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Chip-based frequency combs sources for optical coherence tomographyFeb 20 2019The Optical coherence tomography (OCT) is a powerful interferometric imaging technique widely used in medical fields such as ophthalmology, cardiology and dermatology, for which footprint and cost are becoming increasingly important. Here we present a ... More

Fully integrated ultra-low power Kerr comb generationApr 01 2018Optical frequency combs are broadband sources that offer mutually-coherent, equidistant spectral lines with unprecedented precision in frequency and timing for an array of applications. Kerr frequency combs in microresonators require a single-frequency ... More

Low-Loss Silicon Platform for Broadband Mid-Infrared PhotonicsMar 10 2017Broadband mid-infrared (mid-IR) spectroscopy applications could greatly benefit from today's well-developed, highly scalable silicon photonics technology; however, this platform lacks broadband transparency due to its reliance on absorptive silicon dioxide ... More

Turn-key, high-efficiency Kerr comb sourceJul 16 2019We demonstrate an approach for automated Kerr comb generation in the normal group-velocity dispersion (GVD) regime. Using a coupled-ring geometry in silicon nitride, we precisely control the wavelength location and splitting strength of avoided mode crossings ... More

Aneka: A Software Platform for .NET-based Cloud ComputingJul 26 2009Aneka is a platform for deploying Clouds developing applications on top of it. It provides a runtime environment and a set of APIs that allow developers to build .NET applications that leverage their computation on either public or private clouds. One ... More

Visible Nonlinear PhotonicsJul 10 2019Over the past decade, remarkable advances have been realized in chip-based nonlinear photonic devices for classical and quantum applications in the near- and mid-infrared regimes. However, few demonstrations have been realized in the visible and near-visible ... More

Synchronization of coupled optical microresonatorsJun 06 2018The phenomenon of synchronization occurs universally across the natural sciences and provides critical insight into the behavior of coupled nonlinear dynamical systems. It also offers a powerful approach to robust frequency or temporal locking in diverse ... More

Coherent, directional supercontinuum via cascaded dispersive wave generationAug 11 2017We demonstrate a novel approach to producing coherent, directional supercontinuum via cascaded dispersive wave generation. By pumping in the normal group-velocity dispersion regime, pulse compression of the first dispersive wave results in the generation ... More

Dynamics of mode-coupling-induced microresonator frequency combs in normal dispersionOct 04 2016We experimentally and theoretically investigate the dynamics of microresonator-based frequency comb generation assisted by mode coupling in the normal group-velocity dispersion (GVD) regime. We show that mode coupling can initiate intracavity modulation ... More

Gas-phase microresonator-based comb spectroscopy without an external pump laserJun 04 2018We present a novel approach to realize microresonator-comb-based high resolution spectroscopy that combines a fiber-laser cavity with a microresonator. Although the spectral resolution of a chip-based comb source is typically limited by the free spectral ... More

A review and prospects for Nb3Sn superconductor developmentJun 30 2017Nb3Sn superconductors have significant applications in constructing high-field (> 10 T) magnets. This article briefly reviews development of Nb3Sn superconductor and proposes prospects for further improvement. It is shown that significant improvement ... More

Counter-rotating cavity solitons in a silicon nitride microresonatorNov 13 2017We demonstrate the generation of counter-rotating cavity solitons in a silicon nitride microresonator using a fixed, single-frequency laser. We demonstrate a dual 3-soliton state with a difference in the repetition rates of the soliton trains that can ... More

Strong Nonlinear Coupling due to Induced Photon Interaction on a Si$_{3}$N$_{4}$ ChipFeb 27 2018Jun 28 2018Second-order optical processes lead to a host of applications in classical and quantum optics. With the enhancement of parametric interactions that arise due to light confinement, on-chip implementations promise very-large-scale photonic integration. ... More

On-chip dual comb source for spectroscopyNov 23 2016Dual-comb spectroscopy is a powerful technique for real-time, broadband optical sampling of molecular spectra which requires no moving components. Recent developments with microresonator-based platforms have enabled frequency combs at the chip scale. ... More

Breaking the Loss Limitation of On-chip High-confinement ResonatorsSep 27 2016On-chip optical resonators have the promise of revolutionizing numerous fields including metrology and sensing; however, their optical losses have always lagged behind their larger discrete resonator counterparts based on crystalline materials and flowable ... More

Breather soliton dynamics in microresonatorsSep 06 2016The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part ... More

Thermally Controlled Comb Generation and Soliton Modelocking in MicroresonatorsMar 25 2016Apr 21 2016We report the first demonstration of thermally controlled soliton modelocked frequency comb generation in microresonators. By controlling the electric current through heaters integrated with silicon nitride microresonators, we demonstrate a systematic ... More

A Reconfigurable Nanophotonics Platform for Sub-Millisecond, Deep Brain Neural StimulationMay 14 2018Nanophotonics provides the ability to rapidly and precisely reconfigure light beams on a compact platform. Infrared nanophotonic devices are widely used in data communications to overcome traditional bandwidth limitations of electrical interconnects. ... More

Probit Normal Correlated Topic ModelsOct 03 2014The logistic normal distribution has recently been adapted via the transformation of multivariate Gaus- sian variables to model the topical distribution of documents in the presence of correlations among topics. In this paper, we propose a probit normal ... More

A model for the compositions of non-stoichiometric intermediate phases formed by diffusion reactions, and its application to Nb3Sn superconductorsNov 16 2015In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations ... More

Proton Tomography Through Deeply Virtual Compton ScatteringMay 03 2016In this prize talk, I recall some of the history surrounding the discovery of deeply virtual Compton scattering, and explain why it is an exciting experimental tool to obtain novel tomographic pictures of the nucleons at Jefferson Lab 12 GeV facility ... More

Comment on "Spin and Orbital Angular Momentum in Gauge Theories" by X. S. Chen et. al. (PRL100, 232002 (2008))Oct 27 2008The individual parts of the total angular momentum operator in interacting theories cannot satisfy the canonical angular momentum commutation rule, including those proposed in the above paper. Furthermore, the operators in the new proposal a) are non-local ... More

Generalized Parton Distributions and the Spin Structure of the NucleonNov 09 2002Generalized parton distributions are a new type of hadronic observables which has recently stimulated great interest among theorists and experimentalists alike. Introduced to delineate the spin structure of the nucleon, the orbital angular momentum of ... More

Deeply Virtual Compton ScatteringSep 17 1996Apr 10 1997We study in QCD the physics of deeply-virtual Compton scattering (DVCS)---the virtual Compton process in the large s and small t kinematic region. We show that DVCS can probe a new type of off-forward parton distributions. We derive an Altarelli-Parisi ... More

HADRON SUBSTRUCTURE PROBED WITH HADRON BEAMSFeb 09 1995In this talk, I focus on the quark-gluon structure of hadrons probed using high-energy hadron beams. I start with a brief review on recent major achievements in measuring parton distributions of the nucleon, pion, and kaon, with hadron facilities at CERN ... More

Parton Physics on Euclidean LatticeMay 07 2013I show that the parton physics related to correlations of quarks and gluons on the light-cone can be studied through the matrix elements of frame-dependent, equal-time correlators in the large momentum limit. This observation allows practical calculations ... More

Viewing the Proton Through "Color"-FiltersApr 04 2003Jun 18 2003While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type ... More

Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-OffMar 08 1996I introduce a gauge invariant decomposition of the nucleon spin into quark helicity, quark orbital, and gluon contributions. The total quark (and hence the quark orbital) contribution is shown to be measurable through virtual Compton scattering in a special ... More

Interpolating the Nucleon's Spin-Dependent Sum Rules at High and Low EnergiesJul 20 1993I discuss a few interpolating sum rules for spin structure functions of the nucleon. Using the concept of duality, I argue that the $G_1$ sum rule, including the elastic contribution, is useful for learning higher twist matrix elements of the nucleon. ... More

Chiral-Odd and Spin-Dependent Quark Fragmentation Functions and their ApplicationsJul 08 1993We define a number of quark fragmentation functions for spin-0, -1/2 and -1 hadrons, and classify them according to their twist, spin and chirality. As an example of their applications, we use them to analyze semi-inclusive deep-inelastic scattering on ... More

Higher Moments of Net-Kaon Multiplicity Distributions at STARNov 22 2016Fluctuations of conserved quantities such as baryon number (B), electric charge number (Q), and strangeness number (S), are sensitive to the correlation length and can be used to probe non-gaussian fluctuations near the critical point. Experimentally, ... More

Curvature formulas of holomorphic curves on $C^*$-algebras and Cowen-Douglas OperatorsFeb 22 2014Jan 05 2018For $\Omega\subseteq \mathbb{C}$ a connected open set, and ${\mathcal U}$ a unital $C^*$-algebra, let ${\mathcal I} ({\mathcal U})$ and ${\mathcal P}({\mathcal U})$ denote the sets of all idempotents and projections in ${\mathcal U}$ respectively. ${\mathcal ... More

Enumerative Properties of Posets Corresponding to a Certain Class of No Strategy GamesAug 22 2016In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be modeled as a graded poset with the rank of a node equal to the cardinality ... More

A Masked Photocathode in a PhotoinjectorJan 26 2011Feb 02 2011In this paper, we propose a masked photocathode inside a photoinjector for generating high brightness electron beam. Instead of mounting the photocathode onto an electrode, an electrode with small hole is used as a mask to shield the photocathode from ... More

Mitigation of envelope instability through fast accelerationJun 19 2018Jul 16 2018The space-charge driven envelope instability can be of great danger in high intensity accelerators. Linear accelerators were designed to avoid this instability by keeping the zero current phase advance per lattice period below 90 degrees. In this paper, ... More

On the cumulative Parisian ruin of multi-dimensional Brownian motion modelsNov 25 2018Consider a multi-dimensional Brownian motion which models different lines of business of an insurance company. Our main result gives an approximation for the cumulative Parisian ruin probability as the initial capital becomes large. An approximation for ... More

On the Martin boundary of rank 1 manifolds with nonpositive curvatureJun 14 2017Nov 20 2017For a manifold with nonpositive curvature, the Martin boundary is described by the behavior of normalized Green's functions at infinity. A classical result by Anderson and Schoen states that if the manifold has pinched negative curvature, the geometric ... More

The Asymptotic Dirichlet Problems on manifolds with unbounded negative curvatureJan 10 2014Nov 23 2017Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature conditions $-C e^{2-\eta}r(x) \leq K_M(x)\leq -1$ with $\eta>0$. We give an analytical proof of the same statement. In addition, ... More

Prime Graphs and Exponential Composition of SpeciesMay 01 2007Nov 10 2009In this paper, we enumerate prime graphs with respect to the Cartesian multiplication of graphs. We use the unique factorization of a connected graph into the product of prime graphs given by Sabidussi to find explicit formulas for labeled and unlabeled ... More

Classical Verification of Quantum ProofsMay 27 2015We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to inverse polynomial ... More

Structure Regularized Bidirectional Recurrent Convolutional Neural Network for Relation ClassificationNov 06 2017Relation classification is an important semantic processing task in the field of natural language processing (NLP). In this paper, we present a novel model, Structure Regularized Bidirectional Recurrent Convolutional Neural Network(SR-BRCNN), to classify ... More

Comment on "Laser refrigeration of hydrothermal nanocrystals in physiological media"Jan 06 2016The recent report on laser cooling of liquid may contradict the law of energy conservation.

On Credit-based Incentive Mechanisms of Voluntary User Comment Reviewing in Social NetworksAug 14 2016With the recent advance of micro-blogs and social networks, people can view and post comments on the websites in a very convenient way. However, it is also a big concern that the malicious users keep polluting the cyber environment by scamming, spamming ... More

Dual method for continuous-time Markowitz's Problems with nonlinear wealth equationsJun 30 2008Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through ... More

Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curvesNov 08 2012Let $\mathrm{Out}(F_n)$ be the outer automorphism group of the free group $F_n$. It acts properly on the outer space $X_n$ of marked metric graphs, which is a finite-dimensional infinite simplicial complex with some simplicial faces missing. In this paper, ... More

WILSON'S EXPANSION WITH POWER ACCURACYJun 01 1995Because of the infrared renormalons, it is difficult to get power accuracy in the traditional approach to the Wilson's operator product expansion. Based on a new perturbative renormalization scheme for power-divergent operators, I propose a practical ... More

Chiral-Symmetry and Strange Four-Quark Matrix ElementsJul 08 1993We consider the matrix elements of the left-handed flavor-conserving four-quark operators in the nucleon and pion states. Using chiral symmetry, we derive relationships among these matrix elements. We argue that the $\Delta I = 1/2$ rule of hyperon and ... More

Exact Matching Condition for Matrix Elements in Lattice and $\overline{MS}$ SchemesJun 30 1995The exact matching condition is given for hadron matrix elements calculated in any two different schemes, in particular, in the lattice and dimensional regularization, (modified) minimal subtraction $\overline{\rm MS}$ schemes. The result provides insight ... More

PHYSICS OF $Q^2$-DEPENDENCE IN THE NUCLEON'S $G_1(x,Q^2)$ STRUCTURE FUNCTION SUM RULEFeb 13 1995I discuss in this talk the physics of the $Q^2$ dependence of the $G_1(x,Q^2)$ structure function sum rule. For $Q^2>3$ GeV$^2$, the $Q^2$ variation is controlled by pure QCD radiative corrections. For $0.5<Q^2<3$ GeV$^2$, the twist-four contribution ... More

The Asymptotic Dirichlet Problems on manifolds with unbounded negative curvatureJan 10 2014Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature conditions $-C e^{2-\eta}r(x) \leq K_M(x)\leq -1$ with $\eta>0$. We give an analytical proof of the same statement. In addition, ... More

Three-dimensional envelope instability model in periodic focusing channelsJan 21 2018The space-charge driven envelope instability can be of great danger in high intensity accelerators and was studied using a two-dimensional (2D) envelope model and three-dimensional (3D) macroparticle simulations before. In this paper, we propose a three-dimensional ... More

Turbulent Dynamos and Magnetic HelicityFeb 19 2001It is shown that the turbulent dynamo $\alpha$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence ... More

Division Theorems for the Koszul ComplexMay 23 2011Jun 19 2011We establish a twisted version of Skoda's estimate for the Koszul complex from which we get division theorems for the Koszul complex. This generalizes Skoda's division theorem. We also show how to use Skoda triples to produce division theorems for the ... More

Sentence Correction Based on Large-scale Language ModellingSep 22 2017Nov 02 2017With the further development of informatization, more and more data is stored in the form of text. There are some loss of text during their generation and transmission. The paper aims to establish a language model based on the large-scale corpus to complete ... More

Remarks on Entropy Formulae for Linear Heat EquationMay 02 2017Mar 11 2019In this note, we prove some new entropy formulae for linear heat equation on static Riemannian manifold with nonnegative Ricci curvature. The results are simpler versions of Cao and Hamilton's entropies for Ricci flow coupled with heat-type equations. ... More

Simulation-Based Analytics for Fabrication Quality-Associated Decision SupportMar 18 2019Automated, data-driven quality management systems, which facilitate the transformation of data into useable information, are desired to enhance decision-making processes. Integration of accurate, reliable, and straightforward approaches that measure uncertainty ... More

Division Theorems for Exact SequencesFeb 19 2011Dec 01 2011Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial ... 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

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

Simultaneous Deformations of Lie Algebroids and Lie SubalgebroidsJul 18 2012Feb 28 2013The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie algebroids and ... More

Lorentz Symmetry and the Internal Structure of the NucleonOct 08 1997To investigate the internal structure of the nucleon, it is useful to introduce quantities that do not transform properly under Lorentz symmetry, such as the four-momentum of the quarks in the nucleon, the amount of the nucleon spin contributed by quark ... More

Spin Structure Functions of the NucleonOct 20 1995I begin with a general discussion about importance of constructing a picture of the nucleon in terms of QCD degrees of freedom, emphasizing the role of spin structure functions. I then give a short overview on the theoretical and experimental status of ... More

$Q^2$-Dependence of Deep Inelastic Sum RulesMar 09 1994In this talk, I will concentrate on $Q^2$-dependence of deep inelastic sum rules. I will first give a modern definition of deep-inelastic sum rules and then discuss physical origins of their scaling violation at finite $Q^2$. Following this, I discuss ... More

Gluon Condensate from Lattice QCDJun 23 1995Jun 29 1995After making some critical comments about the traditional method of extracting the gluon condensate from lattice QCD data, I present an alternative analysis. The result is more than a factor of five larger than the phenomenological value. Two closely ... More

A Symplectic Multi-Particle Tracking Model for Self-Consistent Space-Charge SimulationOct 15 2016Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional ... More

Remarks on Entropy Formulae for Linear Heat EquationMay 02 2017May 17 2017In this note, we prove some new entropy formulae for linear heat equation on static Riemannian manifold with nonnegative Ricci curvature. The results are simpler versions of Cao and Hamilton's entropies for Ricci flow coupled with heat-type equations. ... More

A Fast 3D Poisson Solver with Longitudinal Periodic and Transverse Open Boundary Conditions for Space-Charge SimulationsOct 29 2016A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson ... More

A Symplectic Multi-Particle Tracking Model for Self-Consistent Space-Charge SimulationOct 15 2016Dec 21 2016Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional ... More

Modified Ringel-Hall algebras, naive lattice algebras and lattice algebrasAug 13 2018For a given hereditary abelian category satisfying some finiteness conditions, in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall ... More

Image Retrieval Method Using Top-surf DescriptorApr 04 2011This report presents the results and details of a content-based image retrieval project using the Top-surf descriptor. The experimental results are preliminary, however, it shows the capability of deducing objects from parts of the objects or from the ... More

Second-order Dirac equation of graphene electrons in an electromagnetic field and their novel spinMar 29 2013May 06 2013The second-order Dirac equation (DE) and its velocity operator of graphene electrons in an electromagnetic field are obtained according to tight-binding k.p method. With extra terms included, they demonstrate the motion of graphene electrons more completely ... More

HG-Caffe: Mobile and Embedded Neural Network GPU (OpenCL) Inference Engine with FP16 SupportingJan 03 2019Breakthroughs in the fields of deep learning and mobile system-on-chips are radically changing the way we use our smartphones. However, deep neural networks inference is still a challenging task for edge AI devices due to the computational overhead on ... More

Compression of Quantum Multi-Prover Interactive ProofsOct 10 2016We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the promise problem ... More

Three-body systems in physics of cold atoms and halo nucleiDec 18 2015May 13 2016Few-body systems, such as cold atoms and halo nuclei, share universal features at low energies, which are insensitive to the underlying inter-particle interactions at short ranges. These low-energy properties can be investigated in the framework of effective ... More

Hunting for the Remaining Spin in the NucleonOct 15 1996This talk consists of four parts. In part one, I give an elementary discussion on constructing a Lorentz-invariant spin sum rule for the nucleon. In part two, I discuss a gauge-dependent spin sum rule, explore its relation with the polarized gluon distribution, ... More

Matching Perturbative and Non-Perturbative Physics With Power Accuracy in Heavy-Quark Effective TheoryJul 17 1995I discuss a scheme to match perturbative and non-perturbative physics with power accuracy in the heavy-quark effective theory. I elaborate on two important aspects of the scheme: 1) a multi-loop subtraction of soft contributions from the perturbation ... More

Validity Of The Vafa-Witten Proof On Absence Of Spontaneous Parity Breaking In QCDAug 21 2001Aug 22 2001The vacuum energy response of a quantum field theory is studied as a function of complex external fields coupled to the symmetry-breaking observables of the theory. It is found that the energy density is insensitive to spontaneous symmetry breaking effects ... More

Polarizabilities of Gluon Fields in a Polarized NucleonSep 13 1995Sep 26 1995This paper has been withdrawn by the author.

A QCD Analysis of the Mass Structure of the NucleonOct 12 1994{}From the deep-inelastic momentum sum rule and the trace anomaly of the energy-momentum tensor, I derive a separation of the nucleon mass into the contributions of the quark and gluon kinetic and potential energies, the quark masses, and the trace anomaly. ... More

Parton Physics from Large-Momentum Effective Field TheoryApr 26 2014Parton physics, when formulated as light-front correlations, are difficult to study non-perturbatively, despite the promise of light-front quantization. Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture ... More

High Order Numerical Integrators for Relativistic Charged Particle TrackingFeb 15 2017In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth order algorithm ... More

A symplectic particle-in-cell model for space-charge beam dynamics simulationJan 12 2018Space-charge effects play an important role in high intensity particle accelerators and were studied using a variety of macroparticle tracking models. In this paper, we propose a symplectic particle-in-cell (PIC) model and compare this model with a recently ... More

A Rational Decision Maker with Ordinal Utility under Uncertainty: Optimism and PessimismDec 27 2009Jun 11 2010In game theory and artificial intelligence, decision making models often involve maximizing expected utility, which does not respect ordinal invariance. In this paper, the author discusses the possibility of preserving ordinal invariance and still making ... More

Subdiagonal algebras with the Beurling type invariant subspacesApr 03 2019Let $\mathfrak A$ be a maximal subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$. If every right invariant subspace of $\mathfrak A$ in the non-commutative Hardy space $H^2$ is of Beurling type, then we say $\mathfrak A$ to be ... More

One-dimensional electronic solitons of graphene in an electromagnetic fieldApr 05 2013May 03 2013Electronic energy-eigen-states of graphene in an orthogonal electromagnetic field with relative magnitude beta=E/vf*B>=1 or in a pure electric field are obtained by a differential-equation method. Gaussian wave packets of probability density are constructed ... More

Electronic orbital angular momentum and magnetism of grapheneAug 10 2013May 23 2014Orbital angular momentum (OAM) of graphene electrons in a perpendicular magnetic field is calculated and corresponding magnetic moment is used to investigate the magnetism of perfect graphene. Variation in magnetization demonstrates its decrease with ... More

Differential Transfer Relations of Physical Flux Density Between Time Domains of the Flux Source and ObserverApr 08 2003Differential transfer relations of flux density, general physics quantities' and its corresponding energy's, between time domains of source and observer are derived from conservative rule of various physical quantities and time function between the two ... More

Ground state solutions of fractional Schrödinger equations with potentials and weak monotonicity condition on the nonlinear termJun 08 2017In this paper we are concerned with the fractional Schr\"{o}dinger equation $(-\Delta)^{\alpha} u+V(x)u =f(x, u)$, $x\in \rn$, where $f$ is superlinear, subcritical growth and $u\mapsto\frac{f(x, u)}{\vert u\vert}$ is nondecreasing. When $V$ and $f$ are ... More

Well-rounded equivariant deformation retracts of Teichmüller spacesFeb 04 2013Jan 22 2014In this paper, we construct spines, i.e., $\Mod_g$-equivariant deformation retracts, of the Teichm\"uller space $\T_g$ of compact Riemann surfaces of genus $g$. Specifically, we define a $\Mod_g$-stable subspace $S$ of positive codimension and construct ... More

Comment on "Does Gluons Carry Half of the Nucleon Momentum?" by X. S. Chen et. al. (PRL103, 062001 (2009))Oct 27 2009The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge symmetry by ... More

Purely-Nonperturbative Composite Operators and Parton DistributionsMay 14 1997A class of purely-nonperturbative (PNP) composite operators is defined in Quantum Chromodynamics, which is perturbative scheme and scale independent and are useful to describe the internal structure of a strong interacting system. The operator product ... More

Off-Forward Parton DistributionsJul 13 1998Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the realization that ... More

BREAKUP OF HADRON MASSES AND ENERGY-MOMENTUM TENSOR OF QCDFeb 01 1995Hadron masses are shown to be separable in QCD into contributions of quark and gluon kinetic and potential energies, quark masses, and the trace anomaly. The separation is based on a study of the structure of the QCD energy-momentum tensor and its matrix ... More

Energy Dependence of Moments of Net-Proton, Net-Kaon, and Net-Charge Multiplicity Distributions at STARNov 22 2016One of the main goals of the RHIC Beam Energy Scan (BES) program is to study the QCD phase structure, which includes the search for the QCD critical point, over a wide range of chemical potential. Theoretical calculations predict that fluctuations of ... More

Distinguishing Numbers and GeneralizationsAug 03 2018The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets; taking the set to be the vertex set of a graph ... More

Ground state sign-changing solutions for a class of nonlinear fractional Schrödinger-Poisson system in $\mathbb{R}^{3}$Mar 10 2017In this paper, we are concerned with the existence of the least energy sign-changing solutions for the following fractional Schr\"{o}dinger-Poisson system: \begin{align*} \left\{ \begin{aligned} &(-\Delta)^{s} u+V(x)u+\lambda\phi(x)u=f(x, u),\quad &\text{in}\, ... More

Distinguishing Numbers and GeneralizationsAug 03 2018Apr 07 2019The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets; taking the set to be the vertex set of a graph ... More

Binary Constraint System Games and Locally Commutative ReductionsOct 14 2013Nov 04 2013A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve and R. Mittal, ... More

Non-wandering Fatou components for strongly attracting polynomial skew productsFeb 16 2018Dec 12 2018We show a partial generalization of Sullivan's non-wandering domain theorem in complex dimension two. More precisely, we show the non-existence of wandering Fatou components for polynomial skew products of $ \mathbb{C}^2$ with an invariant attracting ... More