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Canonical Basis for Type $A_4$ (II)-Polynomial Elements in One VariableSep 18 2003All the 62 monomial elements in the canonical basis B of the quantized enveloping algebra for type $A_4$ have been determined in [2]. According to Lusztig's idea [7], the elements in the canonical basis B consist of monomials and linear combinations of ... More

Towards a Fatality-Aware Benchmark of Probabilistic Reaction Prediction in Highly Interactive Driving ScenariosSep 10 2018Autonomous vehicles should be able to generate accurate probabilistic predictions for uncertain behavior of other road users. Moreover, reactive predictions are necessary in highly interactive driving scenarios to answer "what if I take this action in ... More

Distributed Bandit Learning: Near-Optimal Regret with Efficient CommunicationApr 12 2019May 29 2019We study the problem of regret minimization for distributed bandits learning, in which $M$ agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal ... More

Distributed Bandit Learning: How Much Communication is Needed to Achieve (Near) Optimal RegretApr 12 2019We study the communication complexity of distributed multi-armed bandits (MAB) and distributed linear bandits for regret minimization. We propose communication protocols that achieve near-optimal regret bounds and result in optimal speed-up under mild ... More

A Question Answering Approach to Emotion Cause ExtractionAug 18 2017Sep 24 2017Emotion cause extraction aims to identify the reasons behind a certain emotion expressed in text. It is a much more difficult task compared to emotion classification. Inspired by recent advances in using deep memory networks for question answering (QA), ... More

Precise Condition Synthesis for Program RepairAug 28 2016Oct 10 2016A well-known problem of automatic defect repair is overfitting: the system tends to overfit to the test suite and has a low precision. In this paper we aim to produce precise patches, that is, any patch we produce has a relatively high probability to ... More

A Relativistic Disc Reflection Model for 1H0419-577: Multi-Epoch Spectral Analysis with XMM-Newton and NuSTARNov 27 2018We present a detailed analysis of the spectral properties of the Seyfert 1 galaxy 1H0419-577, based on the archival XMM-Newton, NuSTAR and simultaneous Swift observations taken between 2002-2015. All the observations show a broad emission line feature ... More

Factorials of infinite cardinals in ZFOct 14 2018For a set $x$, let $\mathcal{S}(x)$ be the set of all permutations of $x$. We study several aspects of this notion in $\mathsf{ZF}$. The main results are as follows: (1) $\mathsf{ZF}$ proves that for all sets $x$, if $\mathcal{S}(x)$ is Dedekind infinite, ... More

A New Multiplicity Formula for the Weyl Modules of Type ASep 18 2003A monomial basis and a filtration of subalgebras for the universal enveloping algebra $U(g_l)$ of a complex simple Lie algebra $g_l$ of type $A_l$ is given in this note. In particular, a new multiplicity formula for the Weyl module $V(\lambda)$ of $U(g_l)$ ... More

Some observations on Karoubian complete strongly exceptional posets on the projective homogeneous varietiesNov 13 2009Dec 23 2009Let $\cP=G/P$ be a homogeneous projective variety with $G$ a reductive group and $P$ a parabolic subgroup. In positive characteristic we exhibit for $G$ of low rank a Karoubian complete strongly exceptional poset of locally free sheaves appearing in the ... More

A study of the strong gravity region of the black hole in GS 1354-645Jul 26 2018Oct 01 2018It is thought that the spacetime metric around astrophysical black holes is well described by the Kerr solution of Einstein's gravity. However, a robust observational evidence of the Kerr nature of these objects is still lacking. Here we fit the X-ray ... More

Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$May 11 2015Dec 20 2015Majid developed in \cite{majid3} his double-bosonization theory to construct $U_q(\mathfrak g)$ and expected to generate inductively not just a line but a tree of quantum groups starting from a node. In this paper, the authors confirm the Majid's first ... More

Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$Jan 17 2016Feb 05 2016Double-bosonization construction in Majid \cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing ... More

Symplectic group and Heisenberg group in p-adic quantum mechanicsFeb 06 2015Feb 16 2015This paper treats mathematically some problems in p-adic quantum mechanics. We first deal with p-adic symplectic group corresponding to the symmetry on the classical phase space. By the filtrations of isotropic subspaces and almost self-dual lattices ... More

An Efficient Steady-State Solver for Microflows with High-Order Moment ModelAug 14 2018In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order moment model correction ... More

Fractional diffusion in Gaussian noisy environmentFeb 19 2015We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: $D_t^\alpha u(t, x)=\textit{B}u+u\cdot W^H$, where $D_t^\alpha$ is the fractional derivative of ... More

Double-bosonization and Majid's Conjecture, (IV): Type-Crossings from $A$ to $BCD$May 11 2015Dec 20 2015Both in Majid's double-bosonization theory and in Rosso's quantum shuffle theory, the rank-inductive and type-crossing construction for $U_q(\mathfrak g)$'s is still a remaining open question. In this paper, working with Majid's framework, based on our ... More

Nonlinear filtering in target tracking using cooperative mobile sensorsAug 09 2011Collaborative signal processing and sensor deployment have been among the most important research tasks in target tracking using networked sensors. In this paper, the mathematical model is formulated for single target tracking using mobile nonlinear scalar ... More

Degenerate and Stable Yang-Mills-Higgs PairsFeb 06 2015Feb 09 2015In this paper, we introduce some notions on the pair consisting of a Chern connection and a Higgs field closely related to the first and second variation of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair, degenerate Yang-Mills-Higgs ... More

Interaction-aware Multi-agent Tracking and Probabilistic Behavior Prediction via Adversarial LearningApr 04 2019In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although many research ... More

Revealing the ultra-fast outflow in IRAS 13224-3809 through spectral variabilityApr 18 2017We present an analysis of the long-term X-ray variability of the extreme narrow-line Seyfert 1 (NLS1) galaxy IRAS 13224-3809 using principal component analysis (PCA) and fractional excess variability (Fvar) spectra to identify model-independent spectral ... More

Double-bosonization and Majid's Conjecture, (II): cases of irregular $R$-matrices and type-crossings of $F_4$, $G_2$Dec 29 2015The purpose of the paper is to build up the related theory of weakly quasitriangular dual pairs suitably for non-standard $R$-matrices (irregular), and establish the generalized double-bosonization construction theorem for irregular $R$, which generalize ... More

Asymptotic properties of covariate-adaptive randomizationOct 17 2012Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics ... More

Substructuring preconditioners with novel interface solvers for general elliptic-type equations in three dimensionsNov 27 2016In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver associated with the ... More

Testing the Kerr metric with the iron line and the KRZ parametrizationJul 17 2016Sep 05 2016The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$\alpha$ lines are commonly ... More

Generic Vehicle Tracking Framework Capable of Handling Occlusions Based on Modified Mixture Particle FilterSep 20 2018Accurate and robust tracking of surrounding road participants plays an important role in autonomous driving. However, there is usually no prior knowledge of the number of tracking targets due to object emergence, object disappearance and false alarms. ... More

Conditional Generative Neural System for Probabilistic Trajectory PredictionMay 05 2019Effective understanding of the environment and accurate trajectory prediction of surrounding dynamic obstacles are critical for intelligent systems such as autonomous vehicles and wheeled mobile robotics navigating in complex scenarios to achieve safe ... More

Using iron line reverberation and spectroscopy to distinguish Kerr and non-Kerr black holesJun 22 2014Apr 21 2015The iron K$\alpha$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates is produced by the illumination of a cold accretion disk by a hot corona. In this framework, the activation of a new flaring region ... More

Fully Automatic Liver Attenuation Estimation Combing CNN Segmentation and Morphological OperationsJun 23 2019Jun 29 2019Manually tracing regions of interest (ROIs) within the liver is the de facto standard method for measuring liver attenuation on computed tomography (CT) in diagnosing nonalcoholic fatty liver disease (NAFLD). However, manual tracing is resource intensive. ... More

A study for testing the Kerr metric with AGN iron line eclipsesMar 14 2016Apr 21 2016Recently, two of us have studied iron line reverberation mapping to test black hole candidates, showing that the time information in reverberation mapping can better constrain the Kerr metric than the time-integrated approach. Motivated by this finding, ... More

Testing the Kerr Nature of Black Hole Candidates using Iron Line Spectra in the CPR FrameworkApr 08 2015Sep 05 2015The iron K$\alpha$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around ... More

Testing the Kerr black hole hypothesis: comparison between the gravitational wave and the iron line approachesMar 15 2016Jul 14 2016The recent announcement of the detection of gravitational waves by the LIGO/Virgo collaboration has opened a new window to test the nature of astrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data of GW 150914 can constrain possible ... More

Testing the Kerr nature of black hole candidates using iron line reverberation mapping in the CPR frameworkJan 05 2016Jun 09 2016The iron K$\alpha$ line commonly observed in the X-ray spectrum of black hole candidates is produced by X-ray fluorescence of the inner accretion disk. This line can potentially be quite a powerful tool to probe the spacetime geometry around these objects ... More

Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short reviewNov 24 2015Feb 23 2016The continuum-fitting and the iron line methods are leading techniques capable of probing the spacetime geometry around astrophysical black hole candidates and testing the no-hair theorem. In the present paper, we review the two approaches, from the astrophysical ... More

Lecture Notes on CMB Theory: From Nucleosynthesis to RecombinationFeb 25 2008These lecture notes comprise an informal but pedagogical introduction to the well established physics and phenomenology of the cosmic microwave background (CMB) between big bang nucleosynthesis and recombination. The dominant properties of the spectrum, ... More

The Nature versus Nurture of AnisotropiesJun 28 1994With the rapidly growing number of cosmic microwave background measurements on various scales, there is real hope that the number of acceptable models for structure formation will be limited to a very few in the near future. Yet any given model can always ... More

Covariant Linear Perturbation FormalismFeb 03 2004Lecture notes on covariant linear perturbation theory and its applications to inflation, dark energy or matter and the cosmic microwave background.

An Isocurvature Mechanism for Structure FormationSep 11 1998We examine a novel mechanism for structure formation involving initial number density fluctuations between relativistic species, one of which then undergoes a temporary downward variation in its equation of state and generates superhorizon-scale density ... More

Finite element approximations of symmetric tensors on simplicial grids in Rn: the high order caseSep 27 2014Apr 14 2015The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the ... More

Identifying the Genes of Unconventional High Temperature SuperconductorsDec 31 2015We elucidate a recently emergent framework in unifying the two families of high temperature (high $T_c$) superconductors, cuprates and iron-based superconductors. The unification suggests that the latter is simply the counterpart of the former to realize ... More

Hausdorff dimension of concentration for isentropic compressible Navier-Stokes equationsJun 22 2016The concentration phenomenon of the kinetic energy, $\rho|\mathbf{u}|^2$, associated to isentropic compressible Navier-Stokes equations, is addressed in $\mathbb{R}^n$ with $n=2,3$ and the adiabatic constant $\gamma\in[1,\frac{n}{2}]$. Except a space-time ... More

Moduli Spaces of Stable Polygons and Symplectic Structures on $\bar{M}_{0,n}$Jan 27 1997Aug 28 1998In this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, \epsilon}$ of stable polygons are constructed as complex analytic spaces. ... More

Combinatorial proof of the transcendence of $L(1,χ_s)/Π$Jun 13 2016Jun 20 2016We give a combinatorial proof of the transcendence of $L(1,\chi_s)/\Pi$, where $L(1,\chi_s)$ (resp. $\Pi$) is the analogue in characteristic $p$ of the function $L$ of Dirichlet (resp. $\pi$). This result has been proven by G. Damamme using the criteria ... More

Weighted vector-valued bounds for the singular integral operators with nonsmooth kernelsJul 19 2016Let $T$ be a singular integral operator with non-smooth kernel which were introduced by Duong and McIntosh. In this paper, we prove that for such an operator, its corresponding grand maximal operator satisfies certain weak type endpoint vector-valued ... More

Topological Orbital Angular Momentum Hall CurrentMar 07 2005Mar 11 2005We show that there is a fundamental difference between spin Hall current and orbital angular momentum Hall current in Rashba- Dresselhaus spin orbit coupling systems. The orbital angular momentum Hall current has a pure topological contribution which ... More

Spin Polarization and Dichroism Effects by Electric FieldJan 31 2005We show that electric field can induce spin polarization and dichroism effects in angle resolved photoemission spectroscopy (ARPES) in spin orbit coupling systems. The physical origin behind the effects essentially is the same as the spin Hall effect ... More

Gromov-Witten Invariants of Blow-ups Along Points and CurcesOct 13 1998In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten ... More

Itô type stochastic differential equations driven by fractional Brownian motions of Hurst parameter $H>1/2$Oct 04 2016This paper studies the existence and uniqueness of solution of It\^o type stochastic differential equation $dx(t)=b(t, x(t), \om)dt+\si(t,x(t), \om) d B(t)$, where $B(t)$ is a fractional Brownian motion of Hurst parameter $H>1/2$ and $dB(t)$ is the It\^o ... More

Local times of subdiffusive biased walks on treesDec 15 2014Consider a class of null-recurrent randomly biased walks on a super-critical Gaton-Watson tree. We obtain the scaling limits of the local times and the quenched local probability for the biased walk in the sub-diffusive case. These results are a consequence ... More

Geometry of Bäcklund Transformations I: GeneralityFeb 12 2019Using Cartan's Method of Equivalence, we prove an upper bound for the generality of generic rank-1 B\"acklund transformations relating two hyperbolic Monge-Amp\`ere systems. In some cases, we obtain classifications and new examples of B\"acklund transformations, ... More

Moment bounds for IID sequences under sublinear expectationsApr 28 2011In this paper, with the notion of independent identically distributed (IID) random variables under sublinear expectations introduced by Peng [7-9], we investigate moment bounds for IID sequences under sublinear expectations. We can obtain a moment inequality ... More

Log canonical pairs with boundaries containing ample divisorsDec 19 2017May 08 2019Let $(X,\Delta)$ be a projective log canonical pair such that $\Delta \geq A$ where $A \geq 0$ is an ample $\mathbb{R}$-divisor. We prove that either $(X,\Delta)$ has a good minimal model or a Mori fibre space. Moreover, suppose that $X$ is $\mathbb{Q}$-factorial. ... More

S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the operator levelMar 04 2019Mar 07 2019We consider the $ SL(2,Z) $ transformation of the gauge invariant operators and states in $\mathcal{N}$ $=4$ SYM theory. Duality requires the $ SU(2,2|4) $ generators with the dual coupling constants are related by a unitary transformation $ S $ up to ... More

Deep Fictitious Play for Stochastic Differential GamesMar 22 2019In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential games, for which ... More

Analyticity of Bounded Solutions of Analytic State-Dependent Delay Differential EquationsAug 27 2017We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract ordinary differential ... More

Choquet expectations and g-expectations with multi-dimensional Brownian motionOct 14 2009We prove that a g-expectation is a Choquet expectation if and only if g is independent of y and is linear in z, i.e., classical linear expectation, without the assumptions that the deterministic generator g is continuous in t and the dimension of the ... More

Neutrino Mixing and Discrete SymmetriesDec 12 2012Mar 23 2013In this paper we discuss a new way to derive neutrino mixing patterns, which originates from the idea proposed in a recent article by Hernandez and Smirnov. Its applications to various cases are discussed. We first present the complete set of possible ... More

Diagrammes canoniques et representations modulo $p$ de $\GL_2(F)$Apr 26 2009Jul 02 2010Let $p$ be a prime number and $F$ a local field with residual characteristic $p$. In this article, to an irreducible smooth representation of $GL_2(F)$ over $\bar{\mathbf{F}}_p$ with central character, we associate canonically a diagram which determines ... More

Normes invariantes et existence de filtrations admissiblesSep 19 2007Jan 20 2008Let L be a finite extension of Q_p and d a positive integer. A conjecture, due to C. Breuil and P. Schneider, says that the existence of invariant norms on certain locally algebraic representations of GL_{d+1}(L) should be equivalent to the existence ... More

Emergent elastic waves in skyrmion crystals with finite frequencies at long wavelength limitMay 10 2019A fundamental fact in solids is that the frequencies of elastic waves vanish as the wave number approaches zero\cite{6}. Here we theoretically show that this fact is overturned when studying the lattice vibration of skyrmion crystals (SkX), i.e., periodic ... More

On Suslin homology with integral coefficients in characteristic zeroFeb 03 2019Mar 06 2019We show that the Suslin homology group with integral coefficients of a scheme $X$ separated of finite type over an algebraically closed field of characteristic 0 is a direct sum of a uniquely divisible group, finite copies of $\mathbb{Q}/\mathbb{Z}$, ... More

On Asymptotic Covariances of A Few Unrotated Factor SolutionsNov 12 2018In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are extracted from ... More

Towards a specialization map modulo semi-orthogonal decompositionsOct 07 2018We propose a conjecture on the existence of a specialization map for derived categories of smooth proper varieties modulo semi-orthogonal decompositions, and verify it for K3 surfaces and abelian varieties.

Coherence non-generating channelsApr 01 2016Jul 18 2016We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence non-generating channels. ... More

The compactifications of moduli spaces of Burniat surfaces with $2\leq K^{2}\leq5$Dec 13 2013Jan 30 2014We describe compactifications of moduli spaces of Burniat surfaces with $2\leq K_{X}^{2}\leq5$ obtained by adding KSBA surfaces, i.e. slc surfaces $X$ with ample canonical class $K_{X}$.

Bicritical and tetracritical phenomena and scaling properties of the SO(5) theoryNov 11 2000Mar 25 2001By large scale Monte Carlo simulations it is shown that the stable fixed point of the SO(5) theory is either bicritical or tetracritical depending on the effective interaction between the antiferromagnetism and superconductivity orders. There are no fluctuation-induced ... More

Personalized Neural Embeddings for Collaborative Filtering with TextMar 19 2019Collaborative filtering (CF) is a core technique for recommender systems. Traditional CF approaches exploit user-item relations (e.g., clicks, likes, and views) only and hence they suffer from the data sparsity issue. Items are usually associated with ... More

Cosmic tomographies: baryon acoustic oscillations and weak lensingMay 29 2006Aug 28 2006We explore the complementarity between two tomographic probes of the universe: baryon acoustic oscillations (BAOs) and weak lensing (WL). We find that photometric measurements of BAOs alone do not provide very tight constraints on the dark energy equation ... More

Reduced norms of division algebras over complete discrete valuation fields of local-global typeFeb 18 2019Let $F$ be a complete discrete valuation field whose residue field $k$ is a global field of positive characteristic $p$. Let $D$ be a central division $F$-algebra of $p$-power degree. We prove that the subgroup of $F^*$ consisting of reduced norms of ... More

Quantum Divided Power Algebra, q-Derivatives and Some New Quantum GroupsFeb 17 2009The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is established. The quantum ... More

Characterizing Incomparability in Quantum InformationMar 28 2018Apr 30 2018The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we provide ways to ... More

The Laplacian on homogeneous spacesMay 16 2008The solution of the eigenvalue problem of the Laplacian on a general homogeneous space G/H is given. Here, G is a compact, semisimple Lie group, H is a closed subgroup of G, and the rank of H is equal to the rank of G. It is shown that the multiplicity ... More

Algebraic Cycles of a Fixed DegreeOct 16 2008In this paper, the homotopy groups of Chow variety $C_{p,d}(P^n)$ of effective $p$-cycles of degree $d$ is proved to be stable in the sense that $p$ or $n$ increases. We also obtain a negative answer to a question by Lawson and Michelsohn on homotopy ... More

An Obstacle for Higher Regularity of Geodesics in the Space of Kähler PotentialsAug 10 2018Mar 18 2019In this paper we address the following question regarding the regularity of geodesics in the space of K\"ahler potentials. Given a geodesic which is highly regular, and has smooth boundary value, can we expect that it is actually smooth? We construct ... More

The Pythagoras number and the $u$-invariant of Laurent series fields in several variablesMar 05 2013Jan 12 2015We show that every sum of squares in the three-variable Laurent series field $\mathbb{R}((x,y,z))$ is a sum of 4 squares, as was conjectured in a paper of Choi, Dai, Lam and Reznick in the 1980's. We obtain this result by proving that every sum of squares ... More

Towards Energy Harvesting Powered Sensor Networks for Cyber-Physical SystemsJun 13 2018The concept of sensor networks (WSNs) has become an important component of the recently proposed cyber-physical systems (CPSs) and Internet of Things which can connect the physical world with embedded software systems. Energy- harvesting (EH) as an enabling ... More

Local times of subdiffusive biased walks on treesDec 15 2014Jan 01 2019Consider a class of null-recurrent randomly biased walks on a super-critical Gaton-Watson tree. We obtain the rates of convergence of the local times and the quenched local probability for the biased walk in the sub-diffusive case. These results are a ... More

A model of regulatory dynamics with threshold-type state-dependent delayFeb 02 2017Dec 17 2017We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with constant or zero ... More

On the long-time behavior of a perturbed conservative system with degeneracyAug 04 2018Feb 24 2019We consider in this work a model conservative system subject to dissipation and Gaussian-type stochastic perturbations. The original conservative system possesses a continuous set of steady states, and is thus degenerate. We characterize the long-time ... More

Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristicApr 29 2018Sep 25 2018We show an analogue of Jordan's theorem for algebraic groups defined over a field $\mathbb k$ of arbitrary characteristic. As a consequence, a Jordan-type property holds for the automorphism group of any projective variety over $\mathbb k$.

Infinitely generated Lawson homology groups on some rational projective varietiesFeb 23 2006We construct rational projective 4-dimensional varieties with the property that certain Lawson homology groups tensored with Q are infinite dimensional Q-vector spaces. More generally, each pair of integers p and k, with k\geq 0, p>0, we find a projective ... More

A note on Lawson homology for smooth varieties with small Chow groupsFeb 23 2006Mar 09 2006Let X be a smooth projective variety of dimension n on which rational and homological equivalence coincide for algebraic p-cycles in the range 0\leq p\leq s. We show that the homologically trivial sector of rational Lawson homology L_pH_k(X,Q)_{hom} vanishes ... More

A modern view of the classical Herglotz-Noether theoremApr 12 2010Aug 24 2010In this paper we give a new proof, valid for all dimensions, of the classical Herglotz-Noether theorem that all rotational shear-free and expansion-free flows (rotational Born-rigid flows) in Minkowski spacetime are generated by Killing vector fields ... More

The black hole mass-bulge mass correlation: bulges versus pseudo-bulgesAug 14 2009We investigate the scaling relations between the supermassive black holes mass (M_bh) and the host bulge mass in elliptical galaxies, classical bulges, and pseudo-bulges. We use two-dimensional image analysis software BUDDA to obtain the structural parameters ... More

Chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon zero-recoil semileptonic decayMay 21 2009Sep 21 2010This paper studies the leading chiral corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon semileptonic decay form factors. We derive the coupling between heavy diquarks and weak current in the limit of heavy quark-diquark symmetry, ... More

Iron and nickel diffusion in subdwarf B starsSep 01 2011Pulsations in subdwarf B stars are attributed to radiative levitation of iron-group elements in the stellar envelope. Until now, only iron diffusion is accounted for in stellar models used for sdB seismology. However, nickel has also been suggested as ... More

Generalized Slow Roll for Non-Canonical Kinetic TermsApr 22 2011Jul 13 2011We show that the generalized slow-roll approach for calculating the power spectrum where the inflationary slow roll parameters are neither small nor slowly varying can be readily extended to models with non-canonical kinetic terms in the inflaton action. ... More

Concepts in CMB Anisotropy FormationNov 27 1995These lecture notes form a primer on the theory of cosmic microwave background (CMB) anisotropy formation. With emphasis on conceptual aspects rather than technical issues, we examine the physical foundations of anisotropy evolution in relativistic kinetic ... More

The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisorsNov 03 2016Let $(X,D)$ be a log smooth pair of dimension $n$ and $D$ a reduced effective divisor such that the log canonical divisor $K_X+D$ is pseudo-effective. Let $G$ be a connected (algebraic) subgroup of $\mathrm{Aut}(X,D)$. Then $G$ is a semi-abelian variety ... More

High Order Regularity Obstacle of Geodesics in Space of Kähler PotentialsAug 10 2018In this paper we address following questions regarding regularity of geodesics in space of K\"ahler potentials. First, is the regularity of a geodesic stable under smooth boundary value perturbation? Second, can we expect that any sufficiently regular ... More

General laws of large numbers under sublinear expectationsApr 28 2011Feb 09 2012In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers for capacities ... More

Log canonical pairs with boundaries containing ample divisorsDec 19 2017May 13 2019Let $(X,\Delta)$ be a projective log canonical pair such that $\Delta \geq A$ where $A \geq 0$ is an ample $\mathbb{R}$-divisor. We prove that either $(X,\Delta)$ has a good minimal model or a Mori fibre space. Moreover, if $X$ is $\mathbb{Q}$-factorial, ... More

Least Squares Problems in OrthornormalizationOct 28 2012For any $n$-tuple $(\alpha_1,...,\alpha_n)$ of linearly independent vectors in Hilbert space $H$, we construct a unique orthonormal basis $(\epsilon_1,...,\epsilon_n)$ of $span\{\alpha_1,...,\alpha_n\}$ satisfying: $$\sum_{i=1}^n\|\epsilon_i-\alpha_i\|^2\le\sum_{i=1}^n\|\beta_i-\alpha_i\|^2$$ ... More

Relations of the Nuclear Norms of a Tensor and its Matrix FlatteningsDec 08 2014For a $3$-tensor of dimensions $I_1\times I_2\times I_3$, we show that the nuclear norm of its every matrix flattening is a lower bound of the tensor nuclear norm, and which in turn is upper bounded by $\sqrt{\min\{I_i : i\neq j\}}$ times the nuclear ... More

Is China Entering WTO or shijie maoyi zuzhi--a Corpus Study of English Acronyms in Chinese NewspapersNov 18 2017This is one of the first studies that quantitatively examine the usage of English acronyms (e.g. WTO) in Chinese texts. Using newspaper corpora, I try to answer 1) for all instances of a concept that has an English acronym (e.g. World Trade Organization), ... More

The Independence under Sublinear ExpectationsJul 02 2011We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.

Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine EquationsJul 17 2014Nov 18 2014In this paper, we study residual symmetries in the lepton sector. Our first concern is the symmetry of the charged lepton mass matrix in the basis where the Majorana neutrino mass matrix is diagonal, which is strongly constrained by the requirement that ... More

Trimaximal-Cabibbo neutrino mixing: A parametrization in terms of deviations from tri-bimaximal mixingDec 17 2012Mar 19 2013In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe subleading ... More

Weighted vector-valued bounds for the singular integral operators with nonsmooth kernelsJul 19 2016Nov 20 2016Let $T$ be a singular integral operator with non-smooth kernel which were introduced by Duong and McIntosh. In this paper, we prove that this operator and its corresponding grand maximal operator satisfies certain weak type endpoint vector-valued estimate ... More

Weighted complete continuity for the commutator of Marcinkiewicz integralJan 04 2018Let $\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\mathcal{M}_{\Omega}$ be the higher-dimensional Marcinkiewicz integral associated with $\Omega$. In this paper, the author considers the complete ... More