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Spectral approximation of a variable coefficient fractional diffusion equation in one space dimensionOct 29 2018In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower order, constant ... More

Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximationNov 01 2018In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral operator. Under a suitable transformation the variable coefficient equation ... More

Optimal order finite element approximations for variable-order time-fractional diffusion equationsMay 14 2019We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order accuracy in space) ... More

Numerical approximations for the variable coefficient fractional diffusion equations with non-smooth dataFeb 26 2019In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient fractional diffusion ... More

Data-driven physics informed deep learning of solute transport with anomalous diffusionDec 04 2018Feb 11 2019The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the anomalous diffusion ... More

Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double ArithmeticJan 26 2015Jun 12 2015Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning worsens and hardware ... More

Projected Three-Point Correlation Functions and Galaxy BiasMay 26 2004Sep 06 2004The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF, where these distortions ... More

Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing UnitMay 03 2015Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector algorithms to track ... More

Interpreting the Observed Clustering of Red Galaxies at z~3Jul 01 2003May 20 2004Daddi et al. have recently reported strong clustering of a population of red galaxies at z~3 in the Hubble Deep Field-South. Fitting the observed angular clustering with a power law of index -0.8, they infer a comoving correlation length r_0~8 Mpc/h; ... More

GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmeticFeb 11 2014May 13 2014In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla K20C general purpose graphics processing unit. The focus on this paper is on Newton's ... More

The physics of Lyman-alpha escape from high-redshift galaxiesOct 18 2018Lyman-alpha (Ly{\alpha}) photons from ionizing sources and cooling radiation undergo a complex resonant scattering process that generates unique spectral signatures in high-redshift galaxies. We present a detailed Ly{\alpha} radiative transfer study of ... More

Superluminal Caustics of Close, Rapidly-Rotating Binary MicrolensesJan 12 2000The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary themselves, and can even exceed the speed of light. When $\epsilon > 1$, where $\epsilon c$ is the caustic ... More

Gravitational Lensing by Ring-Like StructuresJan 12 2016Nov 05 2016We study a class of gravitational lensing systems consisting of an inclined ring/belt, with and without an added point mass at the centre. We show that a common feature of such systems are so-called "pseudo-caustics", across which the magnification of ... More

Radiative Transfer Effect on Ultraviolet Pumping of the 21cm Line in the High Redshift UniverseJun 06 2007During the epoch of reionization the 21cm signal is sensitive to the scattering rate of the ultraviolet photons, redshifting across the Lyman_alpha resonance. Here we calculate the photon scattering rate profile for a single ultraviolet source. After ... More

Dependence of Halo Bias and Kinematics on Assembly VariablesOct 18 2017Aug 30 2018Using dark matter haloes identified in a large $N$-body simulation, we study halo assembly bias, with halo formation time, peak maximum circular velocity, concentration, and spin as the assembly variables. Instead of grouping haloes at fixed mass into ... More

Galaxy assembly bias of central galaxies in the Illustris simulationDec 28 2018Galaxy assembly bias, the correlation between galaxy properties and halo properties at fixed halo mass, could be an important ingredient in halo-based modelling of galaxy clustering. We investigate the central galaxy assembly bias by studying the relation ... More

Microlensing of Circumstellar DisksJul 11 2005Aug 26 2005We investigate the microlensing effects on a source star surrounded by a circumstellar disk, as a function of wavelength. The microlensing light curve of the system encodes the geometry and surface brightness profile of the disk. In the mid- and far-infrared, ... More

When points are equivalent in long time behaviorsMar 29 2019We metric the distance between two points in a new way, and then show a new equivalent condition of ergodic measures. We also conclude a necessary and sufficient condition of uniquely ergodicity. What's more, an equivalent condition of when the time average ... More

Accurate and Efficient Halo-based Galaxy Clustering Modelling with SimulationsJun 24 2015Mar 02 2016Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy clustering measurements ... More

Gravitational Lensing by Ring-Like StructuresJan 12 2016We study a class of gravitational lensing systems consisting of an inclined ring/belt, with and without an added point mass at the centre. We show that a common property of such systems is the so-called "pseudo-caustics", across which the magnification ... More

Anisotropic Lyman-alpha EmissionAug 06 2013Sep 10 2014As a result of resonant scatterings off hydrogen atoms, Lyman-alpha (Lya) emission from star-forming galaxies provides a probe of the (hardly isotropic) neutral gas environment around them. We study the effect of the environmental anisotropy on the observed ... More

Nature of Lyman Alpha Blobs: Powered by Extreme StarburstsOct 12 2012We present a new model for the observed Lyman alpha blobs (LABs) within the context of the standard cold dark matter model. In this model, LABs are the most massive halos with the strongest clustering (proto-clusters) undergoing extreme starbursts in ... More

A modified adaptive cubic regularization method for large-scale unconstrained optimization problemApr 16 2019In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique, we also give ... More

Generalized Dynamic Scaling for Critical Magnetic SystemsMay 22 1997The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from an initial state ... More

Deterministic Equations of Motion and Phase Ordering DynamicsSep 22 1999We numerically solve microscopic deterministic equations of motion for the 2D $\phi^4$ theory with random initial states. Phase ordering dynamics is investigated. Dynamic scaling is found and it is dominated by a fixed point corresponding to the minimum ... More

A characterization of homology manifolds with $g_2\leq 2$Jul 19 2016We characterize homology manifolds with $g_2\leq 2$. Specifically, using retriangulations of simplicial complexes, we give a short proof of Nevo and Novinsky's result on the characterization of homology $(d-1)$-spheres with $g_2=1$ for $d\geq 5$ and extend ... More

The Measure of Strong CP ViolationSep 14 1992We investigate a controversial issue on the measure of CP violation in strong in teractions. In the presence of nontrivial topological gauge configurations, the $\theta$-term in QCD has a profound effect: it breaks the CP symmetry. The CP-violating amplitude ... More

Discovery of Scalar Mixed With SM Higgs Via Diboson Excess at the LHCAug 25 2015The prospect for the discovery of scalar weakly mixed with the SM Higgs is studied through the diboson signal excess at the Large Hadron Collider. Such scalar usually exists in scalar singlet extended SM. For illustration to the broad application of our ... More

A User's Guide to CARSKitNov 12 2015Context-aware recommender systems extend traditional recommenders by adapting their suggestions to users' contextual situations. CARSKit is a Java-based open-source library specifically designed for the context-aware recommendation, where the state-of-the-art ... More

Chern-Simons functions on toric Calabi-Yau threefolds and Donaldson-Thomas theoryMar 09 2011May 08 2012In this paper, we give a construction of the global Chern-Simons functions for toric Calabi-Yau stacks of dimension three using strong exceptional collections. The moduli spaces of sheaves on such stacks can be identified with critical loci of these functions. ... More

Combating Malicious DNS TunnelMay 04 2016This paper proposes a defense scheme against malicious use of DNS tunnel. A tunnel validator is designed to provide trustworthy tunnel-aware defensive recursive service. In addition to the detection algorithm of malicious tunnel domains, the tunnel validation ... More

Does Your DNS Recursion Really Time Out as Intended? A Timeout Vulnerability of DNS Recursive ServersJun 30 2016Parallelization is featured by DNS recursive servers to do time-consuming recursions on behalf on clients. As common DNS configurations, recursive servers should allow a reasonable timeout for each recursion which may take as long as several seconds. ... More

An optimal result for global classical and bounded solutions in a two-dimensional Keller-Segel-Navier-Stokes system with sensitivityMar 04 2019This paper deals with a boundary-value problem for a coupled chemotaxis-Navier-Stokes system involving tensor-valued sensitivity with saturation $$ \left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, ... More

The upper bounds on the edge numbers of flag odd dimensional normal pseudomanifoldsMay 23 2018We prove that among all $(2m-1)$-dimensional flag normal pseudomanifolds on $n$ vertices, the join of $m$ circles of as equal length as possible is the unique maximizer of the edge number.

Transverse Fully Nonlinear Equations on Sasakian Manifolds and ApplicationsAug 13 2018We prove a priori estimates for a class of transverse fully nonlinear equations on Sasakian manifolds and give some applications. This is a counterpart to the results of Sz\'ekelyhidi in the K\"ahler case.

ROS Navigation Tuning GuideJun 27 2017The ROS navigation stack is powerful for mobile robots to move from place to place reliably. The job of navigation stack is to produce a safe path for the robot to execute, by processing data from odometry, sensors and environment map. Maximizing the ... More

Learning Large-Scale Topological Maps Using Sum-Product NetworksJun 11 2017Jul 10 2017In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large scale, global maps ... More

The Equilibrium Statistical Model of Economic Systems using Concepts and Theorems of Statistical PhysicsApr 16 2015Economic systems are similar with physic systems for their large number of individuals and the exist of equilibrium. In this paper, we present a model applying the equilibrium statistical model in economic systems. Consistent with statistical physics, ... More

Simultaneous Diophantine Approximation in Function FieldsNov 10 2017There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultaneous approximation. In this paper, we develop a technique of \geometry ... More

Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stabilityMar 26 2018In this article, we prove that the existence of the constant scalar curvature Kaehler (cscK) metrics with cone singularities is equivalent to the properness of the log $K$-energy, assuming that the automorphism group is discrete. We also prove their equivalence ... More

Some Remarks on Exotic ResonancesNov 01 2004Using large $N_c$ counting rule, it is argued that tetra-quark resonances do not exist. Also it is pointed out that there exists the violation of exchange degeneracy in the exotic $KN$ scattering channel. It implies either the failure of resonance saturation ... More

FINAL STATE INTERACTIONS OF $B\to DK$ DECAYSApr 21 1995We study the final state strong interactions of the $B\rightarrow DK$ decay processes, using the Regge model. We conclude that the final state interaction phases are very small, typically a few degrees. Neglecting final state interactions in obtaining ... More

The homology coalgebra and cohomology algebra of generalized moment-angle complexesJan 24 2012In this paper, we compute the homology coalgebra and cohomology algebra over a field of all generalized moment-angle complexes and give a duality theorem on complementary moment-angle complexes.

Face enumeration on flag complexes and flag spheresSep 18 2018Nov 20 2018We give a survey on the recent results and problems on the face enumeration of flag complexes and flag simplicial spheres, with an emphasis on the characterization of face vectors of flag complexes, several lower-bound type of conjectures including the ... More

Ear Decompostion and Balanced 2-neighborly Simplicial ManifoldsDec 12 2016Nov 06 2017We find the first non-octahedral balanced 2-neighborly 3-sphere and the balanced 2-neighborly triangulation of the lens space $L(3,1)$. Each construction has 16 vertices. We also show that the rank-selected subcomplexes of a balanced simplicial sphere ... More

Minimal Balanced Triangulations of Sphere Bundles over the CircleMay 21 2015Apr 15 2016We determine the minimum number of vertices needed to provide balanced triangulations of $\mathbb S^{d-2}$-bundles over $\mathbb S^1$. If $d$ is odd and the bundle is orientable, or $d$ is even and the bundle is non-orientable, the minimum number of vertices ... More

Mirrors and Phases of N=4 in D=3Dec 18 1997We review brane engineering of mirror pairs of 3d N=4 theories. It reveals aspects of 3d physics not known from previous field theoretic studies: novel QFT's without Lagrangian description and transitions to them from conventional QFT's.

On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann SurfacesMay 12 2004May 19 2004In this paper, we study the asymptotic geometry of Teichmuller space of Riemann surfaces and give bounds on the Weil-Petersson sectional curvature of Teichmuller space, in terms of the length of the shortest geodesic on the surface. This will also imply ... More

An Effective Framework for Constructing Exponent Lattice Basis of Nonzero Algebraic NumbersAug 08 2018Jan 29 2019Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm \cite{ge1993algorithms,kauers2005algorithms} ... More

Extended MSSM in Supersymmetric $\rm{SO}(10)$ Grand UnificationNov 15 2017Aug 07 2018We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ ... More

The Early Universe with High-Scale SupersymmetrySep 26 2014Aug 12 2015A small tensor-to-scalar ratio $r$ may lead to distinctive phenomenology of high-scale supersymmetry. Assuming the same origin of SUSY breaking between the inflation and visible sector, we show model independent features. The simplest hybrid inflation, ... More

Dynamical Generation of the Weak Scale and Inflation in High-Scale SupersymmetryMay 12 2014Feb 24 2015Combination of Plank and BICEP2 data reported that tensor to scalar ratio $r\simeq 0.16$ and scalar spectral index $n_{s}\simeq 0.96$. In this short note, it is shown that chaotic inflation with quadratic potential, which perfectly accounts for present ... More

Effective Higgs Theories in Supersymmetric Grand UnificationJun 04 2017Aug 25 2017The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand unification models are systematically derived. Restricted to extensions on $\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of real (vector-like) models ... More

On some root multiplicities for Nichols algebras of diagonal type over arbitrary fieldsAug 28 2018In this paper, our main aim is to determine the multiplicities of a class of roots for Nichols algebra of diagonal type over fields of arbitrary characteristic, which is a generalization of the results on the multiplicities of these roots over fields ... More

A geometric categorification of tensor products of $U_q(sl_2)$-modulesMay 18 2007Jun 09 2007We give a purely geometric categorification of tensor products of finite-dimensional simple $U_q(sl_2)$-modules and $R$-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification theorems are understood ... More

The Cohomology Algebra of Polyhedral Product ObjectsApr 21 2018In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into commutative algebra ... More

A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous SpacesOct 06 2016Oct 08 2018In this paper, we give a definition of Diophantine points of type $\gamma$ for $\gamma\geq0$ in a homogeneous space $G/\Gamma$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $\gamma$ when $G$ is a semisimple ... More

Littlewood-Paley theorem for Schroedinger operatorsSep 06 2006Let $H$ be a Schr\"odinger operator on $\R^n$. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with $H$ are well defined. We further give a Littlewood-Paley ... More

Locating the first nodal set in higher dimensionsNov 30 2013Dec 11 2013This paper estimates the location and the width of the nodal set of the first Neumann eigenfunctions on a smooth convex domain $\Omega \subset \mathbb R^n$, whose length is normalized to be 1 and whose cross-section is contained in a ball of radius $\epsilon$. ... More

Precision Measurement of the Neutron Spin Asymmetries and Spin-dependent Structure Functions in the Valence Quark RegionMay 12 2004Feb 01 2005We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47 and 0.60 and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. These ... More

Interpolation Theorems for Self-adjoint OperatorsDec 22 2008We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where $L$ is a ... More

Monte Carlo Simulation of Lyman Alpha Scattering and Application to Damped Lyman Alpha SystemsMar 18 2002Jun 25 2002A Monte Carlo code to solve the transfer of Lyman alpha (Lya) photons is developed, which can predict the Lya image and two-dimensional Lya spectra of a hydrogen cloud with any given geometry, Lya emissivity, neutral hydrogen density distribution, and ... More

Davenport-Hasse's Theorem for Polynomial Gauss Sums over Finite FieldsOct 25 2016In this paper, we study the polynomial Gauss sums over finite fields, and present an analogue of Davenport-Hasse's theorem for the entire polynomial Gauss sums, which is a generalization of the previous result obtained by Hayes.

An Alternative Explanation of Supernova Ia DataOct 01 2013Dec 12 2013Before 1998 the universe expansion was thought to be slowing down. After 1998 the universe expansion is thought to be accelerating up. This change of the belief is motivated by the observed brightness of the high redshift supernova Ia fainter than expected. ... More

Microscopic Deterministic Dynamics and Persistence ExponentSep 22 1999Numerically we solve the microscopic deterministic equations of motion with random initial states for the two-dimensional $\phi^4$ theory. Scaling behavior of the persistence probability at criticality is systematically investigated and the persistence ... More

Two Differentially Private Rating Collection Mechanisms for Recommender SystemsApr 28 2016We design two mechanisms for the recommender system to collect user ratings. One is modified Laplace mechanism, and the other is randomized response mechanism. We prove that they are both differentially private and preserve the data utility.

Toward a Better Understanding of LeaderboardOct 12 2015The leaderboard in machine learning competitions is a tool to show the performance of various participants and to compare them. However, the leaderboard quickly becomes no longer accurate, due to hack or overfitting. This article gives two advices to ... More

Universally optimal crossover designs under subject dropoutMar 12 2013Subject dropout is very common in practical applications of crossover designs. However, there is very limited design literature taking this into account. Optimality results have not yet been well established due to the complexity of the problem. This ... More

An Estimation Method Using Periodic Inspection of IndicatorsFeb 18 2016This paper proposes a new approach for estimating the failure time distribution using the indicator data. The indicators, which are checked by periodic inspection of a standby redundant system, only convey whether at least one failure occurs per interval. ... More

Do W_L and H form a p-wave bound state?Mar 03 1995We examine the possibility of bound state formation in the W_L H --> W_L H channel. The dynamical calculation using the N/D method indicates that when the interactions among the Goldstone and Higgs bosons become sufficiently strong, a p-wave state [I^G(J^P)=1^-(1^+)] ... More

Angular width of Cherenkov radiation with inclusion of multiple scattering: an path-integral approachApr 13 2016Visible Cherenkov radiation can offers a method of the measurement of the velocity of a charged particles. The angular width of the radiation is important since it determines the resolution of the velocity measurement. In this article, the angular width ... More

An optimal result for global classical and bounded solutions in a two-dimensional Keller-Segel-Navier-Stokes system with sensitivityMar 04 2019Mar 05 2019This paper deals with a boundary-value problem for a coupled chemotaxis-Navier-Stokes system involving tensor-valued sensitivity with saturation $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, t>0, ... More

Focusing NLS with inverse square potentialAug 07 2018In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schr\"odinger equation with inverse square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space $H^1_a(\R^d)$ in dimensions ... More

Regularity in the two-phase free boundary problems under non-standard growth conditionsSep 23 2018In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_{\gamma}(u)=\int_{\Omega}\big(f(x,\nabla u)+\lambda_{+} (u^{+})^{\gamma}+\lambda_{-}(u^{-})^{\gamma}+gu\big)\text{d}x\rightarrow \text{min}$ ... More

Orbifold Aspects of Certain Occult Period MapsNov 07 2017We first characterize the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds. Then we determine for some complex projective manifolds of small dimension (cubic surfaces, cubic threefolds, and non-hyperelliptic curves of genus ... More

Proof of the volume conjecture for Whitehead doubles of a family of torus knotsAug 08 2005Mar 04 2006A technique to calculate the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then we prove the volume conjecture for Whitehead doubles of a family of torus knots and show some interesting observations. ... More

Dynamics of a Two-Level System Coupled to Ohmic Bath: A Perturbation ApproachOct 08 2002The physics of a two-level system coupled to Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. Our main results are: The coherence-incoherence transition is at $\alpha_c={1\over 2}[1+\Delta_r/\omega_c]$; for ... More

An optimal result for global classical and bounded solutions in a two-dimensional Keller-Segel-Navier-Stokes system with sensitivityMar 04 2019Mar 07 2019This paper deals with a boundary-value problem for a coupled chemotaxis-Navier-Stokes system involving tensor-valued sensitivity with saturation $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, t>0, ... More

Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free methodJan 21 2013Max-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. In particular, McEneaney's curse-of-dimensionality free method applies to the equations where the Hamiltonian takes the ... More

Chaotic Neuronal Oscillations in Spontaneous Cortical-Subcortical NetworksJul 21 2015Oscillatory activities are widely observed in specific frequency bands of recorded field potentials in different brain regions, and play critical roles in processing neural information. Understanding the structure of these oscillatory activities is essential ... More

A Study of the Evaporative Deposition Process: Pipes and Truncated Transport DynamicsDec 02 2007We consider contact line deposition and pattern formation of a pinned evaporating thin drop. We identify and focus on the transport dynamics truncated by the maximal concentration, proposed by Dupont, as the single deposition mechanism. The truncated ... More

Complement Spaces, Dual Complexes and Polyhedral Product SpacesSep 08 2016Jul 19 2017In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral join complexes. Then we compute the universal algebra of polyhedral join complexes under certain split conditions and the Alexander ... More

Contribution of Cross-Correlations to the 21cm Angular Power Spectrum in the Epoch of ReionizationNov 24 2009Measurement of the 21cm hyperfine transition of neutral hydrogen provides a unique probe of the epoch of reionization and the Dark Ages. Three major mechanisms are believed to dominate the radiation process: emission from neutral hydrogen surrounding ... More

A representation formula related to Schrodinger operatorsDec 16 2004Let H be a Schrodinger operator on the real line, where the potential is in L^1 and L^2. We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L^2. This property allows us to construct ... More

Sur l'indépendance de l en cohomologie l-adique sur les corps locauxNov 23 2007Mar 06 2009Gabber deduced his theorem of independence of $l$ of intersection cohomology from a general stability result over finite fields. In this article, we prove an analogue of this general result over local fields. More precisely, we introduce a notion of independence ... More

General cycling operations in Garside groupsMay 30 2006Aug 20 2006In this article, we introduce the notion of cycling operations of arbitrary order in Garside groups, which is a full generalization of the cycling and decycling operations. Theoretically, this notion together with other related concepts provides a context ... More

The stability of strong viscous contact discontinuity to a free boundary problem for compressible Navier-Stokes equationsJul 21 2014Oct 08 2014This paper is concerned with nonlinear stability of viscous contact discontinuity to a free boundary problem for the one-dimensional full compressible Navier-Stokes equations in half space $[0,\infty)$. For the case when the local stability of the contact ... More

On rigid stabilizers and invariant random subgroups of groups of homeomorphismsJan 14 2019A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we classify ergodic invariant random subgroups of topological ... More

Low Lying Scalar Resonances and Chiral SymmetryFeb 08 2008Current theoretical studies on the $\sigma$ and $\kappa$ resonances are reviewed. It is emphasized that all evidences accumulated so far are consistent with the picture that the $\sigma$ meson is the chiral partner of the Nambu--Goldstone bosons in a ... More

Technicolor with Scalar Doublet After the Discovery of Higgs BosonMay 29 2013Oct 19 2015The SM-like Higgs boson with mass of 125 GeV discovered at the LHC is subject to a natural interpretation of electroweak symmetry breaking. As a successful theory in offering this naturalness, technicolor with a scalar doublet and two both $SU(3)_c$ and ... More

Perturbative $λ$-Supersymmetry and Small $κ$-PhenomenologyMay 27 2014Apr 17 2015For the minimal $\lambda$-supersymmetry, it stays perturbative to the GUT scale for $\lambda \leq 0.7$. This upper bound is relaxed when one either takes the criteria that all couplings close to $\sim 4\pi$ for non-perturbation or allows new fields at ... More

Effective Field Theory Analysis on μ Problem in Low-Scale Gauge MediationJun 28 2011Oct 13 2011Supersymmetric models based on the scenario of gague mediation often suffer from the well-known $\mu$ problem. In this paper, we reconsider this problem in low-scale gauge mediation in terms of effective field theory analysis. In this paradigm, all high ... More

Focus Point in Dark Matter Selected High-Scale SupersymmetryJan 23 2015Apr 20 2015In this paper, we explore conditions for focus point in the high-scale supersymmetry with the weak-scale gaugino masses. In this context the tension between the naturalness and LHC 2013 data about supersymmetry as well as the cold dark matter candidate ... More

A game model for the multimodality phenomena of coauthorship networksDec 26 2018We provided a game model to simulate the evolution of coauthorship networks, a geometric hypergraph built on a circle. The model expresses kin selection and network reciprocity, two typically cooperative mechanisms, through a cooperation condition called ... More

A Peccati-Tudor type theorem for Rademacher chaosesAug 17 2017In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centred Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is ... More

Categorification of integrable representations of quantum groupsMar 26 2008Apr 23 2008We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As byproducts, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity ... More

On the Polynomial Ramanujan Sums over Finite FieldsDec 26 2016The polynomial Ramanujan sum was first introduced by Carlitz [7], and a generalized version by Cohen [10]. In this paper, we study the arithmetical and analytic properties of these sums, derive various fundamental identities, such as H older formula, ... More

Resolutions of facet idealsJul 17 2003In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by S. Faridi. These simplicial complexes are called trees, and are a generalization (to higher dimensions) of the concept of a tree ... More

The Hilbert schemes of points on surfaces with rational double point singularitiesJan 10 2017We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst rational double point singularities is irreducible.

Deducing the Lifetime of Short Gamma-Ray Burst Progenitors from Host Galaxy DemographyJan 26 2006May 07 2007The frequency of short gamma-ray bursts (GRBs) in galaxies with distinct star formation histories can be used to constrain the lifetime of the progenitor systems. As an illustration, we consider here the constraints that can be derived from separating ... More