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Different Non-extensive Models for heavy-ion collisionsJan 11 2017The transverse momentum ($p_T$) spectra from heavy-ion collisions at intermediate momenta are described by non-extensive statistical models. Assuming a fixed relative variance of the temperature fluctuating event by event or alternatively a fixed mean ... More

Hadronization within Non-Extensive Approach and the Evolution of the ParametersMay 14 2019We review transverse momentum distributions of various identified charged particles stemming from high energy collisions fitted by various non-extensive distributions as well as by the usual Boltzmann-Gibbs statistics. We investigate the best-fit formula ... More

Hadron Spectra Parameters within the Non-Extensive ApproachMay 21 2019We investigate how the non-extensive approach works in high-energy physics. Transverse momentum ($p_T$) spectra of several hadrons are fitted by various non-extensive momentum distributions and by the Boltzmann--Gibbs statistics.~It is shown that some ... More

Mass hierarchy and energy scaling of the Tsallis--Pareto parameters in hadron productions at RHIC and LHC energiesOct 25 2017The latest, high-accuracy identified hadron spectra measurements in high-energy nuclear collisions led us to the investigation of the strongly interacting particles and collective effects in small systems. Since microscopical processes result in a statistical ... More

Bayesian Mode RegressionAug 02 2012Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all elements in a ... More

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum StateDec 04 2017Sep 30 2018In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the ... More

Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical ProbabilitiesFeb 12 2019In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate--the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate ... More

Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical EquivalenceJan 23 2019What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition ... More

The Intrinsic Structure of Quantum MechanicsOct 13 2018The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable ... More

Realism about the Wave FunctionOct 13 2018A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, ... More

A new Bayesian regression model for counts in medicineJan 12 2016Discrete data are collected in many application areas and are often characterised by highly skewed and power-lawlike distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure ... More

A Simple and Adaptive Dispersion Regression Model for Count DataNov 02 2015Aug 01 2018Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically ... More

Discrete Weibull generalised additive model: an application to count fertility dataJan 24 2018Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependencies. This challenge was previously met with the use of non-parametric jittering approaches. This paper ... More

Generic Image Classification Approaches Excel on Face RecognitionSep 22 2013Sep 30 2013The main finding of this work is that the standard image classification pipeline, which consists of dictionary learning, feature encoding, spatial pyramid pooling and linear classification, outperforms all state-of-the-art face recognition methods on ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Apr 01 2017The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Regularity of transition fronts in nonlocal dispersal evolution equationsApr 10 2015Nov 12 2015It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Jan 07 2016The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous mediaJul 14 2015Nov 19 2015The present paper is devoted to the study of transition fronts of nonlocal Fisher-KPP equations in time heterogeneous media. We first construct transition fronts with prescribed interface location functions, which are natural generalizations of front ... More

Stability, Uniqueness and Recurrence of Generalized Traveling Waves in Time Heterogeneous Media of Ignition TypeAug 17 2014Apr 21 2015The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of the present ... More

Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityJan 09 2015The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It ... More

A Simple and Adaptive Dispersion Regression Model for Count DataNov 02 2015Jul 12 2016Regression for count data is widely performed by models such as Poisson, negative Binomial and zero-inflated regression models. A challenge often faced by practitioners is the selection of the right model to take into account dispersion and excessive ... More

Face Image Classification by Pooling Raw FeaturesJun 26 2014Sep 17 2014We propose a very simple, efficient yet surprisingly effective feature extraction method for face recognition (about 20 lines of Matlab code), which is mainly inspired by spatial pyramid pooling in generic image classification. We show that features formed ... More

Face Identification with Second-Order PoolingJun 26 2014Sep 17 2014Automatic face recognition has received significant performance improvement by developing specialised facial image representations. On the other hand, generic object recognition has rarely been applied to the face recognition. Spatial pyramid pooling ... More

Response function of strongly interacting Fermi gas in a virial expansionAug 11 2012Feb 21 2013The dynamic response functions of strongly interacting fermion gas in homogeneous space are investigated in a virial expansion to second order. The density response function exhibits transition from atomic to molecular response, as the interaction strength ... More

$C^{2,α}$-estimate for conical Kähler-Ricci flowDec 08 2014We establish a parabolic version of Tian's $C^{2,\alpha}$-estimate for conical complex Monge-Ampere equations, which includes conical K\"ahler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical K\"ahler-Ricci ... More

Parametrizing an integer linear program by an integerOct 05 2015Nov 01 2015We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the $\ell^{\text{th}}$ largest value ... More

Revealing the missing heritability via cross-validated genome-wide association studiesJul 30 2013Aug 07 2013Presented here is a simple method for cross-validated genome-wide association studies (cvGWAS). Focusing on phenotype prediction, the method is able to reveal a significant amount of missing heritability by properly selecting a small number of loci with ... More

Pentaquark Search and Other Multiquark Candidates at BESOct 29 2004Results are presented on $\psi(2S)$ and $J/\psi$ hadronic decays to $K^0_SpK^-\bar n$ and $K^0_S\bar p K^+n$ final states from data samples of 14 million $\psi(2S)$ and 58 million $J/\psi$ events accumulated at the BES II detector. No $\Theta(1540)$ signal, ... More

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependenceSep 14 2016This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or ... More

Resolvent Estimates in L^p for the Stokes Operator in Lipschitz DomainsFeb 16 2012Feb 21 2012We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain ... More

A relationship between the Dirichlet and Regularity Problems for elliptic equationsJul 10 2006We study the relationship between the solvability of the $L^p$ Dirichlet problem $(D)_p$ and that of the $L^q$ regularity problem $(R)_q$ for second order elliptic equations with bounded measurable coefficients. It is known that the solvability of $(R)_p$ ... More

Tamely ramified geometric Langlands correspondence in positive characteristicOct 30 2018We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with marked points, ... More

The Rigidity and Gap Theorem for Liouville's EquationMar 12 2018In this paper, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral ... More

Global Riemann Solvers for Several $3\times3$ Systems of Conservation Laws with DegeneraciesSep 22 2017We study several $3\times 3$ systems of conservation laws, arising in modeling of two phase flow with rough porous media and traffic flow with rough road condition. These systems share several features. The systems are of mixed type, with various degeneracies. ... More

Smoothing conic Kähler metrics with uniformly upper bisectional curvature boundOct 31 2015Nov 16 2015Based on C. Li and Y. Rubinstein's upper bisectional curvature bound estimate for the conic K\"ahler metric, we can construct a smoothing sequence for the conic metric with uniformly upper bisectional curvature bound. For the conic metric along a simple ... More

End-to-end Training for Whole Image Breast Cancer Diagnosis using An All Convolutional DesignNov 15 2017We develop an end-to-end training algorithm for whole-image breast cancer diagnosis based on mammograms. It requires lesion annotations only at the first stage of training. After that, a whole image classifier can be trained using only image level labels. ... More

J-regular rings with injectivitiesApr 05 2010A ring $R$ is called a J-regular ring if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. It is proved that if R is J-regular, then (i) R is right n-injective if and only if every homomorphism from an $n$-generated small right ideal ... More

Sample-based Population ObserversNov 29 2017In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is established. The results ... More

Acyclic edge coloringMar 10 2008Mar 12 2008This paper has been withdrawn by the author due to an error in the proof.

Singly Generated II_1 FactorsNov 13 2005Dec 13 2005In the paper, we study the generator problem of II$_1$ factors. By defining a new concept related to the number of generators of a von Neumann algebra, we are able to show that a large class of II$_1$ factors are singly generated, i.e., generated by two ... More

Parametrizing an integer linear program by an integerOct 05 2015Apr 26 2017We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the $\ell^{\text{th}}$ largest value ... More

Algorithmic Information Theory and Foundations of ProbabilityJun 24 2009The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

Stochastic quantization of an Abelian gauge theoryJan 14 2018We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant ... More

Analytic torsion, dynamical zeta functions, and the Fried conjectureFeb 01 2016Sep 25 2017We prove the equality of the analytic torsion and the value at zero of a Ruelle dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold. This solves a conjecture of Fried. This article ... More

On the $l$-adic cohomology of some $p$-adically uniformized Shimura varietiesNov 02 2014Nov 13 2016We determine the Galois representations inside the $l$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands-Kottwitz's description ... More

On the Lefschetz trace formula for Lubin-Tate spacesMar 12 2012Jun 19 2012We reprove the Lefschetz trace formula for Lubin-Tate spaces, based on the locally finite cell decompositions of these spaces obtained by Fargues, and Mieda's theorem of Lefschetz trace formula for certain open adic spaces (\cite{Mi1} theorem 3.13). This ... More

Cell decomposition of some unitary group Rapoport-Zink spacesMar 12 2012Apr 21 2014In this paper we study the $p$-adic analytic geometry of the basic unitary group Rapoport-Zink spaces $\M_K$ with signature $(1,n-1)$. Using the theory of Harder-Narasimhan filtration of finite flat groups developed by Fargues in \cite{F2},\cite{F3}, ... More

Astrometric Reverberation MappingAug 03 2012Spatially extended emission regions of Active Galactic Nuclei (AGN) respond to continuum variations, if such emission regions are powered by energy reprocessing of the continuum. The response from different parts of the reverberating region arrives at ... More

Supermassive Black Holes in the Hierarchical Universe: A General Framework and Observational TestsMar 26 2009Aug 05 2009(Abridged) We present a simple framework for the growth and evolution of supermassive black holes (SMBHs) in the hierarchical structure formation paradigm. In our model, black hole accretion is triggered during major mergers (mass ratio>~0.3) between ... More

Does the 2d Higgs-Yukawa Model Have a Symmetric Phase at Small Yukawa Coupling Region?Jan 20 1993We show that at arbitrary value of the scalar self coupling and small Yukawa coupling $y$ the 2d Higgs-Yukawa model with Z(2) symmetry remains in the broken phase and the model is asymptotically free: $y \to 0$ as the cut-off $\Lambda \to \infty$. This ... More

Adjunctions in Quantaloid-enriched CategoriesAug 01 2014Oct 14 2015This dissertation is devoted to a study of adjunctions concerning categories enriched over a quantaloid Q (or Q-categories for short), with the following types of adjunctions involved: (1) adjoint functors between Q-categories; (2) adjoint distributors ... More

Completeness for sparse potential scatteringSep 23 2013Jan 10 2014The current paper is devoted to the scattering theory of a class of continuum Schr\"{o}dinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and modified perturbed ... More

Energy-critical semi-linear shifted wave equation on the hyperbolic spacesAug 02 2014Nov 21 2015In this paper we consider a semi-linear, energy-critical, shifted wave equation on the hyperbolic space ${\mathbb H}^n$ with $3 \leq n \leq 5$: \[ \partial_t^2 u - (\Delta_{{\mathbb H}^n} + \rho^2) u = \zeta |u|^{4/(n-2)} u, \quad (x,t)\in {\mathbb H}^n ... More

Bounded Solutions to an Energy Subcritical Non-linear Wave Equation on R^3Aug 20 2015In this work we consider an energy subcritical semi-linear wave equation ($3 < p < 5$) \[ \partial_t^2 u - \Delta u = \phi(x) |u|^{p-1} u, \qquad (x,t) \in {\mathbb R}^3 \times {\mathbb R} \] with initial data $(u,u_t)|_{t=0} = (u_0,u_1)\in \dot{H}^{s_p} ... More

Energy Distribution of Radial Solutions to Energy Subcritical Wave Equation with an Application on Scattering TheoryAug 27 2018The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space ($3\leq p<5$) whose initial data are radial and come with a finite energy. We split the energy ... More

Lifshitz Tails for Anderson Models with Sign-Indefinite Single-Site PotentialsJun 13 2013We study the spectral minimum and Lifshitz tails for continuum random Schr\"{o}dinger operators of the form \begin{equation*} H_{\om}=-\De+V_{0}+\sum_{i\in\Z^{d}}\om_{i}u(\cdot-i), \end{equation*} where $V_{0}$ is the periodic potential, $\{\om_{i}\}_{i\in\Z^{d}}$ ... More

Hyperkahler manifolds of Jacobian typeJun 10 2012Oct 22 2013In this paper we define the notion of a hyperk\"ahler manifold (potentially) of Jacobian type. If we view hyperk\"ahler manifolds as "abelian varieties", then those of Jacobian type should be viewed as "Jacobian varieties". Under a minor assumption on ... More

Geometric Meanings of Curvatures in Finsler GeometryNov 18 2000In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this note I will briefly discuss various curvatures and their geometric meanings from the metric geometry point of view, without going into the forest of tensors. ... More

Differential projective modules over algebras with radical square zeroMar 31 2018Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite ... More

The singularity category of a Nakayama algebraApr 09 2014Let $A$ be a Nakayama algebra. We give a description of the singularity category of $A$ inside its stable module category. We prove that there is a duality between the singularity category of $A$ and the singularity category of its opposite algebra. As ... More

Stanley depth of complete intersection monomial ideals and upper-discrete partitionsMay 29 2008Dec 21 2008Let $I$ be an $m$-generated complete intersection monomial ideal in $S=K[x_1,...,x_n]$. We show that the Stanley depth of $I$ is $n-\floor{\frac{m}{2}}$. We also study the upper-discrete structure for monomial ideals and prove that if $I$ is a squarefree ... More

On the cohomology of some simple Shimura varieties with bad reductionNov 02 2014We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to arbitrary levels ... More

W-Infinity and String TheoryFeb 20 1992Feb 23 1992We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.

Rationality, universal generation and the integral Hodge conjectureFeb 23 2016We use the universal generation of 1-cycles to relate (stable) rationality to the integral Hodge conjecture. Applications are mainly given to cubic threefolds and cubic fourfolds. We show that if a generic cubic fourfold is stably rational, then a canonical ... More

Designing and Training Feedforward Neural Networks: A Smooth Optimisation PerspectiveNov 17 2016Despite the recent great success of deep neural networks in various applications, designing and training a deep neural network is still among the greatest challenges in the field. In this work, we present a smooth optimisation perspective on designing ... More

Smooth approximation of conic Kähler metric with lower Ricci curvature boundJun 02 2014We apply Tian's method in Kahler-Einstein problem to prove that a conic K\''ahler metric with lower Ricci curvature bound can be approximated by smooth K\''ahler metrics with the same lower Ricci curvature bound. Furthermore, conic singularities here ... More

A note on rings with the summand sum propertyJul 02 2011A ring $R$ is called right SSP (SIP) if the sum (intersection) of any two direct summands of $R_{R}$ is also a direct summand. Left sides can be defined similarly. The following are equivalent: (1) $R$ is right SSP. (2) $R$ is right C3 and right SIP. ... More

$C^{2,α}$-estimate for conical Kähler-Ricci flowDec 08 2014Mar 21 2018We establish a parabolic version of Tian's $C^{2,\alpha}$-estimate for conical complex Monge-Ampere equations, which includes conical K\"ahler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical K\"ahler-Ricci ... More

Understanding Exhaustive Pattern LearningApr 20 2011Pattern learning in an important problem in Natural Language Processing (NLP). Some exhaustive pattern learning (EPL) methods (Bod, 1992) were proved to be flawed (Johnson, 2002), while similar algorithms (Och and Ney, 2004) showed great advantages on ... More

The Kolakoski sequence and related conjectures about orbitsFeb 27 2017Mar 01 2017The Kolakoski sequence is the unique infinite sequence with values in $\{1, 2\}$ and first term twems $1, 2, \ldots$ which equals the sequence of run-lengths of itself, we call this $K(1, 2).$ We define $K(m, n)$ similarly for $m+n$ odd. A well-known ... More

Priority arguments and separation problemsNov 16 2018Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific priority construction, ... More

Decomposition ComplexityDec 03 2010We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.

Rest-frame Optical Properties of Luminous 1.5<z<3.5 Quasars: the Hbeta-[OIII] RegionNov 30 2015We study the rest-frame optical properties of 74 luminous (L_bol=10^46.2-48.2 erg/s), 1.5<z<3.5 broad-line quasars with near-IR (JHK) slit spectroscopy. Systemic redshifts based on the peak of the [OIII]5007 line reveal that redshift estimates from the ... More

The Mass of QuasarsFeb 11 2013I review the current status of quasar black hole (BH) mass estimations. Spectroscopic methods have been developed to estimate BH mass in broad line quasars to an accuracy of ~0.5 dex. Despite their popularity, significant issues and confusion remain regarding ... More

Fluctuation Induced First Order Phase TransitionsNov 17 1993We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum ... More

Burgeoning Data Repository Systems, Characteristics and Development Strategies: Insights of Natural Resources and Environmental ScientistsMar 05 2018Nowadays, we have the emergence and abundance of many different data repositories and archival systems for scientific data discovery, use, and analysis. With the burgeoning data sharing platforms available, this study addresses how natural resources and ... More

Data Sustainability and Reuse Pathways of Natural Resources and Environmental ScientistsMar 05 2018This paper presents a multifarious examination of natural resources and environmental scientists' adventures navigating the policy change towards open access and cultural shift in data management, sharing, and reuse. Situated in the institutional context ... More

On Estimates of Biharmonic Functions on Lipschitz and Convex DomainsOct 03 2005Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in $R^n$. For $n\ge 8$, combined with a result in \cite{S2}, these estimates lead to the solvability of ... More

Mutual Information Scaling and Expressive Power of Sequence ModelsMay 10 2019Sequence models assign probabilities to variable-length sequences such as natural language texts. The ability of sequence models to capture temporal dependence can be characterized by the temporal scaling of correlation and mutual information. In this ... More

A peak in density dependence of electron spin relaxation time in $n$-type bulk GaAs in metallic regimeApr 24 2009We demonstrate that the peak in the density dependence of electron spin relaxation time in $n$-type bulk GaAs in the metallic regime predicted by Jiang and Wu [Phys. Rev. B {\bf 79}, 125206 (2009)] has been realized experimentally in the latest work by ... More

Tamely ramified geometric Langlands correspondence in positive characteristicOct 30 2018Apr 02 2019We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with marked points, ... More

On the cohomology of some simple Shimura varieties with bad reductionNov 02 2014Nov 13 2016We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to arbitrary levels ... More

On the Hodge-Newton filtration for p-divisible groups with additional structuresMar 12 2012Feb 20 2013We prove that, for a $p$-divisible group with additional structures over a complete valuation ring of rank one $O_K$ with mixed characteristic $(0,p)$, if the Newton polygon and the Hodge polygon of its special fiber possess a non trivial contact point, ... More

Foliations and Rational Connectedness in Positive CharacteristicJun 04 2009Oct 17 2009In this paper, the technique of foliations in characteristic $p$ is used to investigate the difference between rational connectedness and separable rational connectedness in positive characteristic. The notion of being freely rationally connected is defined; ... More

The Whittaker-Shintani functions for symplectic groupsNov 15 2012In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof of a conjecture ... More

On relations among 1-cycles on cubic hypersurfacesFeb 13 2011Feb 02 2012In this paper we give two explicit relations among 1-cycles modulo rational equivalence on a smooth cubic hypersurfaces $X$. Such a relation is given in terms of a (pair of) curve(s) and its secant lines. As the first application, we reprove Paranjape's ... More

Automatic Kolmogorov complexity and normality revisitedJan 31 2017Aug 28 2017It is well known that normality (all factors of given length appear in an infinite sequence with the same frequency) can be described as incompressibility via finite automata. Still the statement and proof of this result as given by Becher and Heiber ... More

On small dual ringsAug 03 2013A ring $R$ is called right (small) dual if every (small) right ideal of $R$ is a right annihilator. Left (small) dual rings can be defined similarly. And a ring $R$ is called (small) dual if $R$ is left and right (small) dual. It is proved that $R$ is ... More

Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvatureNov 14 2003The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset ... More

Projectively Flat Finsler Metrics of Constant CurvatureSep 23 2001It is the Hilbert's Fourth Problem to characterize the (not-necessarily-reversible) distance functions on a bounded convex domain in R^n such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ... More

Two-dimensional Finsler metrics of constant curvatureSep 15 2001A Riemannian metric is of constant curvature if and only if it is locally projectively flat. There are infinitely many locally projectively flat Finsler metrics of constant curvature, that are special solutions to the Hilbert's Fourth Problem. In this ... More

Nonrationality of a generic cubic fourfoldJan 23 2016Jan 29 2016An error in Section 4 invalidates all the main results of the paper.

Optimal bounds for a Gaussian Arithmetic-Geometric type mean by quadratic and contraharmonic meansDec 12 2018In this paper, we present the best possible parameters $\alpha_i, \beta_i\ (i=1,2,3)$ and $\alpha_4,\beta_4\in(1/2,1)$ such that the double inequalities \begin{align*} \alpha_1Q(a,b)+(1-\alpha_1)C(a,b)&<AG_{Q,C}(a,b)<\beta_1Q(a,b)+(1-\beta_1)C(a,b),\\ ... More

The ternary Goldbach problem with primes in positive density setsFeb 27 2016Let $\mathcal{P}$ denote the set of all primes. $P_{1},P_{2},P_{3}$ are three subsets of $\mathcal{P}$. Let $\underline{\delta}(P_{i})$ $(i=1,2,3)$ denote the lower density of $P_{i}$ in $\mathcal{P}$, respectively. It is proved that if $\underline{\delta}(P_{1})>5/8$, ... More

On the Energy Subcritical, Non-linear Wave Equation with Radial Data for $p\in (3,5)$Aug 10 2012In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical Sobolev space is ... More

Morawetz Estimates Method for Scattering of Radial Energy Sub-critical Wave EquationAug 21 2018In this short paper we consider a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $p \in (3,5)$. We prove that if the energy of radial initial data $(u_0, u_1)$ outside ... More

The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distributionMay 07 2014We study properties of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Here the harmonic measure refers to the hitting ... More

Convergence Rates and Hölder Estimates in Almost-Periodic Homogenization of Elliptic SystemsApr 23 2014Jun 24 2015For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The ... More

The $L^p$ Dirichlet Problem for Elliptic Systems on Lipschitz DomainsNov 05 2004We develop a new approach to the $L^p$ Dirichlet problem via $L^2$ estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain $\Omega$ in $R^n$. For $n\ge ... More

Quantum Dilaton Gravity in the Light-cone GaugeSep 18 1992Recently, models of two-dimensional dilaton gravity have been shown to admit classical black-hole solutions that exhibit Hawking radiation at the semi-classical level. These classical and semi-classical analyses have been performed in conformal gauge. ... More