomized ... More

Measuring the angle $γ$ of the unitarity triangle in $B_s$ decays into CP eigenstatesJan 16 2007Apr 23 2007In this paper penguin contribution has not been included, so it is not suitable to be published.

Asymptotic behavior of positive solutions to a degenerate elliptic equation in the upper half space with a nonlinear boundary conditionApr 16 2015We consider positive solutions of the problem \begin{equation} \left\{\begin{array}{l}-\mbox{div}(x_{n}^{a}\nabla u)=0\qquad \mbox{in}\;\;\mathbb{R}_+^n,\\ \frac{\partial u}{\partial \nu^a}=u^{q} \qquad \mbox{on}\;\;\partial \mathbb{R}_+^n,\\ \end{array} ... More

Finite dimensional algebras and cellular systemsDec 08 1999We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular system. As a further ... More

Robust Mechanisms Under Common ValuationMar 20 2016Aug 29 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

Ternary quadratic forms and Heegner divisorsApr 19 2014In this paper, I use Siegel-Weil formula and Kudla matching principle to prove some interesting identities between representation number (of ternary quadratic space) and the degree of Heegner divisors.

On the Complexity of Deciding Degeneracy in GamesMay 19 2009We show that it is NP-Complete to decide whether a bimatrix game is degenerate and it is Co-NP-Complete to decide whether a bimatrix game is nondegenerate.

Possible dynamics of the Tsallis distribution from a Fokker-Planck equation (I)May 27 2009Jun 01 2009The dynamical property of the Tsallis distribution is studied from a Fokker-Planck equation. For the Langevin dynamical system with an arbitrary potential function, Markovian friction and Gaussian white noise, we show that no possible nonequilibrium dynamics ... More

Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactionsApr 25 2004The nonextensivity in a non-isothermal plasma system with the Coulombian long-range interactions is studied in the framework of Tsallis statistics. We present for first time a mathematical expression of the nonextensive parameter q based on the mathematical ... More

Jeans criterion in nonextensive statistical mechanicsApr 23 2004The Jeans gravitational instability in nonextensive statistical mechanics is studied and a general form of the generalized Jeans criterion is obtained that is related to the q-function . In this approach, the nonextensive model of classical ideal gas ... More

Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equationsFeb 03 2012Feb 06 2012We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a condition under ... More

Stochastic dynamical theory of power-law distributions induced by multiplicative noiseMar 07 2011Mar 08 2011The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of stationary power-law ... More

Property of Tsallis entropy and principle of entropy increaseFeb 24 2008The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems cannot decrease ... More

Jeans criterion and nonextensive velocity distribution function in kinetic theoryApr 23 2004The effect of nonextensivity of self-gravitating systems on the Jeans criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity ... More

Any admissible harmonic Ritz value set is possible for prescribed GMRES residual normsApr 23 2016We show that any admissible harmonic Ritz value set is possible for prescribed GMRES residual norms, which is a complement for the results in [Duintjer Tebbens and Meurant, {\it SIAM J. Matrix Anal. Appl.}, 33 (2012), no. 3, pp. 958--978].

An Overview of Mobile Capacitive Touch Technologies TrendsDec 25 2016Touch sensing, as a major human/machine interface, is widely used in various commercial products such as smart watches, mobile phones, tablets and TVs. State-of-the-art touch detections are mainly based on mutual capacitive sensing, which requires necessary ... More

Semi-supervised learning of local structured output predictorsApr 11 2016In this paper, we study the problem of semi-supervised structured output prediction, which aims to learn predictors for structured outputs, such as sequences, tree nodes, vectors, etc., from a set of data points of both input-output pairs and single inputs ... More

Staggered chiral perturbation theory in the two-flavor caseNov 13 2009Nov 08 2010I study two-flavor staggered chiral perturbation theory in the light pseudoscalar sector. The pion mass and decay constant are calculated through NLO in the partially-quenched case. In the limit where the strange quark mass is large compared to the light ... More

On Level persistence (Relevant level persistence numbers)Apr 16 2014Apr 20 2014The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for level persistence. ... More

On solvability of an indefinite Riccati equationDec 27 2013This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based ... More

Generating the mapping class groups by torsionsJun 14 2015Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

A Resource Pooling Switch Architecture with High Performance SchedulerApr 28 2018With the rapid development of network-based services and applications, current data plane solutions of network node, which focus on packets forwarding traditionally, are not optimally addressing new requirements such as function flexibility, performance ... More

Optimized Deployment of Network Function for Resource Pooling SwitchApr 24 2018The disadvantages of the combination of traditional switches and middleboxes have being exposed under the condition of increasingly various network function demands,such as function flexibility, performance scalability and resource utilization. To solve ... More

Sharing deep generative representation for perceived image reconstruction from human brain activityApr 25 2017Jul 11 2017Decoding human brain activities via functional magnetic resonance imaging (fMRI) has gained increasing attention in recent years. While encouraging results have been reported in brain states classification tasks, reconstructing the details of human visual ... More

Ranks of the Rational Points of Abelian Varieties over Ramified Fields, and Iwasawa Theory for Primes with Non-Ordinary ReductionAug 10 2016Let $A$ be an abelian variety defined over a number field $F$. Suppose its dual abelian variety $A'$ has good non-ordinary reduction at the primes above $p$. Let $F_{\infty}/F$ be a $\mathbb Z_p$-extension, and for simplicity, assume that there is only ... More

On the generalized restricted sumsets in abelian groupsSep 09 2016Sep 12 2016Suppose that $A$, $B$ and $S$ are non-empty subsets of a finite abelian group $G$. Then the generalized restricted sumset $$ A\stackrel{S}+B:=\{a+b:\,a\in A,\ b\in B,\ a-b\not\in S\} $$ contains at least $$ \min\{|A|+|B|-3|S|,p(G)\} $$ elements, where ... More

Restricted Sumsets in Finite Nilpotent GroupsJun 27 2012Aug 21 2012Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\not=B$, then the cardinality of the restricted sumset $$A\dotplus B={a+b: a\in A, b\in B, a\neq b} $$ is at least $$\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the ... More

A generalization of Frieman's 3k-3 theoremAug 18 2013Sep 12 2016We prove a generalization of Frieman's $3k-3$ theorem for the sumset $$ \Sigma^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}\text{ for all }s\}. $$

Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced TruncationFeb 14 2016Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation method. Firstly, ... More

Prospective Hybrid Consensus for Project PAIFeb 07 2019PAI Coin's Proof-of-Work (PoW) consensus mechanism utilizes the double SHA-256 hashing protocol-- the same mechanism used by Bitcoin Core. This compatibility with classic Bitcoin-style mining provides low barrier to entry for PAI Coin mining, consequently ... More

In-Medium Charmonium Production in Proton-Nucleus CollisionsAug 29 2018We study charmonium production in proton-nucleus (pA) collisions focusing on final-state effects caused by the formation of an expanding medium. Toward this end we utilize a rate equation approach within a fireball model as previously employed for a wide ... More

On the Chaos in Continuous Weakly Mixing MapsMar 28 2018Jan 01 2019Let $\mathcal X$ be an infinite separable locally compact metric space with metric $\rho$ and let $f : \mathcal X \longrightarrow \mathcal X$ be a continuous weakly mixing map. Let $\beta = \sup \big\{ \rho(x, y): \{x, y \} \subset \mathcal X \big\}$. ... More

Three-dimensional gravity-driven deterministic lateral displacementApr 26 2016We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully three-dimensional trajectories. ... More

Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface ApproachesMay 11 2006In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and ... More

On abelian canonical n-folds of general typeDec 16 2016Let $X$ be a Gorenstein minimal projective $n$-fold with at worst locally factorial terminal singularities, and suppose that the canonical map of $X$ is generically finite onto its image. When $n<4$, the canonical degree is universally bounded. While ... More