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Categorization Problem on Controllability of Boolean Control NetworksApr 12 2019A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set $\{0,1\}$. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state ... More

Stability Structures of Conjunctive Boolean NetworksMar 14 2016Sep 19 2016A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a local function, i.e., it depends only on a selected subset of variables. Boolean networks have been widely used ... More

Some sufficient conditions of a given series with rational terms converging to an irrational number or a transcdental numberJul 09 2008Jul 18 2008In this paper, we propose various sufficient conditions to determine if a given real number is an irrational number or a transcendental number and also apply these conditions to some interesting examples, particularly,one of them comes from complex analytic ... More

Effects of interaction and polarization on spin-charge separation: A time-dependent spin-density-functional theory studyJan 18 2011We calculate the nonequilibrium dynamic evolution of a one-dimensional system of two-component fermionic atoms after a strong local quench by using a time-dependent spin-density-functional theory. The interaction quench is also considered to see its influence ... More

On homotopy categories of Gorenstein modules: compact generation and dimensionsJan 16 2014Feb 12 2014Let $A$ be a virtually Gorenstein algebra of finite CM-type. We establish a duality between the subcategory of compact objects in the homotopy category of Gorenstein projective left $A$-modules and the bounded Gorenstein derived category of finitely generated ... More

Continous perturbations of noncommutative Euclidean spaces and toriMay 22 2016We prove a continuous version of the Haagerup and R{\o}rdam's result about the bounded perturbation of the Heisenberg relation. It gives a continuous Moyal deformation of noncommutative plane. This result is also an example of the continuous embedding ... More

Curvature estimate on the finite graph with large girthSep 27 2016The CD inequalities and CDE inequalities are useful in the estimate of curvature on graphs. This article is based on the ufinite graph with large girth, and finally concludes some curvature estimate in CD and CDE.

One example about the relationship between the CD inequality and CDE' inequalityOct 19 2016In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.

From quantum motion to classical motion - seeking the lost realityJan 06 2000Jan 07 2000We show that the natural motion of particles in continuous space-time (CSTM) is not classical continuous motion (CCM), but one kind of essentially discontinuous motion, the wave function in quantum mechanics is the very mathematical complex describing ... More

Quantum superluminal communication must existJul 02 1999We show that the quantum superluminal communication based on the quantum nonlocal influence must exist if a basic principle of science is still valid, which states that if we have demonstrated the existence of something real, we can confirm its existence. ... More

Derivative interactions for a spin-2 field at cubic orderMar 26 2014Sep 09 2014Lorentz invariant derivative interactions for a single spin-2 field are investigated, up to the cubic order. We start from the most general Lorentz invariant terms involving two spacetime derivatives, which are polynomials in the spin-2 field as well ... More

Non-supersymmetric Attractors in Born-Infeld Black Holes with a Cosmological ConstantAug 09 2007Nov 07 2007We investigate the attractor mechanism for spherically symmetric extremal black holes in Einstein-Born-Infeld-dilaton theory of gravity in four-dimensions, in the presence of a cosmological constant. We look for solutions analytic near the horizon by ... More

On Beurling's uncertainty principleJun 17 2015Jul 14 2015We generalise a result of Hedenmalm to show that if a function $f$ on $\mathbb{R}$ is such that $\int_{\mathbb{R}^2} \bigl|f(x) \, \hat f(y)\bigr| \,e^{\lambda \left|xy\right|} \,dx\,dy = O( (1-\lambda)^{-N} )$ as $\lambda \to 1-$, then $f$ is the product ... More

Monte Carlo Study of a 137Cs calibration field of the China institute of atomic energyFeb 10 2015The MCNP code was used to study the characteristics of gamma radiation field with collimated beam geometry. A close-to-reality simulation model of the facility was used for calculation air-kerma along the whole range of source-detector-distance (SDD) ... More

Statistical Inference for Algorithmic LeveragingJun 05 2016Jul 13 2016The age of big data has produced data sets that are computationally expensive to analyze. To deal with such large-scale data sets, the method of algorithmic leveraging proposes that we sample according to some special distribution, rescale the data, and ... More

Non L-space integral homology 3-spheres with no nice orderingsSep 24 2016Nov 02 2016This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.

The Robustness and Super-Robustness of L^p Estimation, when p < 1Jun 22 2012Oct 11 2012In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate reliable estimation ... More

On the metric s-t path Traveling Salesman ProblemApr 30 2014Mar 14 2015We study the metric $s$-$t$ path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing $\frac{5}{3}$-approximation factor and presented an algorithm that achieves an approximation factor of $\frac{1+\sqrt{5}}{2}\approx1.61803$. ... More

Controlled and secure direct communication using GHZ state and teleportationDec 01 2003A theoretical scheme for controlled and secure direct communication is proposed. The communication is based on GHZ state and controlled quantum teleportation. After insuring the security of the quantum channel (a set of qubits in the GHZ state), Alice ... More

Study of Radiative Decays of Psi(2S) MesonsSep 14 2009Sep 16 2009We studied the decay psi(2S) to gamma eta_c(2S) with 25.9 million psi(2S) events collected with the CLEO-c detector. No psi(2S) to gamma eta_c(2S) decays were observed in any of the eleven exclusive eta_c(2S) decay modes studied. The product branching ... More

Kazhdan-Lusztig representations and Whittaker space of some genuine representationsMar 14 2019We propose a conjectural formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups. The formula explicitly relates such dimension to the Kazhdan-Lusztig representations ... More

Joint Source-Channel Coding for Real-Time Video Transmission to Multi-homed Mobile TerminalsJun 29 2015This study focuses on the mobile video delivery from a video server to a multi-homed client with a network of heterogeneous wireless. Joint Source-Channel Coding is effectively used to transmit video over bandwidth-limited, noisy wireless networks. But ... More

Universal model for exoergic bimolecular reactions and inelastic processesOct 24 2010From a rigorous multichannel quantum-defect formulation of bimolecular processes, we derive a fully quantal and analytic model for the total rate of exoergic bimolecular reactions and/or inelastic processes that is applicable over a wide range of temperatures ... More

Age-structured population models with ApplicationsJul 04 2016A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition. Existence, uniqueness ... More

Compound Bi-free Poisson DistributionsJun 04 2018In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible distribution for ... More

Vortex and droplet in holographic D-wave superconductorsDec 12 2011Apr 05 2012We investigate non-trivial localized solutions of the condensate in a (2+1)-dimensional D-wave holographic superconductor model in the presence of a background magnetic field. The calculation is done in the context of the (3+1)-dimensional dual gravity ... More

Introduction of the generalized Lorenz gauge condition into the vector-tensor theoryNov 28 2011Jan 30 2012We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the four dimensional ... More

Adapted bases of Kisin modules and Serre weightsMay 11 2015Jun 13 2016Let $p>2$ be a prime. Let $K$ be a tamely ramified finite extension over $\mathbb Q_p$ with ramification index $e$, and let $G_K$ be the Galois group. We study Kisin modules attached to crystalline representations of $G_K$ whose labeled Hodge-Tate weights ... More

Neutron Electromagnetic Form FactorsNov 08 2004The nucleon electromagnetic form factors have been studied in the past extensively from unpolarized electron scattering experiments. With the development in polarized beam, recoil polarimetry, and polarized target technologies, polarization experiments ... More

Strain Induced Slowdown of Front Propagation in Random Shear Flow via Analysis of G-equationsSep 02 2015It is proved that for the 2-dimensional case with random shear flow of the G-equation model with strain term, the strain term reduces the front propagation. Also an improvement of the main result by Armstrong-Souganidis is provided.

Radon Transform for SheavesDec 18 2017Jul 05 2018We define the Radon transform functor for sheaves and prove that it is an equivalence after suitable microlocal localizations. As a result, the sheaf category associated to a Legendrian is invariant under the Radon transform. We also manage to place the ... More

Strong averaging principle for stochastic Klein-Gordon equation with a fast oscillationMar 16 2017Mar 22 2017This paper investigates an averaging principle for stochastic Klein-Gordon equation with a fast oscillation arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. Stochastic averaging principle is a ... More

A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic CurveSep 30 2018In this paper, the proof of the existence of a rational point on an elliptic curve is transformed into the proof of the existence of an integer solution for a Diophantine equation. By a new formula for calculating the number of elements in intersection ... More

On a mixed arithmetic-geometric mean inequalityMay 15 2013We extend a result of Holland on a mixed arithmetic-geometric mean inequality.

On Some Double-Series InequalitiesDec 19 2011We study certain double--series inequalities, which are motivated by weighted Hardy inequalities.

A note on $l^2$ norms of weighted mean matricesJan 24 2007Jun 11 2007We give a proof of Cartlidge's result on the $l^{p}$ operator norms of weighted mean matrices for $p=2$ on interpreting the norms as eigenvalues of certain matrices.

Distinguished theta representations for certain covering groupsFeb 04 2016Oct 06 2017For Brylinski-Deligne covering groups of an arbitrary split reductive group, we consider theta representations attached to certain exceptional genuine characters. The goal of the paper is to determine when a theta representation has exactly a one-dimensional ... More

Differentiating the production mechanisms of the Higgs-like resonance using inclusive observables at hadron collidersAug 25 2013Feb 20 2014We present a study on differentiating direct production mechanisms of the newly discovered Higgs-like boson at the LHC based on several inclusive observables. The ratios introduced reveal the parton constituents or initial state radiations involved in ... More

The Maurer-Cartan structure of BRST differentialOct 10 2004In this paper, we construct a new sequence of generators of the BRST complex and reformulate the BRST differential so that it acts on elements of the complex much like the Maurer-Cartan differential acts on left-invariant forms. Thus our BRST differential ... More

Chain extensions of D-algebras and their applicationsNov 21 2003In order to unify the methods which have been applied to various topics such as BRST theory of constraints, Poisson brackets of local functionals, and certain developments in deformation theory, we formulate a new concept which we call the {\it chain ... More

Analytical Estimation of the Beam-Beam Interaction Limited Dynamic Apertures and Lifetimes in e^+e^- Circular CollidersDec 22 2000Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. 1, in this paper we investigate analytically the ... More

The lowest two-sided cell of weighted Coxeter groups of rank 3Jan 01 2019Mar 22 2019In this paper, we give precise description for the lowest lowest two-sided cell c_{0} and the left cells in it for a weighted Coxeter group of rank 3. Then we show conjectures P1-P15 and \widetilde{P} hold for c_{0} and do some calculation for the based ... More

Probing light-quark Yukawa couplings via hadronic event shapes at lepton collidersAug 05 2016Jan 11 2018We propose a novel idea for probing the Higgs boson couplings through the measurement of hadronic event shape distributions in the decay of the Higgs boson at lepton colliders. The method provides a unique test of the Higgs boson couplings and of QCD ... More

Hypoelliptic Diffusion Maps I: Tangent BundlesMar 17 2015We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE, ISOMAP, Laplacian ... More

Comment on "Cryptanalysis and improvement of multiparty quantum secret sharing schemes"Jul 22 2011We show that, using Wang et al. attack [T.-y. Wang, Q.-y. Wen, F. Gao, S. Lin, F.-c. Zhu, Phys. Lett. A 373 (2008) 65], the first agent and the last agent cannot eavesdrop all the secret messages in Zhang et al. QSSCM scheme [Z.-j. Zhang, G. Gao, X. Wang, ... More

A discrete model of energy-conserved wavefunction collapseMar 30 2013Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our macroscopic experience. ... More

Descriptive Control Theory: A ProposalSep 11 2014Sep 14 2014Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world systems consists ... More

A conjecture on the origin of dark energyJan 25 2010Jul 16 2011The physical origin of holographic dark energy (HDE) is investigated. The main existing explanations, namely the UV/IR connection argument of Cohen et al, Thomas' bulk holography argument, and Ng's spacetime foam argument, are shown to be not satisfactory. ... More

Dictionary for Sparse Representation of Chirp Echo in Broadband RadarAug 01 2010Aug 03 2010A new dictionary for sparse representation of chirp echo in broadband radar is put forward in this paper. Different with chirplet decomposition which decomposes echo in time-frequency plane, the dictionary transforms the sparsity of target observed by ... More

A Note On Mixed Mean InequalitiesSep 17 2007We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.

Hardy-type Inequalities Via Auxiliary SequencesJan 03 2007May 25 2007We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.

Generic rank of Betti map and unlikely intersectionsOct 30 2018Let $\mathcal{A} \rightarrow S$ be an abelian scheme over an irreducible variety over $\mathbb{C}$ of relative dimension $g$. For any simply-connected subset $\Delta$ of $S^{\mathrm{an}}$ one can define the Betti map from $\mathcal{A}_{\Delta}$ to $\mathbb{T}^{2g}$, ... More

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theorySep 20 2013We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component ... More

2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinementDec 25 2012Density oscillations of confined one-dimensional Fermi gases of contact repulsive interactions in a continuous space are discussed within Bethe-ansatz-based spin-density-functional theory. The results are compared against the exact analytical and the ... More

Effects of disorder on atomic density waves and spin-singlet dimers in one-dimensional optical latticesMar 15 2008Aug 27 2008Using the Bethe-ansatz density-functional theory, we study a one-dimensional Hubbard model of confined attractively interacting fermions in the presence of a uniformly distributed disorder. The strongly-correlated Luther-Emery nature of the attractive ... More

Non L-space integral homology 3-spheres with no nice orderingsSep 24 2016This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.

Extensions of Perron-Frobenius TheoryAug 16 2012The classical Perron-Frobenius theory asserts that for two matrices $A$ and $B$, if $0\leq B \leq A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$. This was recently extended in Bernik et al. (2012) to positive operators on $L_p(\mu)$ with either ... More

The bijection between exceptional subcategories and non-crossing partitionsJan 28 2016This note discusses the bijection between the exceptional subcategories of representations of quivers and generalized non-crossing partitions of Weyl groups. We give a new proof of the Ingalls-Thomas-Igusa-Schiffler bijection by using the exchange property ... More

On Thurston's core entropy algorithmNov 20 2015The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant extending topological entropy for real maps to complex polynomials, whence providing a new tool to study the parameter space of polynomials. The base is a combinatorial ... More

Everyone can understand quantum mechanicsJan 06 2000We show that everyone can understand quantum mechanics, only if he rejects the following prejudice, namely classical continuous motion (CCM) is the only possible and objective motion of particles.

Conserved cosmological perturbation in Galileon modelsJun 01 2011Oct 17 2011We prove the existence of a fully nonlinear conserved curvature perturbation on large scales in Galileon-type scalar field models in two approaches. The first approach is based on the conservation of energy-momentum tensor of the Galileon field, which ... More

On the Ohno-Nakagawa TheoremAug 02 2016In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of $L$-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky \& Wright's Theorem ... More

Cosmological Perturbations and Non-Gaussianities in Hořava-Lifshitz GravityApr 27 2009May 03 2009We investigate cosmological perturbations and non-gaussianities in Ho\v{r}ava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in Ho\v{r}ava theory is naturally scale-invariant, ignoring the details of the expansion of the universe. ... More

Using k-nearest neighbors to construct cancelable minutiae templatesAug 29 2016Aug 30 2016Fingerprint is widely used in a variety of applications. Security measures have to be taken to protect the privacy of fingerprint data. Cancelable biometrics is proposed as an effective mechanism of using and protecting biometrics. In this paper we propose ... More

The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne ExtensionsOct 28 2014We firstly discuss properties of the L-group for Brylinski-Deligne (BD) extensions constructed by M. Weissman. Secondly, the Gindikin-Karpelevich (GK) formula for arbitrary BD extensions is computed and expressed in terms of naturally defined elements ... More

The Residual Spectrum of Mp_4(A_k)Dec 04 2012We compute the residual spectrum of the global metaplectic group Mp_4(A_k), by using the theory of Eisenstein series. The residual spectra obtained are interpreted as near equivalence classes in the framework of the Arthur conjecture.

The Diffusion Geometry of Fibre BundlesFeb 07 2016Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph associated with ... More

Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential NonlinearityFeb 19 2019In this work, we consider the one dimensional very singular fourth-order equation for solid-on-solid model in attachment-detachment-limit regime with exponential nonlinearity $$h_t = \nabla \cdot (\frac{1}{|\nabla h|} \nabla e^{\frac{\delta E}{\delta ... More

Non-Gaussian Random Matrix Models for Two-faced Families of Random Variables Having Bi-free Central Limit DistributionsJun 14 2018Jun 21 2018In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a two-faced family of random variables having a bi-free central limit distribution. We prove that, under modest conditions weaker than independence, ... More

Characteristics of highly excited diatomic rovibrational spectra and slow atomic collisionsMay 25 2000We show that the highly excited rovibrational spectra of a diatomic molecule and the closely related slow atomic collision processes contain more systematics and require less parameters to characterize than the Rydberg spectrum of an atom. In the case ... More

Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonanceMay 30 2011Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances ... More

Full blow-up range for co-rotaional wave maps to surfaces of revolutionSep 02 2014We construct blow-up solutions of the energy critical wave map equation on $\mathbb{R}^{2+1}\to \mathcal N$ with polynomial blow-up rate ($t^{-1-\nu}$ for blow-up at $t=0$) in the case when $\mathcal{N}$ is a surface of revolution. Here we extend the ... More

Modified Entropic ForceJan 26 2010Apr 19 2010The theory of statistical thermodynamics tells us the equipartition law of energy does not hold in the limit of very low temperatures. It is found the Debye model is very successful in explaining the experimental results for most of the solid objects. ... More

Scalar Field, Four Dimensional Spacetime Volume and the Holographic Dark EnergyAug 30 2011Sep 05 2011We explore the cosmic evolution of a scalar field which is identified with the four dimensional spacetime volume. Given a specific form for the Lagrangian of the scalar field, a new holographic dark energy model is present. The energy density of dark ... More

Extensions of Copson's inequalitiesJan 04 2012We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.

Finite Sections of Weighted Carleman's InequalityJun 30 2007We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.

Some extensions of Diananda's inequalityJul 17 2018Let $M_{n,r}=(\sum_{i=1}^{n}q_ix_i^r)^{\frac {1}{r}}, r \neq 0$ and $M_{n,0}=\lim_{r \rightarrow 0}M_{n,r}$ be the weighted power means of $n$ non-negative numbers $x_i$ with $q_i > 0$ satisfying $\sum^n_{i=1}q_i=1$. For a real number $\alpha$ and mutually ... More

The first k-regular subgraph is largeMar 21 2013Feb 04 2014We prove that for sufficiently large k, there exist $0\le\sigma_k\le\eps_k\to 0$ as $k\to\infty$, such that asymptotically almost surely the first k-regular subgraph appeared in the random graph process where one edge is added at a time has size between ... More

On $l^2$ norms of some weighted mean matricesFeb 24 2008Mar 11 2008We give another proof of a result of Bennett on the $l^{p}$ operator norms of some weighted mean matrices for the case $p=2$ and we also present some related results.

4d-5d connection and the holomorphic anomalyJan 03 2007In this short note, we report a curious appearance of the recently discovered 4d-5d connection of extremal blackholes in the topological string B-model. The holomorphic anomaly equations in the Schrodinger-Weil representation are written {\it formally} ... More

A complete monotonicity result involving the $q$-polygamma functionsAug 05 2015Jan 21 2016We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

Analysis of the parallel peeling algorithm: a short proofFeb 28 2014A recent paper by Jiang, Mitzenmacher and Thaler upper bounded the number of rounds needed in a parallel peeling algorithm applied to a random hypergraph whose edge density is below the k-core emergence threshold. I gave a very short proof of their result ... More

Cortex Neural Network: learning with Neural Network groupsApr 10 2018Neural Network has been successfully applied to many real-world problems, such as image recognition and machine translation. However, for the current architecture of neural networks, it is hard to perform complex cognitive tasks, for example, to process ... More

A special point problem of André-Pink-Zannier in the universal family of abelian varietiesJul 21 2014Nov 06 2015The Andr\'e-Pink-Zannier conjecture concerns the intersection of subvarieties and the generalized Hecke orbit of a given point in mixed Shimura varieties. It is part of the Zilber-Pink conjecture. In this paper we focus on the universal family of principally ... More

Some completely monotonic functions involving the polygamma functionsDec 02 2010Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

Generalized Bump-Hoffstein conjecture for coverings of the general linear groupsDec 14 2016Mar 02 2017In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special cases.

Functors of wrapped Fukaya categories from Lagrangian correspondencesDec 01 2017Apr 11 2018We study wrapped Floer theory on product Liouville manifolds and prove that the wrapped Fukaya categories defined with respect to two different kinds of natural Hamiltonians and almost complex structures are equivalent. The implication is we can do quilted ... More

Wrapped Floer cohomology and Lagrangian correspondencesMar 11 2017We study Lagrangian correspondences between Liouville manifolds and construct functors between wrapped Fukaya categories. The study naturally brings up the question on comparing two versions of wrapped Fukaya categories of the product manifold, which ... More

An argument for psi-ontology in terms of protective measurementsAug 31 2015The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality ... More

A constructive proof of the Wedderburn-Artin theoremMar 19 2014Apr 10 2014In this short note, we use the idempotent decomposition to give an explicit isomorphism from a semisimple Artinian ring to an external direct sum of finite full matrix rings over division rings.

The Meaning of the Wave Function: In Search of the Ontology of Quantum MechanicsNov 07 2016The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, ... More

The boundness of weighted Coxeter groups of rank 3Jul 08 2016Mar 22 2019We prove that a weighted Coxeter group (W,S,L) is bounded in the sense of G.Lusztig if the rank of W is 3.

On the representations of $N(T)$ via prime numbersMar 23 2010Apr 19 2010In this paper, under the RH, we give a new representation of $N(T)$ in term of sum of the logarithms of the powers of prime numbers and compute the difference between the new representation and Guinand representation.

Massive charged-current coefficient functions in deep-inelastic scattering at NNLO and impact on strange-quark distributionsOct 11 2017Mar 24 2018We present details on calculation of next-to-next-to-leading order QCD corrections to massive charged-current coefficient functions in deep-inelastic scattering. Especially we focus on the application to charm-quark production in neutrino scattering on ... More

Simple Sheaves for Knot ConormalsMay 02 2018We classify the simple sheaves microsupported along the conormal bundle of a knot. We also establish a correspondence between simple sheaves up to local systems and augmentations, explaining the underlying reason why knot contact homology representations ... More

Status on nucleon electromagnetic form factorsJan 09 2003Sep 11 2003Nucleon electromagnetic form factors are fundamental quantities related to the charge and magnetization distributions inside the nucleon. Understanding the nucleon electromagnetic structure in terms of the underlying quark and gluon degrees of freedom ... More

A note on torsion Breuil modules in the case er=p-1Oct 15 2014We prove that the category of unipotent torsion Breuil modules is an abelian category, under the condition er=p-1, r<p-1. As a side product, we point out that some of the approaches in \cite{Car08} on torsion log-syntomic cohomologies cannot be generalized ... More

Stochastic homogenization of certain nonconvex Hamilton-Jacobi equationsMar 23 2018In this paper, we prove the stochastic homogenization of certain nonconvex Hamilton-Jacobi equations. The nonconvex Hamiltonians, which are generally uneven and inseparable, are generated by a sequence of quasiconvex Hamiltonians and a sequence of quasiconcave ... More

Random homogenization of coercive Hamilton-Jacobi equations in 1dJul 25 2015In this paper, we will prove the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimensional case. This extends the result of Armstrong, Tran and Yu when the Hamiltonian has a separable form $H(p,x,\omega)=H(p)+V(x,\omega)$ ... More

Crystalline liftings and weight part of Serre's conjectureApr 06 2015Apr 29 2015We prove some new cases of weight part of Serre's conjecture for mod p Galois representations associated to automorphic representations on unitary groups U(d), by (partially) generalizing the main local results of Gee-Liu-Savitt to higher dimensions. ... More