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Hillview: A trillion-cell spreadsheet for big dataJul 10 2019Hillview is a distributed spreadsheet for browsing very large datasets that cannot be handled by a single machine. As a spreadsheet, Hillview provides a high degree of interactivity that permits data analysts to explore information quickly along many ... More

Distribution-Free Tests of Independence with Applications to Testing More StructuresOct 15 2014We consider the problem of testing mutual independence of all entries in a d-dimensional random vector X=(X_1,...,X_d)^T based on n independent observations. For this, we consider two families of distribution-free test statistics that converge weakly ... More

High Dimensional Semiparametric Scale-Invariant Principal Component AnalysisFeb 18 2014We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate ... More

ECA: High Dimensional Elliptical Component Analysis in non-Gaussian DistributionsOct 14 2013Oct 03 2016We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical ... More

BayeSED: A General Approach to Fitting the Spectral Energy Distribution of GalaxiesAug 27 2014We present a newly developed version of BayeSED, a general Bayesian approach to the spectral energy distribution (SED) fitting of galaxies. The new BayeSED code has been systematically tested on a mock sample of galaxies. The comparison between estimated ... More

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distributionMay 29 2013Sep 28 2016Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. ... More

Decoding spectral energy distributions of dust-obscured starburst-AGNFeb 28 2012We present BayeSED, a general purpose tool for doing Bayesian analysis of SEDs by using whatever pre-existing model SED libraries or their linear combinations. The artificial neural networks (ANNs), principal component analysis (PCA) and multimodal nested ... More

On Bayes' theorem for improper mixturesDec 14 2011Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good example. However, ... More

A Comprehensive Bayesian Discrimination of the Simple Stellar Population Model, Star Formation History and Dust Attenuation Law in the Spectral Energy Distribution Modeling of GalaxiesNov 10 2018When modeling and interpreting the spectral energy distributions (SEDs) of galaxies, the simple stellar population (SSP) model, star formation history (SFH) and dust attenuation law (DAL) are three of the most important components. However, each of them ... More

On the Feasibility of Detecting Satellites of Extrasolar Planets via MicrolensingJul 17 2002Although many methods of detecting extra-solar planets have been proposed and successful implementation of some of these methods enabled a rapidly increasing number of exoplanet detections, little has been discussed about the method of detecting satellites ... More

Spectral Ratio for Positive MatricesJun 12 2019It is well known from the Perron-Frobenius theory that the spectral gap of a positive square matrix is positive. In this paper, we give a more quantitative characterization of the spectral gap. More specifically, using a complex extension of the Hilbert ... More

The effective action of D-branes in Calabi-Yau orientifold compactificationsJul 05 2005Jul 13 2005In this review article we study type IIB superstring compactifications in the presence of space-time filling D-branes while preserving N=1 supersymmetry in the effective four-dimensional theory. This amount of unbroken supersymmetry and the requirement ... More

Affine Circle Geometry over Quaternion Skew FieldsApr 14 2012We investigate the a{\pm}ne circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

Divisible Designs, Laguerre Geometry, and BeyondFeb 13 2011In these notes we aim at bringing together design theory and projective geometry over a ring. Both disciplines are well established, but the results on the interaction between them seem to be rare and scattered over the literature. Thus our main goal ... More

Building Robust Crowdsourcing Systems with Reputation-aware Decision Support TechniquesFeb 07 2015Jan 22 2016Crowdsourcing refers to the arrangement in which contributions are solicited from a large group of unrelated people. Due to this nature, crowdsourcers (or task requesters) often face uncertainty about the workers' capabilities which, in turn, affects ... More

Microlensing by free-floating brown dwarfsJan 06 2003We propose a near-infrared microlensing survey of the central 2 degree field of the Galactic Center, in an attempt to estimate the surface density and mass distribution of distant free-floating brown dwarfs in the bulge and in the disk, acting as lenses ... More

On Non-homogeneity of Takagi functionsNov 13 2016Here we study the non-homogeneity via the Assouad dimension of graphs of Takagi functions $T_{a,b}(x):[0,1]\to\mathbb{R}$ with real parameters $a,b$ such that the product $ab$ is a root of a Littlewood polynomial. Such algebraic integers can be proved ... More

Chow Rings of Fine Quiver Moduli are Tautologically PresentedJul 11 2013Jan 15 2015A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will show that defining relations between these Chern classes arise geometrically ... More

2D Detectors for Particle Physics and for Imaging ApplicationsMar 10 2005Apr 01 2005The demands on detectors for particle detection as well as for medical and astronomical X-ray imaging are continuously pushing the development of novel pixel detectors. The state of the art in pixel detector technology to date are hybrid pixel detectors ... More

What is the optimal anthropoid primate diet?Dec 04 2001Dec 05 2001Following Socrates' advice "You should learn all you can from those who know. Everyone should watch himself throughout his life, and notice what sort of meat and drink and what form of exercise suit his constitution, and he should regulate them in order ... More

Longest Life in the Best of HealthAug 31 2002Throughout history, for reasons of health, well known personalities have opted not to eat to satiety - to under-eat - with known benefits. Here, for the benefits of under-eating a very simple explanation is offered and discussed in some detail. Our distant ... More

On Non-homogeneity of Takagi functionsNov 13 2016Nov 15 2016Here we study the non-homogeneity via the Assouad dimension of graphs of Takagi functions $T_{a,b}(x):[0,1]\to\mathbb{R}$ with real parameters $a,b$ such that the product $ab$ is a root of a Littlewood polynomial. Such algebraic integers can be proved ... More

Proof of Riemann HypothesisJun 13 2007Nov 03 2016The Riemann Hypothesis is a famous hypothesis about distribution of non-trivial zeros of zeta function. The non-trivial zeros of zeta function is related to prime number theorem. Based on the prime number theorem, we introduce a functional integral that ... More

Isomorphisms of Affine Plücker SpacesOct 06 2012All isomorphisms of Pl\"ucker spaces on affine spaces with dimensions $\geq 3$ arise from collineations of the underlying affine spaces.

Strong WW Scattering Physics: A Comparative Study for the LHC, NLC and a Muon ColliderApr 02 1997We discuss the model independent parameterization for a strongly interacting electroweak sector. Phenomenological studies are made to probe such a sector for future colliders such as the LHC, $e^+e^-$ Linear collider and a muon collider.

Fracton Topological Order and HolographyJul 16 2018Oct 12 2018We propose that the fracton topological order is a class of toy models for holography. The discovery of AdS/CFT correspondence as a concrete construction of holography, and the subsequent developments including the Ryu-Takanayagi formula of entanglement ... More

On some subgroups of linear groups over $\mathbb{F}_2$ generated by elements of order $3$Jul 07 2017Let $V$ be a vector space over the field of order $2$. We investigate subgroups of the linear group $GL(V)$ which are generated by a conjugacy class $D$ of elements of order $3$ such that all $d$ in $D$ have $2$-dimensional commutator space $[V,d]$.

On the computation of harmonic maps by unconstrained algorithms based on totally geodesic embeddingsOct 17 2016In this paper, we present an algorithm for the computation of harmonic maps, and respectively, of the harmonic map heat flow between two closed Riemannian manifolds. Our approach is based on the totally geodesic embedding of the target manifold into $\mathbb{R}^N$ ... More

On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinatesJun 06 2016Feb 26 2017We give asymptotics for Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null infinity and homogeneous towards time like infinity. We use the asymptotics to show that the outgoing ... More

Pulsars as excellent probes for the magnetic structure in our Milky WayOct 26 2012In this invited talk, I first discuss the advantages and disadvantages of many probes for the magnetic fields of the Milky Way. I conclude that pulsars are the best probes for the magnetic structure in our Galaxy, because magnetic field strength and directions ... More

Proof of the Hilbert's Eighth ProblemJan 08 2007Oct 26 2008In this paper, we first prove Riemann Hypothesis and General Riemann Hypothesis. Then, we improve the result of prime number theorems for arithmetic progression. Finally, we provide a proof that Goldbach Conjecture and Twin Prime Conjecture are true. ... More

A new integrating understanding of superconductivity and superfluidityAug 06 2002An integrating theoretical scenario of superconductivity and superfluidity has been built. It reduces to the special BCS superconductivity mechanism for conventional superconductor and to a new theory for high transition temperature superconductors, which ... More

Criteria in the Selection of Target Events for Planetary Microlensing Follow-Up ObservationApr 07 2007To provide criteria in the selection of target events preferable for planetary lensing follow-up observations, we investigate the variation of the probability of detecting planetary signals depending on the observables of the lensing magnification and ... More

Secure Identification of Free-Floating PlanetsMar 02 2006Among the methods proposed to detect extrasolar planets, microlensing is the only technique that can detect free-floating planets. Free-floating planets are detected through the channel of short-duration isolated lensing events. However, if a seemingly ... More

Microlensing Zone of Planets Detectable through the Channel of High-Magnification EventsAug 22 2008A microlensing lensing zone refers to the range of planet-star separations where the probability of detecting a planetary signal is high. Its conventional definition as the range between $\sim 0.6$ and 1.6 Einstein radii of the primary lens is based on ... More

Astrometric Microlensing: A Channel to Detect Multiple Lens SystemsApr 08 2002If a source star is gravitationally microlensed by a multiple lens system, the resulting light curve can have significant deviations from the standard form of a single lens event. The chance to produce significant deviations becomes important when the ... More

On the Baseline Flux Determination of Microlensing Events Detectable with the Difference Image Analysis MethodOct 12 1999To improve photometric precision by removing blending effect, a newly developed technique of difference image analysis (DIA) is adopted by several gravitational microlensing experiment groups. However, the principal problem of the DIA method is that, ... More

Binary modules and their endomorphismsDec 10 2012Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative ring. In particular, ... More

Classification of secant defective manifolds near the extremal caseAug 22 2011May 03 2012Let $X\subset \P^N$ be a nondegenerate irreducible closed subvariety of dimension $n$ over the field of complex numbers and let $SX\subset\P^N$ be its secant variety. $X\subset\P^N$ is called `secant defective' if $\dim(SX)$ is strictly less than the ... More

Ultracompact plasmonic racetrack resonators in metal-insulator-metal waveguidesJan 22 2010Apr 09 2010Among various plasmonic waveguides, the metal-insulator-metal (MIM) type is the most promising for true subwavelength photonic integration. To date, many photonic devices based on MIM waveguides have been investigated, including resonators. However, most ... More

Applications of Cutoff Resolvent Estimates to the Wave EquationSep 05 2007Nov 19 2007We consider solutions to the linear wave equation on non-compact Riemannian manifolds without boundary when the geodesic flow admits a filamentary hyperbolic trapped set. We obtain a polynomial rate of local energy decay with exponent depending only on ... More

Rationality of Rigid Quiver GrassmanniansMar 11 2019We show that any quiver Grassmannian associated with a rigid representation of a quiver is a rational variety using torus localization techniques.

Ideals in the ring of Colombeau generalized numbersJul 04 2007In this paper, the structure of the ideals in the ring of Colombeau generalized numbers is investigated. Connections with the theories of exchange rings, Gelfand rings and lattice-ordered rings are given. Characterizations for prime, projective, pure ... More

Cosmological perturbations with inverse-volume corrections in loop quantum cosmologySep 02 2018Oct 17 2018Although the cosmological perturbations with inverse-volume corrections from loop quantum cosmology have been studied using the anomaly-free algebra approach in much of the literature, there still remains an important issue that some counterterms in the ... More

Analytical and numerical investigation of radiative heat transfer in semitransparent MediaSep 13 2017This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and uniqueness of solution ... More

$C^*-$crossed product of groupoid actions on categoriesOct 18 2007Suppose that $G$ is a groupoid acting on a small category $H$ in the sense of \cite[Definition 4]{NOT} and $H\times_\alpha G$ is the resulting semi-direct product category (as in \cite[Proposition 8]{NOT}). We show that there exists a subcategory $H_r ... More

Shnol's theorem and the spectrum of long range operatorsApr 15 2017Sep 16 2018We extend some basic results known for finite range operators to long range operators with off-diagonal decay. Namely, we prove an analogy of Sch'nol's theorem. We also establish the connection between the almost sure spectrum of long range random operators ... More

Vector boson (W,Z) Studies with CMSJul 26 2016We report on recent measurements of W and Z boson production at CMS. These include measurements of inclusive and differential W and Z boson production cross sections at $\sqrt{s}$ = 8 and 13 TeV, measurements of the angular coefficients of Z boson production, ... More

Machine Translation Evaluation Resources and Methods: A SurveyMay 15 2016Sep 19 2018We introduce the Machine Translation (MT) evaluation survey that contains both manual and automatic evaluation methods. The traditional human evaluation criteria mainly include the intelligibility, fidelity, fluency, adequacy, comprehension, and informativeness. ... More

Nonhomogeneous Wavelet Systems in High DimensionsFeb 11 2010It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal M-wavelet basis can ... More

Explicit Burgess-like subconvex bounds for $\mathrm{GL}_2 \times \mathrm{GL}_1$Dec 12 2017Dec 06 2018We make the polynomial dependence on the fixed representation $\pi$ in our previous subconvex bound of $L(1/2,\pi \otimes \chi)$ for $\mathrm{GL}_2 \times \mathrm{GL}_1$ explicit, especially with respect to the usual conductor $\mathbf{C}(\pi_{\mathrm{fin}})$. ... More

A Simple Quantifier-free Formula of Positive Semidefinite Cyclic Ternary Quartic FormsJul 30 2012Oct 17 2012Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called Criterions on Equality ... More

Semiclassical Analysis of Spinfoam Model with a Small Barbero-Immirzi ParameterApr 20 2013Jun 15 2013We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of the sum over spins in the large spin regime. The large spin parameter \lambda and small Barbero-Immirzi parameter \gamma are ... More

Microlocal analysis in generalized function algebras based on generalized points and generalized directionsOct 02 2015Jan 14 2016We develop a refined theory of microlocal analysis in the algebra ${\mathcal G}(\Omega)$ of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of $\Omega$, whereas in the theory developed ... More

A non-concentration estimate for partially rectangular billiardsMay 20 2013Sep 13 2013We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any $\epsilon_0>0$, an $\O(\lambda^{-\epsilon_0})$ quasimode must have $L^2$ mass in the "wings" bounded below by $\lambda^{-2-\delta}$ for any $\delta>0$. ... More

An integral type Brezis-Nirenberg problem on the Heisenberg groupMar 01 2018This paper is devoted to study a class of integral type Brezis-Nirenbreg problem on the Heisenberg group. It is a class of new nonlinear integral equations on the bounded domains of Heisenberg group and related to the CR Yamabe problems on the CR manifold. ... More

Equivalence between estimates for quasi-commutators and commutatorsJan 25 2017In this short note we show that under some mild conditions on the space and the operators, an estimate for $\|Sf(A) - f(B)S\|$ needs only to be studied for invertible $S$ and $B$ equal to $A$. Thus estimates for a quasi-commutator can be derived from ... More

On the Matrices of Central Linear MappingsOct 06 2012We show that a central linear mapping of a projectively embedded Euclidean $n$-space onto a projectively embedded Euclidean $m$-space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain ... More

On Kernel Mengerian Orientations of Line MultigraphsJul 22 2015Oct 07 2015We present a polyhedral description of kernels in orientations of line multigraphs. Given a digraph $D$, let $FK(D)$ denote the fractional kernel polytope defined on $D$, and let ${\sigma}(D)$ denote the linear system defining $FK(D)$. A digraph $D$ is ... More

A dynamic programming principle with continuous solutions related to the $p$-Laplacian, $1 < p < \infty$Apr 30 2015We study a Dynamic Programming Principle related to the $p$-Laplacian for $1 < p < \infty$. The main results are existence, uniqueness and continuity of solutions.

Compact embeddings of some weighted fractional Sobolev spaces on $\Rn$Mar 21 2019In this paper, we study a family of general fractional Sobolev spaces $\MsqpOm$ when $\Om=\Rn$ or $\Om$ is a bounded domain, having a compact, Lipschitz boundary $\Bdy$, in $\Rn$ for $n\geq2$. Among other results, some compact embedding results of $\MVsqpRn\hookrightarrow\LqRn$ ... More

Erdős Semi-groups, arithmetic progressions and Szemerédi's theoremFeb 12 2018Apr 23 2018In this paper we introduce and study a certain type of sub semi-group of $\mathbb{R}/\mathbb{Z}$ which turns out to be closely related to \sz's theorem on arithmetic progressions.

Discrepancies of irrational rotations, binary expansions of powers of 3 and an improvement on Furstenberg's slicing problemNov 27 2018In this paper, we study binary expansions of powers of $3$ using discrepancy estimates for irrational rotations. We show that for almost all integers $k\in\mathbb{N},$ the positions of digit $1$ in the binary expansion of $3^k$, viewed as a sequence of ... More

Log-terminal singularities and vanishing theoremsMar 15 2003Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over $\mathbb C$, in terms of purity properties of ultraproducts of characteristic $p$ Frobenii. The first application is ... More

Giuseppe Veronese and Ernst Witt -- Neighbours in PG(5,3)Oct 06 2012Let $P$ be a point of the Veronese surface $\Vcal$ in \PG53. Then thereare four conics of $\Vcal$ through $P$. We show that the internal points of those conics form a 12-cap which is a point model for Witt's 5-$(12,6,1)$ design. In fact, this construction ... More

The asymptotic behavior of solid closure in mixed characteristicSep 30 2004We study how solid closure in mixed characteristic behaves after taking ultraproducts. The ultraproduct will be chosen so that we land in equal characteristic, and therefore can make a comparison with tight closure. As a corollary we get an asymptotic ... More

Simplices over finite fieldsJun 13 2016Dec 08 2016We prove that, provided $d > k$, every sufficiently large subset of $\mathbf{F}_q^d$ contains an isometric copy of every $k$-simplex that avoids spanning a nontrivial self-orthogonal subspace. We obtain comparable results for simplices exhibiting self-orthogonal ... More

Geometry of genus 9 Fano 4-foldJan 08 2009Jan 11 2009References to the works of Iliev-Ranestad and Kuznetsov added. ----- In a first part we detail the construction, on a general Fano 4-fold of genus 9, of a canonical set of four stable vector bundles of rank 2, and prove that they are rigid. Those results ... More

Pfaffian bundles on cubic surfaces and configurations of planesOct 05 2012Apr 20 2013We give a canonical birational map between the moduli space of pfaffian vector bundles on a cubic surface and the space of complete pentahedra inscribed in the cubic surface. The universal situation is also considered, and we obtain a rationality result. ... More

Limit Theorems in Hidden Markov ModelsFeb 02 2011Apr 12 2012In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit theorems are ... More

Generalized PSK in Space Time CodingJan 14 2004A wireless communication system using multiple antennas promises reliable transmission under Rayleigh flat fading assumptions. Design criteria and practical schemes have been presented for both coherent and non-coherent communication channels. In this ... More

Random Search Algorithms for the Sparse Null Vector ProblemApr 21 2008We consider the following problem: Given a matrix A, find minimal subsets of columns of A with cardinality no larger than a given bound that are linear dependent or nearly so. This problem arises in various forms in optimization, electrical engineering, ... More

A variational model with fractional-order regularization term arising in registration of diffusion tensor imageNov 23 2016In this paper, a new variational model with fractional-order regularization term arising in registration of diffusion tensor image(DTI) is presented. Moreover, the existence of its solution is proved to ensure that there is a regular solution for this ... More

Quantum Communication and DecoherenceAug 02 2002Aug 21 2002In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It is shown that ... More

Private entanglement over arbitrary distances, even using noisy apparatusAug 10 2000Nov 16 2001We give a security proof of quantum cryptography based entirely on entanglement purification. Our proof applies to all possible attacks (individual and coherent). It implies the security of cryptographic keys distributed with the help of entanglement-based ... More

Strategy Independent Reduction Lengths in Rewriting and Binary ArithmeticApr 25 2012In this paper we give a criterion by which one can conclude that every reduction of a basic term to normal form has the same length. As a consequence, the number of steps to reach the normal form is independent of the chosen strategy. In particular this ... More

Generically trivial derived categoriesAug 10 2013Dec 02 2014We study generic objects in triangulated categories and characterize the finite dimensional algebras $A$ such that the derived categories $D(\Mod A)$ are generically trivial. This is an analogue of a result of Crawley-Boevey for module categories. As ... More

Basic aspects of high-power semiconductor laser simulationFeb 01 2013The aim of this paper is to review some of the models and solution techniques used in the simulation of high-power semiconductor lasers and to address open questions. We discuss some of the peculiarities in the description of the optical field of wide-aperture ... More

Concrete incompleteness & Bell's theoremAug 11 2014Jan 07 2015For a subset of 2 dimensional unit parameter vectors, Bell's correlation formula with local hidden variables reproduces the quantum correlation. This is unexpected considering a general no-go LHV claim derived from the same function.

Why one can maintain that there is a probability loophole in the CHSHJul 04 2015In the paper it is demonstrated that the particular form of CHSH, S=E{A(1)[B(1)-B(2)]-A(2)[B(1)+B(2)]} with, S maximally 2 and minimally -2,for A and B functions in {-1,1}, is not generally valid. The nonzero probability that local hidden extra parameters ... More

An Exponential Inequality for U-Statistics under Mixing ConditionsSep 22 2016Nov 02 2016The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the bound proves ... More

Generalized Ellipsoidal and Sphero-Conal HarmonicsOct 24 2006Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl ... More

On Cohomology Rings of Non-Commutative Hilbert Schemes and CoHa-ModulesDec 05 2013Jul 25 2016We prove that Chow groups of certain non-commutative Hilbert schemes have a basis consisting of monomials in Chern classes of the universal bundle. Furthermore, we realize the cohomology of non-commutative Hilbert schemes as a module over the Cohomological ... More

A Model of the Witt Design $W_{12}$ based on Quadrics of PG(2,3)Mar 30 2013An elementary geometric proof for the existence of Witt's 5-(12,6,1) design is given.

On generalized trigonometric functions and series of rational functionsOct 15 2016Here we introduce a way to construct generlized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$. We will show that those generalized trigonometric ... More

Burgess-like subconvexity for $GL_1$Apr 28 2016Oct 17 2016We generalize our previous method on subconvexity problem for $GL_2 \times GL_1$ with cuspidal representations to Eisenstein series, and deduce a Burgess-like subconvex bound for Hecke characters, i.e. the bound $|L(1/2,\chi)| \ll_{\mathbf{F},\epsilon} ... More

Higgs Boson And $W_L W_L$ Scattering At $e^-e^-$ CollidersFeb 01 1996We discuss the Standard-Model Higgs boson production in the channels $e^-e^-\to e^-e^- H$, $e^-\nu W^- H$, and $e^-e^- ZH We also illustrate the enhancements in the $W^-W^-$ cross section that would result from a strongly-interacting Higgs sector or from ... More

Strongly-Interacting Electroweak Sector at Future CollidersJul 29 1993If there are no light Higgs bosons found below $\cal O$(800 GeV) or so, the interactions among longitudinally-polarized vector bosons ($\wl$) will become strong at the TeV region, and new physics that is responsible for the electroweak symmetry breaking ... More

A note on Clifford parallelisms in characteristic twoApr 08 2014Oct 01 2014It is well known that a purely inseparable field extension $L/F$ with some extra property and degree $[L:F]=4$ determines a Clifford parallelism on the set of lines of the three-dimensional projective space over $F$. By extending the ground field of this ... More

An Exponential Inequality for U-Statistics under Mixing ConditionsSep 22 2016Nov 15 2016The family of U-statistics plays a fundamental role in statistics. This paper proves a novel exponential inequality for U-statistics under the time series setting. Explicit mixing conditions are given for guaranteeing fast convergence, the bound proves ... More

Supersymmetric QFT, Super Loop Spaces and Bismut-Chern CharacterNov 24 2007Jul 24 2008In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in ... More

Proof of Riemann HypothesisJun 13 2007Oct 30 2018The Riemann Hypothesis is a famous hypothesis about the distribution of non-trivial zeros of zeta function.It is well known, the prime number theorem is related to Riemann Hypothesis, which has two equivalence propositions about Riemann Hypothesis. In ... More

Quantitative Oppenheim conjecture for $S$-arithmetic quadratic forms of rank $3$ and $4$Apr 04 2019The celebrated result of Eskin, Margulis and Mozes (1998) and Dani and Margulis (1993) on quantitative Oppenheim conjecture says that for irrational quadratic forms $q$ of rank at least 5, the number of integral vectors $\mathbf v$ such that $q(\mathbf ... More

Veronese Varieties over Fields with non-zero Characteristic: A SurveyMar 31 2013In the present survey we collect some recent results on nuclei of Veronese varieties and invariant subspaces of normal rational curves. We must assume, however, that the ground field is not "too small", since otherwise a Veronese variety is like dust: ... More

The Asymptotic Expansion of Kummer Functions for Large Values of the $a$-Parameter, and Remarks on a Paper by OlverJan 10 2016May 06 2016It is shown that a known asymptotic expansion of the Kummer function $U(a,b,z)$ as $a$ tends to infinity is valid for $z$ on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver ... More

The modulus of Whittaker functionsAug 15 2016The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral representation for ... More

An application of internal objects to microlocal analysis in generalized function algebrasJan 30 2016We illustrate the use of internal objects in the nonlinear theory of generalized functions by means of an application to microlocal analysis in Colombeau algebras.

Asymptotic stability of traveling wave solutions for perturbations with algebraic decayMar 02 2001For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation of the traveling ... More

Von Staudt's theorem revisitedFeb 17 2013May 21 2013We establish a version of von Staudt's theorem on mappings which preserve harmonic quadruples for projective lines over (not necessarily commutative) rings with "sufficiently many" units, in particular 2 has to be a unit.