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Secure Phrase Search for Intelligent Processing of Encrypted Data in Cloud-Based IoTSep 21 2018Phrase search allows retrieval of documents containing an exact phrase, which plays an important role in many machine learning applications for cloud-based IoT, such as intelligent medical data analytics. In order to protect sensitive information from ... More

When Homomorphic Cryptosystem Meets Differential Privacy: Training Machine Learning Classifier with Privacy ProtectionDec 06 2018Machine learning (ML) classifiers are invaluable building blocks that have been used in many fields. High quality training dataset collected from multiple data providers is essential to train accurate classifiers. However, it raises concern about data ... More

Content-Based Multi-Source Encrypted Image Retrieval in Clouds with Privacy PreservationSep 22 2018Content-based image retrieval (CBIR) is one of the fundamental image retrieval primitives. Its applications can be found in various areas, such as art collections and medical diagnoses. With an increasing prevalence of cloud computing paradigm, image ... More

Cloud-Based Approximate Constrained Shortest Distance Queries Over Encrypted Graphs With Privacy ProtectionSep 21 2018Constrained shortest distance (CSD) querying is one of the fundamental graph query primitives, which finds the shortest distance from an origin to a destination in a graph with a constraint that the total cost does not exceed a given threshold. CSD querying ... More

PRIF: A Privacy-Preserving Interest-Based Forwarding Scheme for Social Internet of VehiclesApr 06 2018Recent advances in Socially Aware Networks (SANs) have allowed its use in many domains, out of which social Internet of vehicles (SIOV) is of prime importance. SANs can provide a promising routing and forwarding paradigm for SIOV by using interest-based ... More

LPTD: Achieving Lightweight and Privacy-Preserving Truth Discovery in CIoTApr 05 2018In recent years, cognitive Internet of Things (CIoT) has received considerable attention because it can extract valuable information from various Internet of Things (IoT) devices. In CIoT, truth discovery plays an important role in identifying truthful ... More

Privacy-Preserving DDoS Attack Detection Using Cross-Domain Traffic in Software Defined NetworksSep 19 2018Existing distributed denial-of-service attack detection in software defined networks (SDNs) typically perform detection in a single domain. In reality, abnormal traffic usually affects multiple network domains. Thus, a cross-domain attack detection has ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019Feb 14 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

A Privacy-Preserving Traffic Monitoring Scheme via Vehicular CrowdsourcingFeb 12 2019The explosive growth of vehicle amount has given rise to a series of traffic problems, such as traffic congestion, road safety, and fuel waste. Collecting vehicles' speed information is an effective way to monitor the traffic condition and avoid vehicles ... More

Research on the Security of Blockchain Data: A SurveyDec 05 2018Dec 07 2018With the more and more extensive application of blockchain, blockchain security has been widely concerned by the society and deeply studied by scholars. Moreover, the security of blockchain data directly affects the security of various applications of ... More

Towards Delay-Tolerant Flexible Data Access Control for Smart Grid with Renewable Energy ResourcesOct 25 2018In the Smart Grid with Renewable Energy Resources (RERs), the Residential Units (RUs) with Distributed Energy Resources (DERs) are considered to be both power consumers and suppliers. Specifically, RUs with excessive renewable generations can trade with ... More

ESAS: An Efficient Semantic and Authorized Search Scheme over Encrypted Outsourced DataOct 25 2018Nowadays, a large amount of user privacy-sensitive data is outsourced to the cloud server in ciphertext, which is provided by the data owners and can be accessed by authorized data users. When accessing data, the user should be assigned with the access ... More

Toward Practical Differential Privacy in Smart Grid with Capacity-Limited Rechargeable BatteriesJul 10 2015Jul 22 2015The technology of differential privacy, adding a noise drawn from the Laplace distribution, successfully overcomes a difficulty of keeping both the privacy of individual data and the utility of the statistical result simultaneously. Therefore, it is prevalent ... More

SDN Controllers: Benchmarking & Performance EvaluationFeb 12 2019Software Defined Networks offer flexible and intelligent network operations by splitting a traditional network into a centralized control plane and a programmable data plane. The intelligent control plane is responsible for providing flow paths to switches ... More

EPDA: Enhancing Privacy-Preserving Data Authentication for Mobile Crowd SensingNov 09 2018As a popular application, mobile crowd sensing systems aim at providing more convenient service via the swarm intelligence. With the popularity of sensor-embedded smart phones and intelligent wearable devices, mobile crowd sensing is becoming an efficient ... More

Achieving Trust-Based and Privacy-Preserving Customer Selection in Ubiquitous ComputingFeb 12 2019The recent proliferation of smart devices has given rise to ubiquitous computing, an emerging computing paradigm which allows anytime & anywhere computing possible. In such a ubiquitous computing environment, customers release different computing or sensing ... More

PPLS: A Privacy-Preserving Location-Sharing Scheme in Vehicular Social NetworksApr 06 2018Recent advances in Socially Aware Networks (SANs) have allowed its use in many domains, out of which social Internet of vehicles (SIOV) is of prime importance. SANs can provide a promising routing and forwarding paradigm for SIOV by using interest-based ... More

IriTrack: Liveness Detection Using Irises Tracking for Preventing Face Spoofing AttacksOct 08 2018Face liveness detection has become a widely used technique with a growing importance in various authentication scenarios to withstand spoofing attacks. Existing methods that perform liveness detection generally focus on designing intelligent classifiers ... More

A Wong-Zakai theorem for $Φ^4_3$ modelApr 16 2015We prove a version of the Wong-Zakai theorem for the dynamical $\Phi_3^4$ model driven by space-time white noise on $\mathbb{T}^3$. For the $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear ... More

Dimension reduction-based significance testing in nonparametric regressionOct 13 2015A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing ... More

Piecewise linear approximation for the dynamical $Φ^4_3$ modelApr 16 2015Oct 22 2017We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed ... More

Random attractor associated with the quasi-geostrophic equationMar 24 2013We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the existence of a ... More

Weak universality of the dynamical $Φ_3^4$ model on the whole spaceNov 04 2018Nov 06 2018We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $\mathbb{R}^3$ to the dynamical $\Phi^4_3$ model by paracontrolled distributions on weighted Besov space. Our approach depends on the delicate ... More

Dirichlet form associated with the $Φ_3^4$ modelMar 29 2017Jun 25 2017We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient ... More

Lattice approximation to the dynamical $Φ_3^4$ modelAug 23 2015We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally ... More

Strong-Feller property for Navier-Stokes equations driven by space-time white noiseSep 27 2017Sep 29 2017In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jan 04 2017In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

Approximating three-dimensional Navier-Stokes equations driven by space-time white noiseSep 17 2014In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jun 10 2015In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

A Generalization of the Kodaira Vanishing and Embedding TheoremFeb 02 1995We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg ... More

Log rationally connected surfacesDec 08 2014Jul 02 2015In this paper, combining the works of Miyanishi-Tsunoda and Keel-McKernan, we prove the log Castelnuovo's rationality criterion for smooth quasiprojective surfaces over complex numbers.

Exotic Charmonium-like States at BESIIIMay 18 2015The recent measurement results of exotic charmonium-like states, the so called XYZ particles, at BESIII have been presented. I mainly discussed the charged Zc(3900) state, its neutral partner, and possible excited states.

Charmonium and Light Meson SpectroscopyDec 10 2012This talk reviews recent experimental results on selected topics in the spectroscopy of charmonia, charmonium-like states and light mesons.

On the gluing formula of real analytic torsion formsMay 13 2014In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that ... More

The RPC-based proposal for the ATLAS forward muon trigger upgrade in view of super-LHCOct 25 2012The innermost station of the present ATLAS forward muon detector needs to be upgraded for the super-LHC. We present a proposal to replace it with a sandwiched detector composed of several layers of small-radius Monitored Drift Tube chambers (sMDT) for ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 15 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Global classical solutions of 3D compressible viscoelastic system near equilibriumSep 12 2018In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with previous works. It ... More

Statistical Physics and Information Theory Perspectives on Linear Inverse ProblemsMay 15 2017Jul 12 2017Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement vector (SMV) ... More

Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological SpacesSep 01 2017Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$ and $B$ to ... More

K3 surfaces associated to Abelian Fourfolds of Mumford's TypeDec 17 2018Apr 15 2019Mumford constructed a family of abelian fourfolds with special stucture not characterized by endomorphism ring. Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of Mumford-Tate group, ... More

Constructing a CM Mumford fourfold from Shioda's fourfoldOct 23 2018Apr 15 2019Shioda proved that the Jacobian $A_S$ of the curve $y^2 = x^9 -1$ is a 4-dimensional CM abelian variety with codimension 2 Hodge cycles not generated by divisors. It was noted by Shioda that this behavior resembles the abelian varieties constructed by ... More

Hodge structure of K3 type with real multiplication and Simple Abelian Fourfolds with Definite Quaternionic MultiplicationJun 24 2019In this paper we give a general construction of transcendental lattices for K3 surfaces with real multiplication by arbitrary field up to degree 6 along with formula for their discriminants. We also show that all simple Abelian fourfolds with definite ... More

Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational SignaturesDec 04 2018We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced ... More

A New View of Classification in Astronomy with the Archetype Technique: An Astronomical Case of the NP-complete Set Cover ProblemJun 23 2016We introduce a new generic Archetype technique for source classification and identification, based on the NP-complete set cover problem (SCP) in computer science and operations research (OR). We have developed a new heuristic SCP solver, by combining ... More

WIMPless dark matter and the excess gamma rays from the Galactic centerJan 23 2011Apr 05 2011In this paper we discuss the excess gamma rays from the Galactic center, the WMAP haze and the CoGeNT and DAMA results in WIMPless models. At the same time we also investigate the low energy constraints from the anomalous magnetic moment of leptons and ... More

Some sufficient conditions on Hamiltonian digraphDec 23 2008Z-mapping graph is a balanced bipartite graph $G$ of a digraph $D$ by split each vertex of $D$ into a pair of vertices of $G$. Based on the property of the $G$, it is proved that if $D$ is strong connected and $G$ is Hamiltonian, then $D$ is Hamiltonian. ... More

The Complexity of Determining Existence a Hamiltonian Cycle is $O(n^3)$Jun 19 2007The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is $O(n^3)$.

Deformations of glassy polymers in very low temperature regime within cylindrical microporesAug 28 2008Apr 09 2009The deformation kinetics for glassy polymers confined in microscopic domain at very low temperature regime was investigated using a transition-rate-state dependent model considering the shear thinning behavior which means, once material being subjected ... More

When is the majority-vote classifier beneficial?Jul 24 2013In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification ... More

The second variation of the Ricci expander entropyJan 19 2009We compute the second variation of the Ricci expander entropy and briefly discuss the linear stability of compact negative Einstein manifolds.

Kernels and Ensembles: Perspectives on Statistical LearningDec 06 2007Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. ... More

Some inequalities related to isoperimetric inequalities with partial free boundaryJan 09 2001Feb 16 2001The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free boundary, and the ... More

Integral Solutions to Linear Indeterminate EquationMar 08 2011In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1x_1+a_2x_2+...+a_sx_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and the free term ... More

n-Groupoids and Stacky GroupoidsJan 14 2008Jun 29 2009We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 ... More

Lie n-groupoids and stacky Lie groupoidsSep 14 2006Nov 13 2006We discuss two sorts of generalization of Lie groupoids. One is Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence ... More

Integrating Lie algebroids via stacks and applications to Jacobi manifoldsMay 09 2005Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out ... More

Harmonic maps from degenerating Riemann surfacesMar 25 2008We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles ... More

An axiomatic approach to the roughness measure of rough setsNov 28 2009May 25 2010In Pawlak's rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of ... More

Covering rough sets based on neighborhoods: An approach without using neighborhoodsNov 28 2009Dec 10 2010Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough ... More

On the Well-posedness of a Generalized Moment Problem and Its Numerical SolutionFeb 26 2018We show that the unique solution to a parametric version of the generalized moment problem depends continuously on the prior function, and thus the problem is well-posed in the sense of Hadamard. Based on this result, the problem is reparametrized via ... More

Information complementarity: A new paradigm for decoding quantum incompatibilityJun 26 2014Sep 14 2015The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality ... More

Nonexistence of sharply covariant mutually unbiased bases in odd prime dimensionsJun 18 2015Aug 23 2015Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order $d(d+1)$ from a ... More

Riesz transform characterization of weighted Hardy spaces associated to Schrödinger operatorsMay 21 2014In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{1}^{\rho,\,\infty}(\mathbb{R}^{n})$ by localized Riesz transforms $\widehat{R}_j$, in addition, ... More

Nonuniform Dichotomy Spectrum Intervals: Theorem and ComputationFeb 12 2019Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical spectrums (the Lyapunov ... More

Robustness of nonuniform mean-square exponential dichotomiesFeb 12 2019Jun 13 2019For linear stochastic differential equations (SDEs) with bounded coefficients, we establish the robustness of nonuniform mean-square exponential dichotomy (NMS-ED) on $[t_{0},+\oo)$, $(-\oo,t_{0}]$ and the whole $\R$ separately, in the sense that such ... More

Spectra and elliptic flow of (multi-)strange hadrons at RHIC and LHC within viscous hydrodynamics+hadron cascade hybrid modelJul 14 2016Aug 15 2016Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb ... More

Optimal Strategies for a Long-Term Static InvestorNov 24 2013Oct 14 2014The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the wealth. When the ... More

Generalized PMC model for the hybrid diagnosis of multiprocessor systemsSep 17 2017Sep 19 2017Fault diagnosis is important to the design and maintenance of large multiprocessor systems. PMC model is the most famous diagnosis model in the system level diagnosis of multiprocessor systems. Under the PMC model, only node faults are allowed. But in ... More

Branching interlacements and tree-indexed random walks in torusDec 28 2018Jan 15 2019In this article, we introduce a model of branching interlacements made of a countable collection of tree-indexed random walk trajectories on $\mathbb{Z}^d,d\geq 5$ for general critical offspring distributions. We show that this model turns out to be the ... More

The higher order terms in asymptotic expansion of color Jones polynomialsApr 03 2011Color Jones polynomial is one of the most important quantum invariants in knot theory. Finding the geometric information from the color Jones polynomial is an interesting topic. In this paper, we study the general expansion of color Jones polynomial which ... More

Vertex operator algebras associated to modified regular representations of affine Lie algebrasNov 17 2006Nov 20 2007Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras associated to $\mf ... More

The Lp Minkowski problem for polytopes for negative pFeb 25 2016May 07 2016Existence of solutions to the Lp Minkowski problem is proved for all p less than 0. For the cirtical case of p=-n, which is known as the centro-affine Minkowski problem, this paper contains the main result in [71] as a special case.

Auxiliary space preconditioners for virtual element methods on polytopal meshesNov 28 2018In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are constructed based ... More

The internal structure of $\mathrm{HOD}^{L[x]}$ up to its WoodinNov 06 2017Nov 08 2017Assume $\boldsymbol{\Delta}^1_3$-determinacy. It is shown that for any $x \geq_T M_1^{\#}$, $\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\omega_2^{L[x]}$.

Dirac-harmonic maps from degenerating spin surfaces I: the Neveu-Schwarz caseMar 26 2008We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition ... More

Explicit Maximum Likelihood Loss Estimator in Multicast TomographyApr 27 2010For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern is focused ... More

A regularity theory for multiple-valued Dirichlet minimizing mapsAug 07 2006This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the previous work ... More

A geometrizing higher twist effect on nuclear targetAug 30 2004Feb 13 2005The higher twist effects in deep inelastic scattering on the nuclear target are studied using time ordered perturbation theory. We showed that the collinear rescattering of the outgoing quark on the extra nucleons via the contacting gluon-pair is dominant ... More

The Morse index theorem for regular Lagrangian systemsSep 18 2001In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

A few results on the infimum of regular polygons equal-size split lineMay 15 2018If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt {\frac{{\sqrt 3 \pi ... More

Constructing a CM Mumford fourfold from Shioda's fourfoldOct 23 2018Jun 06 2019Shioda proved that the Jacobian $A_S$ of the curve $y^2 = x^9 -1$ is a 4-dimensional CM abelian variety with codimension 2 Hodge cycles not generated by divisors. It was noted by Shioda that this behavior resembles the abelian varieties constructed by ... More

Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential ClaimsApr 06 2013Oct 14 2014In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival ... More

The optimal control related to Riemannian manifolds and the viscosity solutions to H-J-B equationsJan 16 2010This paper is concerned with the Dynamic Programming Principle (DPP in short) with SDEs on Riemannian manifolds. Moreover, through the DPP, we conclude that the cost function is the unique viscosity solution to the related PDEs on manifolds.

A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systemsAug 01 2018In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous ... More

Functors and morphisms determined by subcategoriesOct 24 2017We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a Hom-finite hereditary abelian category with enough projectives, we prove that the Auslander-Reiten-Smal{\o}-Ringel formula of the minimal right ... More

Applications of BGP-reflection functors: isomorphisms of cluster algebrasNov 15 2005Jun 19 2006Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism ... More

Generalized cluster complexes via quiver representationsJul 06 2006May 23 2007We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. By using $d-$cluster categories which are defined by Keller as triangulated orbit categories of (bounded) derived categories of representations ... More

Equivalences between cluster categoriesNov 15 2005Jun 19 2006Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object $T$ in a hereditary abelian ... More

BGP-reflection functors and cluster combinatoricsNov 15 2005Jul 14 2006We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost positive roots ... More

Towards a dictionary for the Bargmann transformJun 21 2015There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of $F^2$. Examples ... More

Uncertainty principles for the Fock spaceJan 12 2015Several uncertainty principles are proved for the Fock space.

The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applicationsJan 05 2010By the same method introduced in [9], we calculate the Laplace transform of the celebrated cut-and-join equation of Mari\~no-Vafa formula discovered by C. Liu, K. Liu and J. Zhou [17]. Then, we study the applications of the polynomial identity (1) obtained ... More

On a proof of the Bouchard-Sulkowski conjectureAug 14 2011In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for the case of C^3 has been finished.

Nonlinear Model Reduction Based On The Finite Element Method With Interpolated Coefficients: Semilinear Parabolic EquationsApr 01 2013Apr 28 2013For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its computational efficiency, ... More

Spin-dependent electron grating effect from helical magnetization in multiferroic tunnel junctionsApr 27 2012In multiferroic oxides with a transverse helical magnetic order, the magnetization exchange coupling is sinusoidally space-dependent. We theoretically investigate the spin-dependent electron grating effect in normal-metal/helical-multiferroic/ferromagnettic ... More

Conductance in the Helimagnet- and Skyrmion-Lattice-Embedded Electron WaveguideNov 22 2013The helimagnet (HM) and skyrmion lattice (SL) are topologically nontrivial magnetic states. Their spin texture gives rise to finite topological magnetic field and Lorentz force. As a demonstration of the emergent electrodynamics besides the Hall effect, ... More

A scattering matrix approach to quantum pumping: Beyond the small-ac-driving-amplitude limitNov 06 2009In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to the other by absorbing or emitting an energy quantum $\hbar \omega $ from or to the reservoirs. In our approach, high-order dependence of the scattering ... More

On the semi-regular module and vertex operator algebrasNov 20 2007Dec 03 2007We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.

Jet schemes and singularities of W^r_d(C) lociDec 05 2012Kempf proved that the theta divisor of a smooth projective curve C has rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular, we recover ... More