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Exploiting Unlabeled Data in CNNs by Self-supervised Learning to RankFeb 17 2019For many applications the collection of labeled data is expensive laborious. Exploitation of unlabeled data during training is thus a long pursued objective of machine learning. Self-supervised learning addresses this by positing an auxiliary task (different, ... More

Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018Dec 12 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

Memory Replay GANs: learning to generate images from new categories without forgettingSep 06 2018Oct 29 2018Previous works on sequential learning address the problem of forgetting in discriminative models. In this paper we consider the case of generative models. In particular, we investigate generative adversarial networks (GANs) in the task of learning new ... More

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalingsFeb 26 2018Jul 16 2018In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior leading to the drift diffusion-Poisson system as the Knudsen number goes to zero. The random inputs ... More

On the arithmetic of the endomorphism ring End($\mathbb{Z}_{p}\times\mathbb{Z}_{p^{m}}$)May 03 2016For a prime $p$, let $E_{p,p^m}=\{\begin{pmatrix}a&b\\p^{m-1}c&d\end{pmatrix}|a,b,c\in\mathbb{Z}_{p},~\mathrm{and}~d\in \mathbb{Z}_{p^{m}}\}$. We first establish a ring isomorphism from $\mathrm{End}(\mathbb{Z}_p\times\mathbb{Z}_p^m)$ onto $E_{p,p^m}$. ... More

$T$-adic exponential sums of polynomials in one variableNov 03 2009The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential ... More

The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer ApproachNov 05 2008In this paper, the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized ... More

On surjectivity of smooth maps into Euclidean spaces and the fundamental theorem of algebraJun 16 2017In this note we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As application we give a new proof of the Fundamental Theorem of Algebra. We also observe that any $C^1$-map from a compact manifold into Euclidean space ... More

Hypocoercivity for a BGK model for gas mixturesOct 19 2018Jan 08 2019We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential ... More

A blow-up criterion for the compressible liquid crystals systemNov 19 2010Nov 23 2010In this paper, we establish a blow-up criterion for the compressible liquid crystals equations in terms of the gradient of the velocity only, similar to the Beale-Kato-Majda criterion \cite{majda} for ideal incompressible flows and the criterion obtained ... More

Fine Magnetic Characteristics of a Light Bridge by HinodeFeb 01 2019Light bridge (LB) is bright structure crossing the umbra of sunspots and associated to the breakup or assembly of sunspots. In this paper, a LB is presented and studied using the observatory data obtained by {\it Hinode} satellites. Force-free factor ... More

Relationship between Magnetic Field Properties and an X-class Flare in Active Region NOAA 9077Feb 01 2019The magnetic field plays a key role in producing solar flares, so that the investigation on the relationship between the magnetic field properties and flares is significant. In this paper, based on the magnetic field extrapolated from the photospheric ... More

$σ$-self-orthogonal constacyclic codes of length $p^s$ over $\mathbb F_{p^m}+u\mathbb F_{p^m}$Jul 25 2018In this paper, we study the $\sigma$-self-orthogonality of constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb F_{p^m} + u \mathbb F_{p^m}$, where $u^2=0$ and $\sigma$ is a ring automorphism of $\mathbb F_{p^m} + u \mathbb ... More

Higher Toda Mechanics and Spectral CurvesJun 01 2003For each one of the Lie algebras $\mathfrak{gl}_{n}$ and $\widetilde {\mathfrak{gl}}_{n}$, we constructed a family of integrable generalizations of the Toda chains characterized by two integers $m_{+}$ and $m_{-}$. The Lax matrices and the equations of ... More

Group Learning and Opinion Diffusion in a Broadcast NetworkSep 14 2013We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly ... More

Rapid variability of BL Lac 0925+504: interstellar scintillation induced?Apr 25 2018Analysis of rapid variability at 4.85 GHz for the BL BLac object 0925+504 is presented and discussed. The structure functions (SF) are investigated with both refractive and weak interstellar scintillation (RISS/WISS) models analytically. Parameters obtained ... More

On the $A_α$-characteristic polynomial of a graphNov 09 2017Let $G$ be a graph with $n$ vertices, and let $A(G)$ and $D(G)$ denote respectively the adjacency matrix and the degree matrix of $G$. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The $A_{\alpha}$-characteristic ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016Nov 10 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Formula of Volume of Revolution with Integration by Parts and ExtensionSep 04 2016A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly monotone and differential ... More

A class of cyclic codes whose dual have five zerosFeb 07 2015In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

An Online Approach to Dynamic Channel Access and Transmission SchedulingApr 04 2015Making judicious channel access and transmission scheduling decisions is essential for improving performance as well as energy and spectral efficiency in multichannel wireless systems. This problem has been a subject of extensive study in the past decade, ... More

To Stay Or To Switch: Multiuser Dynamic Channel AccessSep 14 2013In this paper we study opportunistic spectrum access (OSA) policies in a multiuser multichannel random access cognitive radio network, where users perform channel probing and switching in order to obtain better channel condition or higher instantaneous ... More

On a Qualitative Difference between the Dynamics of Particle Production in Soft and Hard Processes of High Energy CollisionsDec 10 1998The qualitative difference between the anomalous scaling properties of hadronic final states in soft and hard processes of high energy collisions is studied in some detail. It is pointed out that the experimental data of e^+e^- collisions at $E_{cm}=$91.2 ... More

Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systemsMar 24 2005Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper, we study the persistence and tangent frequencies preservation of lower ... More

Uniqueness in inverse elastic scattering with one incident waveAug 03 2016Aug 07 2016In this paper, we solve a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far field pattern by an incoming plane ... More

A Ranking Algorithm for Re-findingFeb 16 2016Feb 18 2016Re-finding files from a personal computer is a frequent demand to users. When encountered a difficult re-finding task, people may not recall the attributes used by conventional re-finding methods, such as a file's path, file name, keywords etc., the re-finding ... More

On Stability of Nodal $L_k^p$-Maps ISep 24 2015We give a general definition of weakly stable nodal $L_k^p$-maps as a natural generalization of the stability for $J$-holomorphic nodal maps in GW theory. A complete characterization of the weakly stable nodal $L_k^p$-maps are given in term of their isotropy ... More

The first moment of central values of symmetric square $L$-functions in the weight aspectOct 24 2016In this note we investigate the behavior at the central point of the symmetric square $L$-functions, the most frequently used $\rm{GL}(3)$ $L$-functions. We establish an asymptotic formula with arbitrary power saving for the first moment of $L(\frac{1}{2},{\rm{sym}}^2f)$ ... More

On the Phase Space Partition in High Energy CollisionsMar 30 2002In high energy hadron-hadron and e+e- collisions, to isolate a part of the phase space in multi-hadron final states is necessary for exploring the underlying dynamics. It is shown that the partition of phase space according to the value of rapidity, popularly ... More

Estimate the Ranges of rho and eta only from the Kobayashi-Maskawa Matrix Elements of the First Two GenerationsSep 02 1998Based on the relation between weak CP phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, the ranges of rho and eta have been estimated by using the best known two KM matrix elements Vud and Vcd (or Vus). ... More

Solutions to the Problem of K-SAT / K-COL Phase Transition LocationJan 19 2016As general theories, currently there are concentration inequalities (of random walk) only for the cases of independence and martingale differences. In this paper, the concentration inequalities are extended to more general situations. In terms of the ... More

A Class of Noncommutative SpectraApr 20 2011We construct a class of noncommutative spectra and give the basic properties of the class of noncommutative spectra.

Sheaf Structures On a Class of Noncommutative SpectraFeb 14 2012We introduce a class of noncommutative spectra and give the sheaf structure on the class of noncommutative spectra.

Some Results about Triangular Representations of Lie AlgebrasJun 21 2014We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.

Generalized Cohn's TheoremDec 02 2007We introduce the notion of a free associative $\mathcal{Z}_2$-algebra on the union of two disjoint sets and prove a generalization of Cohn's Theorem on Jordan algebras.

Modular Invariance and Characteristic NumbersApr 08 1994We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we have shown ... More

Restriction des séries discrètes de SU(2,1) à un sous-groupe exponentiel maximal et à un sous-groupe de BorelAug 05 2012We give an explicit description of the restriction of discrete series representations of SU(2,1) to a Borel subgroup and to a maximal exponential solvable subgroup and we interpret our results in the framework of orbit method, Hamiltonian geometry and ... More

Approximate Acoustic Cloaking in Inhomogeneous Isotropic SpaceOct 27 2010Apr 30 2012In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve ... More

Hidden symmetries for thermodynamics and emergence of relativityFeb 02 2010Apr 16 2010Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment ... More

Fermionic formula for double Kostka polynomialsFeb 29 2016The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\Bla,\Bmu}(t),$ ... More

Functoriality of equivariant eta formsMay 17 2015May 03 2016In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta forms with respect to the composition of two submersions.

Relics Theory of Dark Matter in quantum evaporating Black HoleDec 29 2008We introduce first a new road to quantize the Schwarzschild black hole. Then we find that the ground state or relic of the quantum evaporating black hole can be identified as dark matter.

On the Gravitational Wave in de Sitter SpacetimeNov 25 2004For there is always a wrong sign in the mass of graviton in the so-called perturbation expansion approximation of both Minkowski and de Sitter spacetimes, the existence of gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. ... More

On instability and mixing on the UK Continental ShelfDec 22 2015The stability of stratified flows at locations in the Clyde, Irish and Celtic Seas on the UK Continental Shelf is examined. Flows are averaged over periods of 12-30 min in each hour, corresponding to the times taken to obtain reliable estimates of the ... More

Graphical Exponential ScreeningMar 09 2015Jul 03 2016In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different ... More

A Monte Carlo Study of Erraticity Behavior in Nucleus-Nucleus Collisions at High EnergiesOct 10 2001It is demonstrated using Monte Carlo simulation that in different nucleus$-$nucleus collision samples, the increase of the fluctuation of event factorial moments with decreasing phase space scale, called erraticity, is still dominated by the statistical ... More

Hawking Radiation as Tunnelling in Static Black HolesDec 16 2005Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. The conservation of energy implies the effect of self-gravitation. For a static black hole, a generalized Painleve coordinate system ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 27 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. That is, we show that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, known ... More

Researches on Dynamic Load Balancing Algorithms and hp-Adaptivity in 3-D Parallel Adaptive Finite Element ComputationsNov 24 2016This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The main results ... More

A note on discrete monotonic dynamical systemsJul 29 2004Aug 10 2004We give a upper bound of Lebesgue measure $V(S(f,h,\Omega))$ of the set $S(f,h,\Omega)$ of points $q\in Q_h^d$ for which the triple $(h,q,\Omega)$ is dynamically robust when $f$ is monotonic and satisfies certain condition on some compact subset $\Omega ... More

The Poincaré inequality and quadratic transportation-variance inequalitiesFeb 12 2019It is known that the Poincar\'e inequality is equivalent to the quadratic transportation-variance inequality (namely $W_2^2(f\mu,\mu) \leqslant C_V \mathrm{Var}_\mu(f)$), see Ledoux \cite{Ledoux18} most recently. We give an alternative proof to this fact. ... More

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifoldsNov 27 2016We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative ... More

Kernelized Deep Convolutional Neural Network for Describing Complex ImagesSep 15 2015With the impressive capability to capture visual content, deep convolutional neural networks (CNN) have demon- strated promising performance in various vision-based ap- plications, such as classification, recognition, and objec- t detection. However, ... More

Height fluctuations of stationary TASEP on a ring in relaxation time scaleOct 14 2016We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional to the $3/2$ power of the ring size. We obtain the limit ... More

On the Algebraic Representation of One-Tape Deterministic Turing MachineJul 13 2016An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to model the ... More

Quantile tests in frequency domain for sinusoid modelsMay 11 2016For second order stationary processes, the spectral distribution function is uniquely deter- mined by the autocovariance functions of the processes. We define the quantiles of the spectral distribution function and propose two estimators for the quantiles. ... More

On chromatic functors and stable partitions of graphsMar 28 2016Jul 17 2016The chromatic functor of a simple graph is a functorization of the chromatic polynomial. M. Yoshinaga showed in \cite{Yoshinaga2015} that two finite graphs have isomorphic chromatic functors if and only if they have the same chromatic polynomial. The ... More

Strong solutions to the Cauchy problem of the two-dimensional compressible Navier-Stokes-Smoluchowski equations with vacuumAug 29 2016This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D local well-posedness ... More

A new characterization of quadratic transportation-information inequalitiesJun 08 2015Jun 07 2016It is known that a quadratic transportation-information inequality $\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). The aim of the present paper is threefold: (1) To prove ... More

Some remarks on log surfacesDec 02 2016Dec 16 2016Fujino and Tanaka established the minimal model theory for $\mathbb Q$-factorial log surfaces in characteristic $0$ and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal model program ... More

Harnessing Low-Fidelity Data to Accelerate Bayesian Optimization via Posterior RegularizationFeb 11 2019Feb 14 2019Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive if the maximum number of allowed function ... More

On radii of spheres determined by subsets of Euclidean spaceApr 19 2013In this paper we consider the problem of how large the Hausdorff dimension of $E\subset\R^d$ needs to be in order to ensure that the radii set of $(d-1)$-dimensional spheres determined by $E$ has positive Lebesgue measure. We also study the question of ... More

Well-posedness of strong solutions to the anelastic equations for viscous flowsMar 04 2019We address the local and global well-posedness issues of strong solutions to the anelastic equations for viscous flows. The density profile is taken to satisfy physical vacuum singularity, and the interaction of the density profile with the velocity fields ... More

Various Theorems on TournamentsJul 01 2012In this thesis we prove a variety of theorems on tournaments. A \emph{prime} tournament is a tournament $G$ such that there is no $X \subseteq V(G)$, $1 < |X| < |V(G)|$, such that for every vertex $v \in V(G) \minus X$, either $v \ra x$ for all $x \in ... More

A note on lattice-face polytopes and their Ehrhart polynomialsOct 26 2008We give a new definition of lattice-face polytopes by removing an unnecessary restriction in the paper "Ehrhart polynomials of lattice-face polytopes", and show that with the new definition, the Ehrhart polynomial of a lattice-face polytope still has ... More

A combinatorial analysis of Severi degreesApr 04 2013Jan 06 2014Based on results by Brugall\'e and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees $N^{d, \delta}$ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a special function ... More

Tangent-like Spaces to Local MonoidsJul 26 2005The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.

A Jorgensen-Thurston theorem for homomorphismsSep 29 2011Dec 27 2011In this note, we provide a description of the structure of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jorgensen-Thurston Theorem in ... More

On invariant subspaces for the shift operator on Bergman spaces and Hardy spacesJun 09 2018It is well known that the structure of nontrival invariant subspaces for the shift operator on the Bergman space is extremely complicated and very little is known about their specific structures. In this paper, we give a explicit description of the specific ... More

Mixture Modeling based Probabilistic Situation AwarenessSep 28 2015Oct 07 2015The problem of situational awareness (SAW) is investigated from the probabilistic modeling point of view. Taking the situation as a hidden variable, we introduce a hidden Markov model (HMM) and an extended state space model (ESSM) to mathematically express ... More

Hook length polynomials for plane forests of a certain typeNov 02 2005The original motivation for study for hook length polynomials was to find a combinatorial proof for a hook length formula for binary trees given by Postnikov, as well as a proof for a hook length polynomial formula conjectured by Lascoux. In this paper, ... More

The random case of Conley's theoremMar 26 2005Dec 09 2005The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where $\mathcal{CR}(\phi)$ denotes ... More

Weight decomposition of de Rham cohomology sheaves and tropical cycle classes for non-Archimedean spacesJan 31 2017We construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over non-Archimedean fields embeddable into $\mathbf{C}_p$, which generalizes a construction of Berkovich and solves a question ... More

Tail approximations of integrals of Gaussian random fieldsJun 14 2010May 28 2012This paper develops asymptotic approximations of $P(\int_Te^{f(t)}\,dt>b)$ as $b\rightarrow\infty$ for a homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of an exponent of a Gaussian ... More

Hirzebruch-Zagier cycles and twisted triple product Selmer groupsNov 25 2015Let $E$ be an elliptic curve over $\mathbb{Q}$ and $A$ be another elliptic curve over a real quadratic number field. We construct a $\mathbb{Q}$-motive of rank $8$, together with a distinguished class in the associated Bloch-Kato Selmer group, using Hirzebruch-Zagier ... More

An optimal dimension-free upper bound for eigenvalue ratiosMay 09 2014Dec 22 2014On a closed weighted Riemannian manifold with nonnegative Bakry-\'{E}mery Ricci curvature, it is shown that the ratio of the $k$-th to first eigenvalues of the weighted Laplacian is dominated by $641k^2$, using an argument via the Cheeger constant. While ... More

Virtual cubulation of nonpositively curved graph manifoldsOct 10 2011Feb 07 2013In this paper, we show that a nontrivial compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right-angled Artin group. As a consequence, nonpositively curved graph manifolds have linear fundamental ... More

On noncommutative distributional symmetries and de Finetti type theorems associated with themNov 18 2015We prove general de Finetti theorems for classical, free and boolean independence. Our general de Finetti theorems work for non-easy quantum groups, which generalizes a recent work of Banica, Curran and Speicher. For infinite sequences, we will determine ... More

Ultra-directional super-scattering of homogenous spherical particles with radial anisotropyMay 20 2015We study the light scattering of homogenous radially-anisotropic spherical particles. It is shown that radial anisotropy can be employed to tune effectively the electric resonances, and thus enable flexible overlapping of electric and magnetic dipoles ... More

The asymptotical behaviour of embedded eigenvalues for perturbed periodic operatorsSep 12 2018Let $H_0$ be a periodic operator on $\R^+$(or periodic Jacobi operator on $\N$). It is known that the absolutely continuous spectrum of $H_0$ is consisted of spectral bands $\cup[\alpha_l,\beta_l]$. Under the assumption that $\limsup_{x\to \infty} x|V(x)|<\infty$ ... More

Free-Boolean independence for pairs of algebrasOct 03 2017Nov 23 2017We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce free-Boolean cumulants ... More

A noncommutative De Finetti theorem for boolean independenceMar 07 2014Oct 27 2014We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for the joint distribution of sequences of selfadjoint noncommutative random ... More

New integral inequalities via $(α,m)$-convexity and quasi-convexityJan 25 2012In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.

The random case of Conley's theorem: III. Random semiflow case and Morse decompositionOct 30 2007In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems. In the second ... More

Stability of tangent bundles of complete intersections and effective restrictionNov 09 2017Oct 22 2018For $n\geq 3$, let $M$ be an $(n+r)$-dimensional irreducible Hermitian symmetric space of compact type and let $\mathcal{O}_M(1)$ be the ample generator of $Pic(M)$. Let $Y=H_1\cap\dots\cap H_r$ be a smooth complete intersection of dimension $n$ where ... More

Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisorsNov 17 2016Oct 11 2017Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^n$. As an application, we derive the classification of projective manifolds containing a $\mathbb{P}^r$-bundle ... More

Degree of $L^2$-Alexander torsion for 3-manifoldsSep 29 2015Nov 23 2015For an irreducible orientable compact $3$-manifold $N$ with empty or incompressible toral boundary, the full $L^2$--Alexander torsion $\tau^{(2)}(N,\phi)(t)$ associated to any real first cohomology class $\phi$ of $N$ is represented by a function of a ... More

Stable reduction of finite covers of curvesDec 03 2004Jan 05 2005Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended to a finite ... More

T-bulge single photon quantum router with three level systemFeb 26 2017This paper considers the transmission characteristics of incidenting from an infinte coupled-resonator waveguide (CRW) or a semi-infinite CRW, respectively. The Nth cavity of a semi-infinite CRW intersecting with an infinite CRW and a cascade three level ... More

Locally analytic vectors of some crystabelian representations of GL_2(Qp)Oct 04 2009Jan 11 2011For V a 2-dimensional p-adic representation of G_Qp, we denote by B(V) the admissible unitary representation of GL_2(Qp) attached to V under the p-adic local Langlands correspondence of GL_2(Qp) initiated by Breuil. In this article, building on the works ... More

Quantum Secret Sharing by applying Analytic GeometryApr 27 2010In this paper, we investigate a novel $(2,2)$-threshold scheme and then generalize this to a $(n,n)$-threshold scheme for quantum secret sharing (QSS) which makes use of the fundamentals of Analytic Geometry. The dealer aptly selects GHZ states related ... More

Counterexamples to a conjecture of Balasubramanian and ParthasarathyFeb 06 2015In 1980, Balasubramanian and Parthasarathy introduced the bivariate permanent polynomials of graphs and conjectured that this graph polynomial is a graph characterising polynomial, that is, any two graphs with the same bivariate permanent polynomial are ... More

A companion of Ostrowski like inequality for mappings whose second derivatives belong to $L^{\infty}$ spaces and applicationsFeb 05 2012Feb 11 2012A companion of Ostrowski like inequality for mappings whose second derivatives belong to $L^{\infty}$ spaces is established. Applications to composite quadrature rules, and to probability density functions are also given.

Operator perturbation theory in the backward Heisenberg pictureApr 23 2012We present a simple operator perturbation theory in the backward Heisenberg picture. Compared with the well-known Heisenberg picture, the revised picture is based on the backward time instead of the forward time. The unique feature of the uncommon picture ... More

Elastic Waves Scattering without Conversion in Metamaterials with Simultaneous Zero Indices for Longitudinal and Transverse wavesMar 08 2015Sep 28 2015We theoretically investigate elastic waves propagating in metamaterials with simultaneous zero indices for both the longitudinal and transverse waves. With scattering objects (here cylinders) present in the metamaterials slabs, while the elastic waves ... More

Twisted exponential sums of polynomials in one variableDec 10 2009The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function ... More

Exploiting Unlabeled Data for Neural Grammatical Error DetectionNov 28 2016Nov 29 2016Identifying and correcting grammatical errors in the text written by non-native writers has received increasing attention in recent years. Although a number of annotated corpora have been established to facilitate data-driven grammatical error detection ... More

The multiplier and cohomology of Lie superalgebrasNov 01 2018In this paper, all (super)algebras are over a field $\mathbb{F}$ of characteristic different from $2, 3$. We construct the so-called 5-sequences of cohomology for central extensions of a Lie superalgebra and prove that they are exact. Then we prove that ... More