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Multiple Hilbert transform associated with polynomialsFeb 07 2013We study conditions determining the $L^p$ boundedness of multiple Hilbert transforms associated with polynomials.

Circular maximal functions on the Heisenberg groupJun 11 2019Aug 04 2019We prove the $L^p$ boundedness of the circular maximal function on the Heisenberg group $\mathbb{H}^1$ for $2<p\le \infty$. The proof is based on the square sum estimate associated with the $2\times 2$ cone $|(\xi_1',\xi_2')|= |(\xi_3',\xi_4')| $ of the ... More

Annulus Maximal Averages on Variable HyperplanesJun 10 2019By giving a thin width of $0<\delta\ll 1$ to both a unit circle and a unit line, we set an annulus and a tube on the Euclidean plane $\mathbb{R}^2$. Consider the maximal means $M_\delta$ over dilations of the annulus, and $N_\delta$ over rotations of ... More

Circular maximal functions on the Heisenberg groupJun 11 2019Sep 07 2019We prove the $L^p$ boundedness of the circular maximal function on the Heisenberg group $\mathbb{H}^1$ for $2<p\le \infty$. The proof is based on the square sum estimate associated with the $2\times 2$ cone $|(\xi_1',\xi_2')|= |(\xi_3',\xi_4')| $ of the ... More

Circular maximal functions on the Heisenberg groupJun 11 2019We prove the $L^p$ boundedness of the circular maximal function on the Heisenberg group $\mathbb{H}^1$ for $2<p\le \infty$. The proof is based on the square sum estimate associated with the $2\times 2$ cone $|(\xi_1',\xi_2')|= |(\xi_3',\xi_4')| $ of the ... More

Triple Hilbert transforms along polynomial surfacesJul 20 2007Jul 24 2007This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

A Deep Ranking Model for Spatio-Temporal Highlight Detection from a 360 VideoJan 31 2018We address the problem of highlight detection from a 360 degree video by summarizing it both spatially and temporally. Given a long 360 degree video, we spatially select pleasantly-looking normal field-of-view (NFOV) segments from unlimited field of views ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Geometrical Interpretation of Electromagnetism in 5-Dimensional ManifoldJul 12 2015Sep 21 2016In this paper Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Concurrence of the Blandford-Payne Process and the Bardeen-Petterson Effect: Theoretical Prediction and its Observational EvidencesAug 21 2015Although the Blandford-Payne process, the standard model for the production of AGN jet outflow, has been fully acknowledged and long-known in both the theoretical Astrophysics and observational Astronomy communities, subsequent research works to gain ... More

Spin filtering in a magnetic barrier structure: in-plane spin orientationMar 01 2014We investigate ballistic spin transport in a two dimensional electron gas system through magnetic barriers of various geometries using the transfer matrix method. While most of the previous studies have focused on the effect of magnetic barriers perpendicular ... More

On variation of gradients of deep neural networksDec 02 2018We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest nodes changes ... More

Jordan Plane and Numerical Range of Operators Involving Two ProjectionsNov 26 2018We use principal angles between two subspaces to define Jordan planes. Jordan planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given two subspaces. We apply Jordan planes to show that two pairs of of subspaces $(M,N)$ and $(M^{\perp},N^{\perp})$ ... More

On deformation spaces of nonuniform hyperbolic latticesOct 04 2013Let $\Gamma$ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of $\Gamma$ in SO(n,1). ... More

Nearest Neighbor Search-Based Bitwise Source Separation Using Discriminant Winner-Take-All HashingAug 26 2019We propose an iteration-free source separation algorithm based on Winner-Take-All (WTA) hash codes, which is a faster, yet accurate alternative to a complex machine learning model for single-channel source separation in a resource-constrained environment. ... More

Projective Normality Of Algebraic Curves And Its Application To SurfacesJan 09 2006Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\frac{3g+3}{2}<\deg L\le 2g-5$. Then $L$ is normally generated if $\deg L>\max\{2g+2-4h^1(C,L), 2g-\frac{g-1}{6}-2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve ... More

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 25 2016We define primitive stable representations of free groups into higher rank semisimple Lie groups and study their properties. Then we show that the positive representations of a compact surface with one boundary component are primitive stable.

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Nov 11 2016We define primitive stable representations of free groups into higher rank semisimple Lie groups and study their properties. Let {\Sigma} be a compact surface with one boundary component. Then we show that the holonomies of convex projective structures ... More

Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter FieldsFeb 29 2012May 09 2012The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established ... More

A Case Study: Exploiting Neural Machine Translation to Translate CUDA to OpenCLMay 18 2019The sequence-to-sequence (seq2seq) model for neural machine translation has significantly improved the accuracy of language translation. There have been new efforts to use this seq2seq model for program language translation or program comparisons. In ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019May 09 2019We proposed an end-to-end deep learning-based simultaneous localization and mapping (SLAM) system following conventional visual odometry (VO) pipelines. The proposed method completes the SLAM framework by including tracking, mapping, and sequential optimization ... More

Simplicial volume, Barycenter method, and Bounded cohomologyMar 09 2015Mar 12 2015We show that codimension one dimensional Jacobian of the barycentric straightening map is uniformly bounded for most of the higher rank symmetric spaces. As a consequence, we prove that the locally finite simplicial volume of most $\mathbb Q$-rank $1$ ... More

Complex and Quaternionic hyperbolic Kleinian groups with real trace fieldsDec 26 2014Jan 29 2015Let $\Gamma$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $\Gamma$ is contained in $\mathbb R$, $\Gamma$ preserves a totally geodesic submanifold of constant negative sectional curvature. Furthermore if ... More

Anderson localization and delocalization of massless two-dimensional Dirac electrons in random one-dimensional scalar and vector potentialsJan 12 2019We study Anderson localization of massless Dirac electrons in two dimensions in one-dimensional random scalar and vector potentials theoretically for two different cases, in which the scalar and vector potentials are either uncorrelated or correlated. ... More

Quaternionic hyperbolic Kleinian groups with commutative trace skew-fieldsOct 08 2018Let $\Gamma$ be a nonelementary discrete subgroup of $\mathrm{Sp}(n,1)$. We show that if the trace skew-field of $\Gamma$ is commutative, then $\Gamma$ stabilizes a copy of complex hyperbolic subspace of quaternionic hyperbolic $n$-space.

Constraints on Flows in Horava-Lifshitz Gravity by Classical SolutionsSep 07 2010Nov 19 2010We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in Horava-Lifshitz ... More

Bounded cohomology and negatively curved manifoldsNov 28 2011We study the bounded fundamental class in the top dimensional bounded cohomology of negatively curved manifolds with infinite volume. We prove that the bounded fundamental class of $M$ vanishes if $M$ is geometrically finite. Furthermore, when $M$ is ... More

Noncommutative Riemann ConditionsOct 11 2004In this paper we study the holomorphic bundles over a noncommutative complex torus. We define a noncommutative abelian variety as a kind of deformation of abelian variety and we show that for a restricted deformation parameter, one can define a noncommutative ... More

On the limit set of Anosov representationsDec 04 2012We study the limit set of discrete subgroups arising from Anosov representations. Specially we study the limit set of discrete groups arising from strictly convex real projective structures and Anosov representations from a finitely generated word hyperbolic ... More

Learning Not to Learn: Training Deep Neural Networks with Biased DataDec 26 2018We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to categorize ... More

Phase transition of quantum corrected Schwarzschild black holeJul 23 2012Nov 07 2012We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019Jun 04 2019Recently it was discovered that twisted superconformal index ${\mathcal{I}}$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called $\mathcal{I}$-extremization ... More

Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral mediaFeb 19 2016It has been found that in the media where the dielectric permittivity $\epsilon$ or the magnetic permeability $\mu$ is near zero and in transition metamaterials where $\epsilon$ or $\mu$ changes from positive to negative values, there occur a strong absorption ... More

Effect of disorder correlation on Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potentialJul 16 2019We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous ... More

Excitation of surface waves on the interfaces of general bi-isotropic mediaMay 20 2016Jun 30 2016We study theoretically the characteristics of surface waves excited at the interface between a metal and a general bi-isotropic medium, which includes isotropic chiral media and Tellegen media as special cases. We derive an analytical dispersion relation ... More

2D Electrophoresis Gel Image and Diagnosis of a DiseaseMay 28 2003The process of diagnosing a disease from the 2D gel electrophoresis image is a challenging problem. This is due to technical difficulties of generating reproducible images with a normalized form and the effect of negative stain. In this paper, we will ... More

A Representation of Changes of Images and its Application for Developmental BiolologyMay 13 2003In this paper, we consider a series of events observed at spaced time intervals and present a method of representation of the series. To explain an idea, by dealing with a set of gene expression data, which could be obtained from developmental biology, ... More

A Novel Statistical Diagnosis of Clinical DataSep 02 2002In this paper, we present a diagnosis method of diseases from clinical data. The data are routine test such as urine test, hematology, chemistries etc. Though those tests have been done for people who check in medical institutes, how each item of the ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019We proposed an end-to-end deep learning-based simultaneous localization and mapping (SLAM) system following conventional visual odometry (VO) pipelines. The proposed method completes the SLAM framework by including tracking, mapping, and sequential optimization ... More

Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic mediaApr 02 2016Bi-isotropic media, which include isotropic chiral media and Tellegen media as special cases, are the most general form of linear isotropic media where the electric displacement and the magnetic induction are related to both the electric field and the ... More

Comments on the symmetry of AdS$_6$ solutions in String/M-theory and Killing spinor equationsApr 27 2016Aug 22 2016It was recently pointed out in \cite{Kim:2015hya} that AdS$_6$ solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to $D=4$ internal space leads to a nonlinear sigma model with target $SL(3,\mathbb{R})/SO(2,1)$. ... More

Unavoidable Subtournaments in Tournaments with Large Chromatic NumberApr 13 2018For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, ... More

Simplicial volume of Q-rank one locally symmetric manifolds covered by the product of R-rank one symmetric spacesApr 24 2011Jan 10 2012In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric mediaDec 04 2017We study theoretically the interplay between the surface confined wave modes and the linear and nonlinear gain of the dielectric layer in the Otto configuration. The surface confined wave modes such as surface plasmons or waveguide modes are excited in ... More

Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potentialJul 16 2019Aug 26 2019We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous ... More

Moduli Spaces of Standard Holomorphic Bundles on a Noncommutative Complex TorusDec 11 2003In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve. We also propose ... More

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 10 2019We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the ... More

Learning Not to Learn: Training Deep Neural Networks with Biased DataDec 26 2018Apr 15 2019We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to categorize ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019We study $\mathcal{I}$-extremization of three-dimensional gauge field theories and its geometric dual, focusing in particular on a seven-dimensional Sasaki-Einstein manifold $M^{1,1,1}$. We generalize recent studies on relations among toric geometry, ... More

Geometrical Interpretation of Electromagnetism in a 5-Dimensional ManifoldJul 12 2015Aug 13 2017In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Application of Support Vector Machine to detect an association between a disease or trait and multiple SNP variationsApr 17 2001May 22 2001After the completion of human genome sequence was anounced, it is evident that interpretation of DNA sequences is an immediate task to work on. For understanding their signals, improvement of present sequence analysis tools and developing new ones become ... More

Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic mediaOct 27 2017May 16 2019Anderson localization of $p$-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of $p$-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random ... More

$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problemAug 28 2017Sep 05 2018We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted ... More

A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fieldsDec 26 2016Let $G$ be a non-elementary discrete subgroup of $\mathrm{Sp}(2,1)$. We show that if the sum of diagonal entries of each element of $G$ is a complex number, then $G$ is conjugate to a subgroup of $\mathrm{U}(2,1)$.

Direct calculation of the strong Goos-Hänchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configurationJan 12 2019We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016Jun 08 2017In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Mirror duality and noncommutative toriOct 06 2007In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence ... More

Volume invariant and maximal representations of discrete subgroups of Lie groupsMay 22 2012Sep 21 2012Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform ... More

On the q-Euler numbers related to modified q-Bernstein polynomialsJul 20 2010In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.

Surplus Solid Angle as an Imprint of Horava-Lifshitz GravityJul 17 2009Dec 08 2009We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly ... More

Neural Network-Hardware Co-design for Scalable RRAM-based BNN AcceleratorsNov 06 2018Recently, RRAM-based Binary Neural Network (BNN) hardware has been gaining interests as it requires 1-bit sense-amp only and eliminates the need for high-resolution ADC and DAC. However, RRAM-based BNN hardware still requires high-resolution ADC for partial ... More

An $L_p$-theory for diffusion equations related to stochastic processes with non-stationary independent incrementMay 03 2017Oct 27 2017Let $X=(X_t)_{t \ge 0}$ be a stochastic process which has an (not necessarily stationary) independent increment on a probability space $(\Omega, \mathbb{P})$. In this paper, we study the following Cauchy problem related to the stochastic process $X$: ... More

Goodness-of-Fit Test: Khmaladze Transformation vs Empirical LikelihoodFeb 18 2016Apr 22 2016This paper compares two asymptotic distribution free methods for goodness-of-fit test of one sample of location-scale family: Khmaladze transformation and empirical likelihood methods. The comparison is made from the perspective of empirical level and ... More

Discrete symmetries and neutrino massesNov 26 2004May 27 2005We constructed a model of neutrino masses using Froggatt-Nielsen mechanism with $U(1) \times Z_3 \times Z_2$ flavor symmetry. The model predicts that $(2/3)m_2/m_3 \sim \sqrt{2}\sin\theta_{13}$ at lepton number violating scale $M_1$. It is shown that ... More

Note on the Complex Networks and Epidemiology Part I: Complex NetworksFeb 17 2013Feb 23 2013Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The research of complex ... More

Isospin Breaking Effects in the Extraction of Isoscalar and Isovector Spectral Functions From $e^+e^-\to hadrons$Sep 29 1997Apr 14 1998We investigate the problem of the extraction of the isovector and isoscalar spectral functions from data on $e^+e^-\to hadrons$, in the presence of non-zero isospin breaking. It is shown that the conventional approach to extracting the isovector spectral ... More

Strong Isospin Mixing Effects on the Extraction of $ΔI=3/2$ Non-Leptonic Hyperon Decay AmplitudesApr 07 1995The existence of isospin admixtures in the physical $\Lambda$, $\pi^o$ complicates the extraction of Delta I=3/2 non-leptonic hyperon decay amplitudes from experimental data, allowing contributions associated with large Delta I=1/2 amplitudes to appear ... More

Comparison of Chiral Perturbation Theory and QCD Sum Rule Results for Pseudoscalar Isoscalar-Isovector MixingApr 07 1995The forms of the neutral, non-strange pseudoscalar propagator matrix and mixed axial current correlator, $\lngle0|T(A_\mu^3 A_\nu^8)|0\rangle$, are discussed at next-to-leading (one-loop) order in chiral perturbation theory, and the results compared to ... More

Comments on the slope functionJun 16 2016The exact slope function was first proposed in $SL(2)$ sector and generalized to $SU(2)$ sector later. In this note, we consider the slope function in $SU(1|1)$ sector of ${\cal N}=4$ SYM. We derive the quantity through the method invented by N. Gromov ... More

Solving Mass-deformed Holography PerturbativelyFeb 01 2019Feb 11 2019We study supergravity BPS equations which correspond to mass-deformation of some representative AdS/CFT examples. The field theory of interest are N=4, D=4 super Yang-Mills, the ABJM model in D=3, and the Brandhuber-Oz fixed point in D=5. For these gauge ... More

A study of strategy to the remove and ease TBT for increasing export in GCC6 countriesMar 09 2018Mar 23 2018The last technical barriers to trade(TBT) between countries are Non-Tariff Barriers(NTBs), meaning all trade barriers are possible other than Tariff Barriers. And the most typical examples are (TBT), which refer to measure Technical Regulation, Standards, ... More

A Potential Outcomes Approach to Answer Reviewing in Multiple-Choice ExamsJan 09 2019Does reviewing previous answers during multiple-choice exams help examinees increase their final score? This article formalizes the question using a rigorous causal framework, the potential outcomes framework. Viewing examinees' reviewing status as a ... More

Partition number identities which are true for all set of partsMar 19 2018Let $B$ be an infinite subset of $\mathbf{N}$. When we consider partitions of natural numbers into elements of $B$, a partition number without a restriction of the number of equal parts can be expressed by partition numbers with a restriction $\alpha$ ... More

Collapsibility of noncover complexes of chordal graphsApr 09 2019Let $G$ be a graph on $V$. A vertex subset $S \subset V$ is called a cover of $G$ if its complement is an independent set, and $S$ is called a noncover if it is not a cover of $G$. A noncover complex $NC(G)$ of $G$ is the simplicial complex on $V$ whose ... More

Sequential training algorithm for neural networksMay 17 2019A sequential training method for large-scale feedforward neural networks is presented. Each layer of the neural network is decoupled and trained separately. After the training is completed for each layer, they are combined together. The performance of ... More

Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theoryDec 10 2003We study rotating strings with multiple spins in the background of $AdS_5\times T^{1,1}$, which is dual to a $\mathcal{N}=1$ superconformal field theory with global symmetry $SU(2)\times SU(2)\times U(1)$ via the AdS/CFT correspondence. We analyse the ... More

Bicommutative Kitaev lattice model I : stabilizer model and chain complex theoryJul 23 2019In this paper, we give a generalization of the bicommutative Kitaev lattice model by using a chain complex theory of bicommutative Hopf monoids in a symmetric monoidal category. We prove that the ground-state space, indeed the codespace, is isomorphic ... More

Instability Results for the Logarithmic Sobolev Inequality and its Application to the Beckner--Hirschman InequalityMay 16 2018Aug 09 2018We provide an example to show that there are no general stability results for the logarithmic Sobolev inequality in terms of the Wasserstein distances and $L^{p}$ distance for $p>1$. The results imply that the stability bounds for the logarithmic Sobolev ... More

AKSZ-type Topological Quantum Field Theories and Rational Homotopy TheorySep 25 2018We reformulate and motivate AKSZ-type topological field theories in pedestrian terms, explaining how they arise as the most general Schwartz-type topological actions subject to a simple constraint, and how they generalize Chern$-$Simons theory and other ... More

The classification of $p$-divisible groups over 2-adic discrete valuation ringsJul 12 2010Dec 30 2011Let $\mathscr{O}_K$ be a 2-adic discrete valuation ring with perfect residue field $k$. We classify $p$-divisible groups and $p$-power order finite flat group schemes over $\mathscr{O}_K$ in terms of certain Frobenius module over $\mathfrak{S}:=W(k)[[u]]$. ... More

Type Ia Supernova Intrinsic Magnitude Dispersion and the Fitting of Cosmological ParametersJan 18 2011I present an analysis for fitting cosmological parameters from a Hubble Diagram of a standard candle with unknown intrinsic magnitude dispersion. The dispersion is determined from the data themselves, simultaneously with the cosmological parameters. This ... More

Wide-Field Surveys from the SNAP MissionOct 02 2002The Supernova/Acceleration Probe (SNAP) is a proposed space-borne observatory that will survey the sky with a wide-field optical/near-infrared (NIR) imager. The images produced by SNAP will have an unprecedented combination of depth, solid-angle, angular ... More

Graded Unification: A Framework for Interactive ProcessingJun 05 1994An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.

On unstabilzed genus three critical Heegaard surfacesMar 25 2012Let $M$ be a compact orientable irreducible 3-manifold and $H$ be an unstabilized genus three Heegaard splitting of $M$. In this article, we will define a simplicial complex of weak reducing pairs for $H$ and find several properties of this complex. Using ... More

On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure TheoremDec 06 2014Mar 09 2015Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of the disk complex D(F) consisting of simplices having at least one vertex from V and at least one vertex ... More

A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is criticalFeb 18 2014Mar 21 2015Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F ... More

Non-negative Wigner-like distributions and Renyi-Wigner entropies of arbitrary non-Gaussian quantum states: The thermal state of the one-dimensional box problemApr 05 2019Jun 20 2019In this work, we consider the phase-space picture of quantum mechanics. We then introduce non-negative Wigner-like (operational) distributions \widetilde{\mathcal W}_{rho;alpha}(x,p) corresponding to the density operator \hat{rho} and being proportional ... More

Jarzynski equality and the second law of thermodynamics beyond the weak-coupling limit: The quantum Brownian oscillatorFeb 27 2014We consider a time-dependent quantum linear oscillator coupled to a bath at an arbitrary strength. We then introduce a generalized Jarzynski equality (GJE) which includes the terms reflecting the system-bath coupling. This enables us to study systematically ... More

The motivic fundamental group of the projective line minus three points and the theorem of SiegelSep 23 2004In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. In particular, we give a p-adic proof of Siegel's theorem.

Parabolic equations with partially VMO coefficients and boundary value problems in Sobolev spaces with mixed normsJun 03 2007Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except $a^{11}$) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient $a^{11}$ is measurable ... More

Conformal scalar curvature rigidity on Riemannian manifoldsJun 01 2017Let $(M, \bar g)$ be an $n$-dimensional complete Riemannian manifold. In this paper, we considers the following conformal scalar curvature rigidity problem: Given a compact smooth domain $\Omega$ with $\partial \Omega$, can one find a conformal metric ... More

A note on the new q-extension of Frobenius-Euler numbers and polynomialsJul 05 2013In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we suggest one open ... More

The number of representations of squares by integral quaternary quadratic formsMar 06 2019Let $f$ be a positive definite (non-classic) integral quaternary quadratic form. We say $f$ is strongly $s$-regular if it satisfies a regularity property on the number of representations of squares of integers. In this article, we prove that there are ... More

Some Identities for the Bernoulli, the Euler and the Genocchi Numbers and PolynomialsDec 25 2009The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.

Symmetry p-adic invariant integral on Z_p for Bernoulli and euler polynomialsDec 02 2007The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integral on Z_p.

An Invarian p-adic q-integral on the rings of p-adic integersJul 31 2006In the recent p-adic q-integral on the p-adic integers' rings was constructed >. The purpose of this paper is to give several interesting integral equation for the p-adic q-integerals on the rings of p-adic integers. As an integral equations, we will ... More

On the analogs of Euler numbers and polynomials associated with p-adic integrals on the rings of p-adic integers at q=-1Jul 07 2006We will study p-adic invariant integerals involving trigonometric functions

On p-adic q-l-functions and sums of powersMay 16 2006The purpose of this paper is to construct p-adic analytically continued function which interpolates q-Euler numbers at negative integer Finally, we give an explicit p-adic expansion as a power series in n.

q-Euler and Genocchi numbersJun 14 2005Carlitz has introduced an interesting $q$-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the $q$-Euler numbers. In this paper we give another construction ... More

Multivariate p-dic L-functionMay 08 2005We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.