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On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical stripApr 05 2019We prove that the integer part of the reciprocal of the tail of $\zeta(s)$ at a rational number $s=\frac{1}{p}$ for any integer with $p \geq 5$ or $s=\frac{2}{p}$ for any odd integer with $p \geq 5$ can be described essentially as the integer part of ... More

The Frobenius problem for four numerical semigroupsJun 28 2017Aug 23 2017The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$ and finding the Frobenius number is called the Frobenius problem. In this paper, we introduce the Frobenius problem for numerical semigroups generated ... More

The Frobenius problem for Generalized Thabit numerical semigroupsOct 16 2015May 03 2016The greatest integer that does not belong to $S$ is the Frobenius number of $S$ and denoted by $F(S)$. To solve the Frobenius problem means the study to find $F(S)$. The Frobenius problem have treated steadily for a long time. In this paper, We will introduce ... More

A reciprocal sum related to the Riemann zeta function at s=6Sep 23 2017We introduce an explicit formula for a reciprocal sum related to the Riemann zeta function at s=6, and pose one question related to a computational formula for larger values of s.

On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequencesJun 27 2016The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the recurrence relation ... More

On the sequence made by the linear combination of k-Fibonacci and k-Lucas sequencesJun 27 2016May 30 2017The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the recurrence relation ... More

The inverses of tails of the Riemann zeta functionMar 01 2018Jul 05 2018We present some bounds of the inverses of tails of the Riemann zeta function on $0 < s < 1$ and compute the integer parts of the inverses of tails of the Riemann zeta function for $s=\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$.

On a generalized $k$-FL sequence and its applicationsJan 02 2017Nov 01 2018We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant matrices ... More

Dynamic Structures of 2-adic Fibonacci PolynomialsMar 13 2019The dynamic structures of Fibonacci polynomials over the ring of 2-adic integers are described by investigating minimal decompositions which consist of minimal subsystems and attracting basins.

Minimality of $5$-adic polynomial dynamical systemsSep 05 2018We characterize the dynamical systems consisting of the set of 5-adic integers and polynomial maps which consist of only one minimal component.

QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement LearningMay 14 2019We explore value-based solutions for multi-agent reinforcement learning (MARL) tasks in the centralized training with decentralized execution (CTDE) regime popularized recently. However, VDN and QMIX are representative examples that use the idea of factorization ... More

Rumor Source Detection under Querying with Untruthful AnswersNov 15 2017Nov 29 2017Social networks are the major routes for most individuals to exchange their opinions about new products, social trends and political issues via their interactions. It is often of significant importance to figure out who initially diffuses the information, ... More

Dynamic Large Spatial Covariance Matrix Estimation in Application to Semiparametric Model Construction via Variable Clustering: the SCE approachJun 20 2011Jun 23 2011To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized ... More

Towards Interactive Object-Oriented ProgrammingJan 29 2013To represent interactive objects, we propose a choice-disjunctive declaration statement of the form S R where S;R are the (procedure or field) declaration statements within a class. This statement has the following semantics: request the user to choose ... More

Incompatibility between Self-Observing Consciousness and the Axioms of Quantum theoryJun 28 2007Based on the standard axioms of quantum theory, we provide a counter-example which invalidates the full compatibility between consciousness and quantum theory. In particular, we present an example of a natural phenomenon in which an observer's the mental ... More

Quantum Theory, Consciousness, and BeingMar 05 2007Sep 29 2008In [NeuroQuantology 6, 46 (2008): arXiv:0706.4180], a certain natural phenomenon of self-observing consciousness was shown to be incompatible with the standard axioms of quantum theory. In order to consider a possibility of removing this inconsistency, ... More

Quark Orbital Angular Momentum in the BaryonDec 21 2000Jun 25 2001Analytical and numerical results, for the orbital and spin content carried by different quark flavors in the baryons, are given in the chiral quark model with symmetry breaking. The reduction of the quark spin, due to the spin dilution in the chiral splitting ... More

Substructure of the Nucleon in the Chiral Quark ModelFeb 18 2000The spin and orbital angular momentum carried by different quark flavors in the nucleon are calculated in the SU(3) chiral quark model with symmetry-breaking. The similar calculation is also performed for other octet and decuplet baryons. Furthermore, ... More

Area rigidity of minimal surfaces in three-manifolds of positive scalar curvatureNov 29 2016Combining Almgren-Pitts min-max theory for minimal surfaces and the Ricci flow with surgery, we prove that if a closed three-manifold $M$ has scalar curvature at least $6$ and is not isometric to the round three-sphere, then $M$ contains an embedded closed ... More

The α-Invariant on Toric Fano ManifoldsJul 22 2003The global holomorphic \alpha-invariant introduced by Tian is closely related with the study in the existence of Kahler-Einstein metric. We apply the result of Tian, Lu and Zelditch on polarized Kahler metrics to approximate plurisubharmonic functions ... More

Degeneration of Kahler-Einstein manifolds of negative scalar curvatureJun 05 2017Let $\pi: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact K\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique K\"ahler-Einstein metric on $\mathcal{X}_t= ... More

Enumeration of Graphs and the Characteristic Polynomial of the Hyperplane Arrangements $\mathcal{J}_n$Jan 25 2017We give a complete formula for the characteristic polynomial of hyperplane arrangements $\mathcal J_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $ 1\leq i, j, k, l\leq n$. The formula is obtained by associating hyperplane arrangements ... More

On a class of stochastic partial differential equationsMar 23 2015Jan 28 2016In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a Gaussian noise. ... More

Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theoremSep 30 2014It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we ... More

Convergence of Yang-Mills-Higgs fieldsMar 04 2014Oct 15 2014In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the Riemann surface is allowed to vary. We show that away ... More

Deep Neural Network for Learning to Rank Query-Text PairsFeb 25 2018This paper considers the problem of document ranking in information retrieval systems by Learning to Rank. We propose ConvRankNet combining a Siamese Convolutional Neural Network encoder and the RankNet ranking model which could be trained in an end-to-end ... More

Local Asymptotic Minimax Estimation of Nonregular Parameters with Translation-Scale Equivariant MapsMar 09 2014When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable. However, when the ... More

Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax RiskMar 10 2014When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation ... More

Nonlocality and the Correlation of Measurement BasesJun 25 2004Aug 26 2008Nonlocal nature apparently shown in entanglement is one of the most striking features of quantum theory. We examine the locality assumption in Bell-type proofs for entangled qubits, i.e. the outcome of a qubit at one end is independent of the basis choice ... More

Universal Grammar and ConsciousnessJun 28 2007Jan 07 2019The orthodox interpretation of quantum theory treats the subject and the object on an equal footing. It has been suggested that the cyclical-time process, which resolves self-reference in consciousness, interconnects the observed universe and the mind ... More

Non-Computability of ConsciousnessMay 11 2007With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain ... More

Construction of multi-default models with full viabilityNov 01 2015We study multi-default model which satisfies the quasi-left-continuity, the martingale representation property, the drift multiplier assumption and the full viability. We use $\natural$-model to construct one such model.

Proper maps, bordism, and geometric quantizationJun 23 2012Jan 22 2013Let $G$ be a compact connected Lie group acting on a stable complex manifold $M$ with equivariant vector bundle $E$. Besides, suppose $\phi$ is an equivariant map from $M$ to the Lie algebra $\mathfrak{g}$. We can define some equivalence relation on the ... More

Some properties on $G$-evaluation and its applications to $G$-martingale decompositionJan 17 2010Feb 03 2010In this article, a sublinear expectation induced by $G$-expectation is introduced, which is called $G$-evaluation for convenience. As an application, we prove that any $\xi\in L^\beta_G(\Omega_T)$ with some $\beta>1$ the decomposition theorem holds and ... More

Time and Space Efficient Algorithms for RNA Folding with the Four-Russians TechniqueMar 19 2015Mar 20 2015In this paper, we develop new algorithms for the basic RNA folding problem. Given an RNA sequence that contains $n$ nucleotides, the goal of the problem is to compute a pseudoknot-free secondary structure that maximizes the number of base pairs in the ... More

Dirac operators on quasi-Hamiltonian G-spacesMar 11 2015Oct 06 2015We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes ... More

On the Induced Matching Problem in Hamiltonian Bipartite GraphsDec 02 2014Dec 05 2014In this paper, we study the parameterized complexity and inapproximability of the {\sc Induced Matching} problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is W[1]-hard and cannot ... More

Theoretical Details of Tunnel Magnetoresistance via inelastic hopping at regime $gμB\ll k_B T \ll eV$Sep 29 2014Oct 12 2014Detailed theoretical derivation is given for the tunnel magnetoresistance via phonon-assisted hopping through an impurity chain under small magnetic field and a large bias window. This derivation provides a rigorous basis for the physical picture of Pauli ... More

Formal Verlinde ModuleApr 18 2014Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor power $\A^{k+h}$ vanishing ... More

A Note On Galilean Invariants In Semi-Relativistic ElectromagnetismApr 25 2013The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean ... More

On Double Smoothed Volatility Estimation of Potentially Nonstationary Jump-Diffusion ModelFeb 13 2018In this paper, we present the double smoothed nonparametric approach for infinitesimal conditional volatility of jump-diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and asymptotic normality ... More

Note on Light-like Tachyon CondensationMar 01 2010Jun 23 2010In this paper closed string emission and open string pair production from the light-like rolling tachyon solution are calculated in subcritical string theory in the background of a linear dilaton. The rolling light-like tachyon represents the inhomogeneous ... More

Properties of hitting times for $G$-martingaleJan 27 2010Feb 03 2010In this article, we consider the properties of hitting times for $G$-martingale and the stopped processes. We prove that the stopped processes for $G$-martingales are still $G$-martingales and that the hitting times for a class of $G$-martingales including ... More

On certain hyperplane arrangements and colored graphsJun 25 2016We exhibit a one-to-one correspondence between $3$-colored graphs and subarrangements of certain hyperplane arrangements denoted $\mathcal J_n$, $n \in \mathbb N$. We define the notion of centrality of $3$-colored graphs which corresponds to the centrality ... More

Some Results on the Scattering Theory for a Schrödinger Equation with Combined Power-Type NonlinearitiesApr 14 2011In this paper, we consider the Cauchy problem {align*} \{{array}{ll}&i u_t+\Delta u=\lambda_1|u|^{p_1}u+\lambda_2|u|^{p_2}u, \quad t\in\mathbb{R}, \quad x\in\mathbb{R}^N &u(0,x)=\phi(x)\in \Sigma, \quad x\in\mathbb{R}^N, {array}. {align*} where $N\geq ... More

The role of potential, Morawetz estimate and spacetime bound for quasilinear Schrödinger equationsApr 22 2019In this paper, we deal with the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t = \Delta u + 2uh'(|u|^2)\Delta h(|u|^2) + V(x)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0) = u_0(x), \quad x \in \mathbb{R}^N. \end{array}\right. \end{equation*} ... More

Morawetz estimates and spacetime bounds for quasilinear Schrödinger equations with critical Sobolev exponentApr 22 2019In this paper, we study the following Cauchy problem \begin{equation*} \left\{ \begin{array}{lll} iu_t=\Delta u + 2uh'(|u|^2)\Delta h(|u|^2) + F(|u|^2)u\mp A[h(|u|^2]^{2^*-1} h'(|u|^2)u,\ x\in \mathbb{R}^N, \ t>0\\ u(x,0)=u_0(x), \quad x\in \mathbb{R}^N. ... More

Measuring the Graph Concordance of Locally Dependent ObservationsApr 14 2015Aug 31 2017This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance measure can be ... More

Gradient Estimates for Nonlinear Diffusion Semigroups by Coupling MethodsJul 21 2014Our purpose is to obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First we derive uniform gradient estimates for a certain semi-linear PDEs based on the coupling method introduced in Wang (2011) and ... More

$L^p$ Solutions of Backward Stochastic Differential Equations with JumpsJul 13 2010Feb 10 2017Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)-$variables. We show that such a BSDEJ with a p-integrable terminal ... More

Mechanism of the Fano resonance in a planar metamaterials: Analysis from the coupled two-oscillator modelMay 03 2016Mechanism of the Fano resonances in planar metamaterials demonstrate based on the coupled two-oscillator model. We have described the optical spectrums like reflectance and transmittance near the resonances of bright mode (continuum mode) and dark mode ... More

Solvability of Dirichlet problem with Nonlinear Integro-differential OperatorFeb 19 2016Jul 26 2016This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the continuity set ... More

Semantics of InformationNov 07 2016Both the choice made by the observer and consciousness are discussed in terms of cyclical time. That is, while the process of classical choice evolves forward in time, the quantum reference frame evolves backward in time to equate itself with the classical ... More

Baryon Magnetic Moments and Quark Orbital Motion in the Chiral Quark ModelApr 30 1998May 13 1998Using the unified scheme for describing both quark spin and orbital angular momenta in the chiral quark model developed in the previous work, the magnetic moments of octet and decuplet baryons are calculated. The numerical result shows that the overall ... More

Intrinsic Charm Flavor and Helicity Content in the ProtonSep 28 2001Oct 28 2001Contributions to the quark flavor and spin observables from the intrinsic charm in the proton are discussed in the SU(4) quark meson fluctuation model. Our results suggest that the probability of finding the intrinsic charm in the proton is less than ... More

Entanglement Entropy Evolution under Double-trace DeformationMay 08 2016May 16 2016In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where quantum corrections of entanglement entropy give the leading contribution. ... More

Molecular Communication Systems Design for Future CityMar 27 2014An area of interest in the modern age is the human migration from rural areas to cities. Cities are characterized by a dense concentration of buildings and key infrastructures. However, what has been lacking is a pervasive sensor technology that can monitor ... More

Stream-based Online Active Learning in a Contextual Multi-Armed Bandit FrameworkJul 11 2016We study the stream-based online active learning in a contextual multi-armed bandit framework. In this framework, the reward depends on both the arm and the context. In a stream-based active learning setting, obtaining the ground truth of the reward is ... More

Relay Selection for Two-way Relaying with Amplify-and-Forward ProtocolsNov 30 2011In this paper, we propose a relay selection amplify-and-forward (RS-AF) protocol in general bi-directional relay networks with two sources and $N$ relays. In the proposed scheme, the two sources first transmit to all the relays simultaneously, and then ... More

Computer-Assisted Interactive Documentary and Performance Arts in Illimitable SpaceDec 26 2012This major component of the research described in this thesis is 3D computer graphics, specifically the realistic physics-based softbody simulation and haptic responsive environments. Minor components include advanced human-computer interaction environments, ... More

Lower central subgroups of a free group and its subgroupJul 11 2018For a given free group $F$ of arbitrary rank (possibly infinite), and its subgroup $G$, we address the question whether a lower central subgroup of $G$ can contain a lower central subgroup of $F$. We show that the answer is no if $G$ does not normally ... More

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFTSep 22 2015Jun 19 2016We study superconformal indices of 4d N=2 class S theories with certain irregular punctures called type $I_{k, N}$. This class of theories include generalized Argyres-Douglas theories of type $(A_{k-1}, A_{N-1})$ and more. We conjecture the superconformal ... More

Ricci flow and birational surgeryApr 09 2013We study the formation of finite time singularities of the Kahler-Ricci flow in relation to high codimensional birational surgery in algebraic geometry. We show that the Kahler-Ricci flow on an n-dimensionl Kahler manifold contracts a complex submanifold ... More

Some Type I solutions of Ricci flow with rotational symmetryMar 13 2012We prove that the Ricci flow on CP^n blown-up at one point starting with any rotationally symmetric Kahler metric must develop Type I singularities. In particular, if the total volume does not go to zero at the singular time, the parabolic blow-up limit ... More

On a conjecture of Candelas and de la OssaJan 20 2012We prove that the metric completion of a canonical Ricci-flat Kahler metric on the nonsingular part of a projective Calabi-Yau variety $X$ with ordinary double point singularities, is a compact metric length space homeomorphic to the projective variety ... More

Finite time extinction of the Kahler-Ricci flowMay 07 2009We investigate the limiting behavior of the unnormalized Kahler-Ricci flow on a Kahler manifold with a polarized initial Kahler metric. We prove that the Kahler-Ricci flow becomes extinct in finite time if and only if the manifold has positive first Chern ... More

Effective mass of phi mesons at finite temperatureMar 10 1996The effective mass of phi meson at non-zero temperature is re-examined with an effective chiral Lagrangian. We find that the phi mass decreases with temperature but the effect is small compared to the result obtained from calculations using QCD sum rules. ... More

Properties of vector mesons at finite temperature -effective lagrangian approach-Jan 24 1995The properties of $\rho$-mesons at finite temperature ($T$) are examined with an effective chiral lagrangian in which vector and axial-vector mesons are included as massive Yang-Mills fields of the chiral symmetry. It is shown that, at $T^2$ order, the ... More

Semiparametric Models with Single-Index Nuisance ParametersJul 22 2013In many semiparametric models, the parameter of interest is identified through conditional expectations, where the conditioning variable involves a single-index that is estimated in the first step. Among the examples are sample selection models and propensity ... More

Remarks on the undecidability of the quantum halting problemJan 22 2007Oct 22 2015The halting problem is a decision problem first posed and proved by Alan Turing in 1936. With the recent surge of interest in quantum computation, one is led to ask if the problem can also be considered for a quantum computer. It is reported that the ... More

Unsolvability of the Halting Problem in Quantum DynamicsOct 07 2006It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider ... More

Post-measurement Nonlocal GatesMar 24 2003Several proposed quantum computer models include measurement processes, in order to implement nonlocal gates and create necessary entanglement resources during the computation. We introduce a scheme in which the measurements can be delayed for two- and ... More

Hydrodynamic Modeling for Relativistic Heavy Ion Collisions at RHIC and the LHCDec 31 2013In this article, we briefly review recent progress on hydrodynamic modeling and its implementations to relativistic heavy-ion collisions at RHIC and the LHC. The related topics include: 1) initial state fluctuations, final state correlations and event-by-event ... More

VISHNU hybrid model for viscous QCD matter at RHIC and LHC energiesJan 24 2012In this proceeding, we briefly describe the viscous hydrodynamics + hadron cascade hybrid model VISHNU for relativistic heavy ion collisions and report the current status on extracting the QGP viscosity from elliptic flow data.

Enumeration of graphs with given weighted number of connected componentsJun 26 2016We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given order, size and ... More

Properties of $G$-martingales with finite variation and the application to $G$-Sobolev spacesJul 03 2016As is known, a process of form $\int_0^t\eta_sd\langle B\rangle_s-\int_0^t2G(\eta_s)ds$, $\eta\in M^1_G(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale could not be form of $\int_0^t\eta_sds$ ... More

From Doob's maximal identity to Azema supermartingaleFeb 14 2016Feb 28 2016We characterize the random times $\rho$ whose Azema supermartingales $Z^\rho$ take the form $Z^\rho=U/U^*$ for some non negative local martingales $U$ starting from 1 vanishing at infinity, where $U^*$ denotes the running maximum process of $U$.

Approximating Functional of Local Martingale Under the Lack of Uniqueness of Black-Scholes PDEFeb 11 2011Sep 21 2012When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest ... More

Vector bundles induced from jet schemesSep 13 2016A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler manifold with holonomy ... More

A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed FlowNov 28 2013Mar 21 2015Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

A Note On $G$-normal DistributionsOct 30 2014As is known, the convolution $\mu*\nu$ of two $G$-normal distributions $\mu, \nu$ with different intervals of variances may not be $G$-normal. We shows that $\mu*\nu$ is a $G$-normal distribution if and only if $\frac{\overline{\sigma}_\mu}{\underline{\sigma}_\mu}=\frac{\overline{\sigma}_\nu}{\underline{\sigma}_\nu}$. ... More

Electric-field-induced extremely large change in resistance in graphene ferromagnetsAug 06 2017Dec 11 2017A colossal magnetoresistance ($\sim 100\times10^3\%$) and an extremely large magnetoresistance ($\sim 1\times10^6\%$) have been previously explored in manganite perovskites and Dirac materials, respectively. However, the requirement of an extremely strong ... More

Magnetic Field-Free Giant Magnetoresistance in a Proximity- and Gate-Induced Graphene Spin ValveMay 02 2017Due to its two dimensional nature, ferromagnetism and charge doping can be induced by proximity and electric field effects in graphene. Taking advantage of these features, we propose an electrically engineered spin valve by combining two magnetic insulators ... More

Entanglement Entropy Evolution under Double-trace DeformationMay 08 2016Jun 02 2017In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where quantum corrections of entanglement entropy give the leading contribution. ... More

A dichotomy for minimal hypersurfaces in manifolds thick at infinityFeb 18 2019Let $(M^{n+1},g)$ be a complete $(n+1)$-dimensional Riemannian manifold with $2\leq n\leq 6$. Our main theorem generalizes the solution of Yau's conjecture for minimal surfaces and builds on a result of Gromov. Suppose that $(M,g)$ is thick at infinity, ... More

On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple NonlinearitiesSep 02 2010In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem \begin{align*} \left\{\begin{array}{ll}&-i u_t=\Delta u-V(x)u+f(x,|u|^2)u+(W\star|u|^2)u, \quad x\in\mathbb{R}^N, \quad t>0, &u(x,0)=u_0(x), \quad x\in\mathbb{R}^N, ... More

Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTsNov 02 2017Jan 08 2019The R\'enyi entanglement entropy (REE) of the states excited by local operators in two-dimensional irrational conformal field theories (CFTs), especially in Liouville field theory (LFT) and $\mathcal{N}=1$ super-Liouville field theory (SLFT), has been ... More

Stabilizing the Richardson Algorithm by Controlling ChaosJun 11 1996By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the ... More

Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type NonlinearitiesSep 02 2010Jun 03 2013In this paper, we consider the Cauchy problem of Nonlinear Schr\"{o}dinger equation \begin{align*} \left\{\begin{array}{ll}&i u_t+\Delta u=\lambda_1|u|^{p_1}u+\lambda_2|u|^{p_2}u, \quad t\in\mathbb{R}, \quad x\in\mathbb{R}^N &u(0,x)=\varphi(x), \quad ... More

A Proof of the Explicit Formula for Product Moments of Multivariate Gaussian Random VariablesApr 29 2017A detailed proof of a recent result on explicit formulae for the product moments $E \left \{ X_1^{a_1} X_2^{a_2} \cdots X_n^{a_n}\right \}$ of multivariate Gaussian random variables is provided in this note.

Stein's Method for Law of Large Numbers under Sublinear ExpectationsApr 09 2019Peng, S. (\cite{P08b}) proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein's method.

One loop quantum fluctuations to the energy of the non-topological soliton in Friedberg-Lee modelJul 06 2016I have used a practical method to calculate the one-loop quantum correction to the energy of the non-topological soliton in Friedberg-Lee model. The quantum effects which come from the quarks of the Dirac sea scattering with the soliton bag are calculated ... More

Solvability of Dirichlet problem with Nonlinear Integro-differential OperatorFeb 19 2016Oct 26 2016This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the continuity set ... More

Locally accessible information from multipartite ensemblesNov 18 2007Nov 25 2007We present a universal Holevo-like upper bound on the locally accessible information for arbitrary multipartite ensembles. This bound allows us to analyze the indistinguishability of a set of orthogonal states under LOCC. We also derive the upper bound ... More

Lower bounds on the squashed entanglement for multi-party systemsDec 03 2007Aug 04 2009Squashed entanglement is a promising entanglement measure that can be generalized to multipartite case, and it has all of the desirable properties for a good entanglement measure. In this paper we present computable lower bounds to evaluate the multipartite ... More

Quark Spin and Orbital Angular Momentum in the BaryonOct 29 1999Aug 11 2000The spin and orbital angular momentum carried by different quark flavors in the nucleon are calculated in the SU(3) chiral quark model with symmetry-breaking. The model is extended to all octet and decuplet baryons. In this model, the reduction of the ... More

New Relations and Constraints on Quark Spin-flavor Contents in Symmetry-breaking Chiral Quark ModelDec 11 1997New relations between the quark spin-flavor contents of the nucleon and axial weak coupling constants are obtained in the chiral quark model with both SU(3) and U(1)-breaking effects. Using the nonsinglet spin combinations, $\Delta_3$ and $\Delta_8$, ... More

Embeddedness of least area minimal hypersurfacesNov 09 2015Nov 28 2016E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the curvature. More ... More

Measuring the Graph Concordance of Locally Dependent ObservationsApr 14 2015Sep 12 2016This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance measure can be ... More

$L^p$ Solutions of Backward Stochastic Differential Equations with JumpsJul 13 2010Jul 01 2016Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z,u)$. We show that such a BSDEJ with a p-integrable terminal data ... More