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Joint Blocklength and Location Optimization for URLLC-enabled UAV Relay SystemsJan 16 2019This letter considers the unmanned aerial vehicle (UAV)-enabled relay system to deliver command information under ultra-reliable and low-latency communication (URLLC) requirements. We aim to jointly optimize the blocklength allocation and the UAV's location ... More

On Consideration of Content Preference and Sharing Willingness in D2D Assisted OffloadingFeb 01 2017Device-to-device (D2D) assisted offloading heavily depends on the participation of human users. The content preference and sharing willingness of human users are two crucial factors in the D2D assisted offloading. In this paper, with consideration of ... More

Pricing-based Distributed Energy-Efficient Beamforming for MISO Interference ChannelsDec 15 2015In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) for multi-input single-output (MISO) interference channels (ICs) which is well acknowledged as general models of heterogeneous networks (HetNets), multicell ... More

Energy Efficient Transmission for Multicast Services in MISO Distributed Antenna SystemsMar 01 2016This paper aims to solve the energy efficiency (EE) maximization problem for multicast services in a multiple-input single-output (MISO) distributed antenna system (DAS). A novel iterative algorithm is proposed, which consists of solving two subproblems ... More

Resource Allocation for D2D Communications Underlaying a NOMA-Based Cellular NetworkOct 14 2017This letter investigates the power control and channel assignment problem in device-to-device (D2D) communications underlaying a non-orthogonal multiple access (NOMA) cellular network. With the successive interference cancellation decoding order constraints, ... More

Optimal Fairness-Aware Time and Power Allocation in Wireless Powered Communication NetworksFeb 14 2018In this paper, we consider the sum $\alpha$-fair utility maximization problem for joint downlink (DL) and uplink (UL) transmissions of a wireless powered communication network (WPCN) via time and power allocation. In the DL, the users with energy harvesting ... More

Energy Efficient Resource Allocation in Machine-to-Machine Communications with Multiple Access and Energy Harvesting for IoTNov 29 2017This paper studies energy efficient resource allocation for a machine-to-machine (M2M) enabled cellular network with non-linear energy harvesting, especially focusing on two different multiple access strategies, namely non-orthogonal multiple access (NOMA) ... More

User-centric C-RAN Architecture for Ultra-dense 5G Networks: Challenges and MethodologiesSep 20 2017Ultra-dense networks (UDN) constitute one of the most promising techniques of supporting the 5G mobile system. By deploying more small cells in a fixed area, the average distance between users and access points can be significantly reduced, hence a dense ... More

Energy Efficiency Optimization for MIMO Distributed Antenna SystemsNov 12 2015In this paper, we propose a transmit covariance optimization method to maximize the energy efficiency (EE) for a single-user distributed antenna system, where both the remote access units (RAUs) and the user are equipped with multiple antennas. Unlike ... More

Joint Time Allocation and Power Control in Multi-Cell Networks with Load Coupling: Energy Saving and Rate ImprovementJul 01 2017In this paper, we consider the problems of minimizing sum power and maximizing sum rate for multi-cell networks with load coupling, where coupling relation occurs among cells due to inter-cell interference. This coupling relation is characterized by the ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

Unified Offloading Decision Making and Resource Allocation in ME-RANMay 29 2017Jun 26 2018In order to support communication and computation cooperation, we propose ME-RAN architecture, which consists of mobile edge cloud (ME) as the computation provision platform and radio access network (RAN) as the communication interface. Cooperative offloading ... More

Tradeoff Caching Strategy of Outage Probability and Fronthaul Usage in Cloud-RANNov 08 2016Feb 05 2018In this paper, optimal content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in cloud radio access network (Cloud-RAN). At first, an accurate closed form expression of the outage probability conditioned ... More

Tradeoff Caching Strategy of Outage Probability and Fronthaul Usage in Cloud-RANNov 08 2016In this paper, optimal content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in cloud radio access network (Cloud-RAN). At first, an accurate closed form expression of the outage probability conditioned ... More

Robust Beamforming Design for Ultra-dense User-Centric C-RAN in the Face of Realistic Pilot Contamination and Limited FeedbackApr 06 2018The ultra-dense cloud radio access network (UD-CRAN), in which remote radio heads (RRHs) are densely deployed in the network, is considered. To reduce the channel estimation overhead, we focus on the design of robust transmit beamforming for user-centric ... More

Joint Pilot Allocation and Robust Transmission Design for Ultra-dense User-centric TDD C-RAN with Imperfect CSIOct 22 2017This paper considers the unavailability of complete channel state information (CSI) in ultra-dense cloud radio access networks (C-RANs). The user-centric cluster is adopted to reduce the computational complexity, while the incomplete CSI is considered ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019Feb 13 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

Compressive Sensing Based User Clustering for Downlink NOMA Systems with Decoding PowerMar 13 2018This letter investigates joint power control and user clustering for downlink non-orthogonal multiple access systems. Our aim is to minimize the total power consumption by taking into account not only the conventional transmission power but also the decoding ... More

Joint User Selection and Energy Minimization for Ultra-Dense Multi-channel C-RAN with Incomplete CSIMay 17 2017This paper provides a unified framework to deal with the challenges arising in dense cloud radio access networks (C-RAN), which include huge power consumption, limited fronthaul capacity, heavy computational complexity, unavailability of full channel ... More

Joint Precoding and RRH selection for User-centric Green MIMO C-RANFeb 10 2017This paper jointly optimizes the precoding matrices and the set of active remote radio heads (RRHs) to minimize the network power consumption (NPC) for a user-centric cloud radio access network (C-RAN), where both the RRHs and users have multiple antennas ... More

Cache Placement in Two-Tier HetNets with Limited Storage Capacity: Cache or Buffer?Jun 06 2018In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay ... More

Power Control for Multi-Cell Networks with Non-Orthogonal Multiple AccessJun 14 2017Nov 02 2017In this paper, we investigate the problems of sum power minimization and sum rate maximization for multi-cell networks with non-orthogonal multiple access. Considering the sum power minimization, we obtain closed-form solutions to the optimal power allocation ... More

Multiple Antenna Assisted Non-Orthogonal Multiple AccessJan 24 2018Non-orthogonal multiple access (NOMA) is potentially capable of circumventing the limitations of the classic orthogonal multiple access schemes, hence it has recently received significant research attention both in industry and academia. This article ... More

Reconfigurable Antenna Multiple Access for 5G mmWave SystemsMar 27 2018This paper aims to realize a new multiple access technique based on recently proposed millimeter-wave reconfigurable antenna architectures. To this end, first we show that integration of the existing reconfigurable antenna systems with the well-known ... More

Improving Wireless Physical Layer Security via D2D CommunicationSep 08 2018This paper investigates the physical layer security issue of a device-to-device (D2D) underlaid cellular system with a multi-antenna base station (BS) and a multi-antenna eavesdropper. To investigate the potential of D2D communication in improving network ... More

Robust Beamforming with Pilot Reuse Scheduling in a Heterogeneous Cloud Radio Access NetworkApr 23 2018This paper considers a downlink ultra-dense heterogeneous cloud radio access network (H-CRAN) which guarantees seamless coverage and can provide high date rates. In order to reduce channel state information (CSI) feedback overhead, incomplete inter-cluster ... More

Widely-Linear Precoding for Large-Scale MIMO with IQI: Algorithms and Performance AnalysisFeb 28 2017In this paper we study widely-linear precoding techniques to mitigate in-phase/quadrature-phase (IQ) imbalance (IQI) in the downlink of large-scale multiple-input multiple-output (MIMO) systems. We adopt a real-valued signal model which takes into account ... More

Joint Altitude, Beamwidth, Location and Bandwidth Optimization for UAV-Enabled CommunicationsJun 06 2018This letter investigates an uplink power control problem for unmanned aerial vehicles (UAVs) assisted wireless communications. We jointly optimize the UAV's flying altitude, antenna beamwidth, UAV's location and ground terminals' allocated bandwidth and ... More

Totally Distributed Energy-Efficient Transmission in MIMO Interference ChannelsMar 13 2015Jul 01 2015In this paper, we consider the problem of maximizing the energy efficiency (EE) for multi-input multi-output (MIMO) interference channels, subject to the per-link power constraint. To avoid extensive information exchange among all links, the optimization ... More

Robust Transmission Design for Multi-Cell D2D Underlaid Cellular NetworksApr 14 2018This paper investigates the robust transmission design (RTD) of a multi-cell device-to-device (D2D) underlaid cellular network with imperfect channel state information (CSI). The bounded model is adopted to characterize the CSI impairment and the aim ... More

Power-and Rate-Adaptation Improves the Effective Capacity of C-RAN for Nakagami-$m$ Fading ChannelsApr 06 2017Jun 13 2018We propose a power-and rate-adaptation scheme for cloud radio access networks (C-RANs), where each radio remote head (RRH) is connected to the baseband unit (BBU) pool through optical links. The RRHs jointly support the users by efficiently exploiting ... More

Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More

Secure Communication through Wireless-Powered Friendly Jamming: Jointly Online Optimization over Geography, Energy and TimeFeb 17 2016Exploring the interference-emitting friendly jammers to protect the sensitive communications in the presence of eavesdroppers has increasingly being investigated in literature. In parallel, scavenging energy from abient radio signals for energy-constrained ... More

On a conjecture of SunMay 24 2010May 25 2010We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.

A note on enumerating colored integer partitionsSep 21 2015In this short note, we give basic enumerative results on colored integer partitions.

A generalized Tian-Todorov theoremOct 27 2013May 24 2016Let X be a smooth proper variety with torsion canonical bundle. Suppose L is a line bundle on X. We prove the pair (X,L) is unobstructed if one of the following conditions holds, (1) the line bundle L is ample, (2) the fundamental group {\pi}_1(X) of ... More

Exact Lagrangian Fillings of Legendrian $(2,n)$ torus linksJul 11 2016For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and K\'alm\'an constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise ... More

Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Feb 21 2017Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More

Landslide Monitoring based on Terrestrial Laser Scanning: A Novel Semi-automatic WorkflowSep 01 2018In this paper, we propose a workflow that uses Terrestrial Laser Scanning(TLS) to semi-automatically monitor landslide and then test it in practice. Firstly, several groups of TLS stations are set on different time to collect the raw point cloud of the ... More

SAT is a problem with exponential complexity measured by negentropyDec 03 2014Sep 21 2015In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of computation and ... More

Colour Dependence of the Distribution of IRAS Galaxies revealed by Multifractal MeasuresApr 11 2006Jul 04 2006Multifractal measures are applied to three IRAS galaxy subsamples selected by colour from the PSCz catalogue. As shown by generalised dimension spectrum, hot IRAS galaxies are found less clustered than cold galaxies, but the difference is very weak. An ... More

A Proof of Milnor conjecture in dimension 3Mar 23 2017We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] that relies on minimal surface theory.

Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groupsSep 26 2018Jan 31 2019We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $\widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $\widetilde{M}$ at infinity is ... More

Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groupsApr 06 2018In this paper we show that the leading coefficients $\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in the affine Weyl group of type $\widetilde{B_n}$ can be $n$; in the cases of types $\widetilde{C_n}$ and $\widetilde{D_n}$ they can ... More

Vague partition, fuzzy sets and their axiomatical foundationsJun 24 2015Based on the in-depth analysis of the nature and features of vague phenomenon, this paper focuses on establishing the axiomatical foundation of the membership degree theory for vague phenomenon, presents an axiomatic system of governing membership degrees ... More

Spaces of conics on low degree complete intersectionsOct 13 2013Jan 09 2017Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criterion ... More

Derived equivalences for Cohen-Macaulay Auslander algebrasSep 20 2010Mar 29 2011Let $A$ and $B$ be Gorenstein Artin algebras of Cohen-Macaulay finite type. We prove that, if $A$ and $B$ are derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent.

A remark on Zoloterav's theoremJan 02 2006Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative residue of x modulo ... More

A generalization of Carlitz's congruenceMar 21 2006Jul 03 2006In this paper, we propose a generalization of a congruence due to Carlitz.

Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent dampingSep 20 2016We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will investigate the global ... More

Non-backtracking operator for Ising model and its application in attractor neural networksSep 10 2014The non-backtracking operator was recently shown to give a redemption for spectral clustering in sparse graphs. In this paper we consider non-backtracking operator for Ising model on a general graph with a general coupling distribution by linearizing ... More

A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifoldsOct 26 2004Dec 15 2004We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It's also proved that the local Gopakumar-Vafa invariants of a given class at large genus vanish.

Factors of Some Lacunary q-Binomial SumsJan 28 2012Jun 03 2012In this paper, we prove a divisibility result for the lacunary $q$-binomial sum $$ \sum_{k\equiv r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}. $$

p-adic deformation of graph cyclesOct 12 2016Oct 14 2016In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. We give a positive answer to Bloch-Esnault-Kerz conjecture for some graph cycles if the infinitesimal Torelli theorem holds.

SAT problem and statistical distanceFeb 26 2015Sep 22 2015In this paper with two equivalent representations of the information contained by a SAT formula, the reason why string generated by succinct SAT formula can be greatly compressed is firstly presented based on Kolmogorov complexity theory. Then what strings ... More

Magnetosphere structure of a Kerr black hole: marginally force-free equatorial boundary conditionJul 15 2018Sep 23 2018The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics ... More

Emergence from Symmetry: A New Type of Cellular AutomataMar 17 2010Jul 25 2010In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, ... More

Automorphism and Cohomology I: Fano variety of lines and CubicNov 17 2015Oct 12 2016In this paper, we prove a general principle of lifting an automorphism from positive characteristic to zero characteristic. We based on the principle to prove the automorphism group of Fano variety of cubic threefold (fourfold) acts on its cohomology ... More

Relative derived equivalences and relative homological dimensionsJan 25 2014Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$ of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the Verdier's quotient category to get a relative derived category, where he localized with respect ... More

Spectral estimation of the percolation transition in clustered networksOct 04 2017There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network ... More

T2Ku: Building a Semantic Wiki of MathematicsJan 27 2012We introduce T2Ku, an open source project that aims at building a semantic wiki of mathematics featuring automated reasoning(AR) techniques. We want to utilize AR techniques in a way that truly helps mathematical researchers solve problems in the real ... More

Evaluating accuracy of community detection using the relative normalized mutual informationJan 15 2015Oct 28 2015The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give ... More

Inference of kinetic Ising model on sparse graphsJul 23 2012Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs ... More

On divisibility of sums of Apery polynomialsAug 07 2011For any positive integers $m$ and $\alpha$, we prove that $$\sum_{k=0}^{n-1}\epsilon^k(2k+1)A_k^{(\alpha)}(x)^m\equiv0\pmod{n}, $$ where $\epsilon\in\{1,-1\}$ and $$ A_n^{(\alpha)}(x)=\sum_{k=0}^n\binom{n}{k}^{\alpha}\binom{n+k}{k}^{\alpha}x^k.$$

First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)Oct 11 2015We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve ... More

The evolution of the Earth-Moon system based on the dark matter field fluid modelApr 01 2007Jan 13 2008The evolution of Earth-Moon system is described by the dark matter field fluid model proposed in the Meeting of Division of Particle and Field 2004, American Physical Society. The current behavior of the Earth-Moon system agrees with this model very well ... More

Local mixing on abelian covers of hyperbolic surfaces with cuspsDec 16 2017We prove the local mixing theorem for geodesic flows on abelian covers finite volume hyperbolic surfaces with cusps, which is a continuation of the work of Oh-Pan. We also describe applications to counting problems and the prime geodesic theorem.

A note on enumerating colored integer partitionsSep 21 2015Mar 28 2018In this short note, we give basic enumerative results on colored integer partitions.

Tensor Transpose and Its PropertiesNov 06 2014Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor ... More

Growth Estimates and Integral Representations of Harmonic and Subharmonic FunctionsJun 09 2009There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization of harmonic ... More

Using Malware Self-Defence Mechanism to Harden Defence and Remediation ToolsJan 06 2018Malware are becoming a major problem to every individual and organization in the cyber world. They are advancing in sophistication in many ways. Besides their advanced abilities to penetrate and stay evasive against detection and remediation, they have ... More

Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groupsOct 16 2017Oct 18 2017We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature. We show that if there is an integer $k$ such that any tangent cone at infinity of the Riemannian universal cover of $M$ is a metric cone, whose maximal Euclidean ... More

Balance functions of (un)identified hadrons in Pb--Pb, p--Pb, and pp collisions at the LHCJul 26 2018In ultrarelativistic heavy-ion collisions, correlations of particles with opposite quantum numbers provide insight into quark production mechanisms and time scales, collective motion, and re-scattering in the hadronic phase. The longitudinal and azimuthal ... More

Spectral Precoding for Out-of-band Power Reduction under Condition Number Constraint in OFDM-Based SystemNov 12 2015Due to the flexibility in spectrum shaping, orthogonal frequency division multiplexing (OFDM) is a promising technique for dynamic spectrum access. However, the out-of-band (OOB) power radiation of OFDM introduces significant interference to the adjacent ... More

The Fontaine-Mazur conjecture in the residually reducible caseJan 22 2019We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles ... More

The Roles of Familiarity Design in Active AgeingJan 26 2016The elderly often struggle when interacting with technologies. This is because the software and hardware components of the technologies are not familiar to the elderly's mental model. This is a lack of empirical studies about how the concept of familiarity ... More

Generalized Auslander-Reiten conjecture and derived equivalencesSep 25 2011In this note, we prove that the generalized Auslander-Reiten conjecture is preserved under derived equivalences between Artin algebras.

Adaptive image processing: a bilevel structure learning approach for mixed-order total variation regularizersMar 16 2019A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous optimization with ... More

Note on polynomial recurrenceFeb 25 2015Feb 26 2015Let $(X,\mu,T_1,...,T_l)$ be a measure-preserving system with those $T_i$ are commuting. Suppose that the polynomials $p_1(t),...,p_{l}(t)\in\Z[t]$ with $p_j(0)=0$ have distinct degrees. Then for any $\epsilon>0$ and $A\subseteq X$ with $\mu(A)>0$, the ... More

A generalization of Wolstenholme's harmonic series congruenceAug 23 2006We give a generalization of Wolstenholme's harmonic series congruence for the Lucas sequences.

The Hilbert metric on Teichmüller space and EarthquakeMar 08 2017Hamenst\"adt gave a parametrization of the Teichm\"uller space of punctured surfaces such that the image under this parametrization is the interior of a polytope. In this paper, we study the Hilbert metric on the Teichm\"uller space of punctured surfaces ... More

On local solvability of nonlinear elliptic partial differential systems of principle type: the second orderJun 17 2012Jun 29 2013We prove results on solvability of nonlinear elliptic partial differential systems of principle type of second order. They are consequences of existence of non-radial solutions for nonlinear partial differential systems of Poisson type. As applications ... More

The augmentation category map induced by exact Lagrangian cobordismsJun 19 2016To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and ... More

Joining measures for horocycle flows on abelian coversJul 12 2016Jul 13 2016Let $S_0$ be a $\mathbb{Z}^d$-cover of a compact hyperbolic surface for $d=1,2$. We classify all locally finite joining measures for horocycle flows on the unit tangent bundle of $S_0\times S$ for any hyperbolic surface $S$. We will also discuss several ... More

A Lucas-type congruence for q-Delannoy numbersAug 09 2015We prove a Lucas-type congruence for q-Delannoy numbers.

Ergodic recurrence and bounded gaps between primesAug 14 2016Aug 19 2016Let $(X,B_X,\mu,T)$ be a measure-preserving probability system with $T$ is invertible. Suppose that $A\in B_X$ with $\mu(A)>0$ and $\epsilon>0$. For any $m\geq 1$, there exist infinitely many primes $p_0,p_1,\ldots,p_m$ with $p_0<\cdots<p_m$ such that ... More

A note on the Polignac numbersJun 09 2013Suppose that $k\geq 3.5\times 10^6$ and $\hH=\{h_1,\ldots,h_{k_0}\}$ is admissible. Then for any $m\geq 1$, the set $$ \{m(h_j-h_i):\,h_i<h_j\} $$ contains at least one Polignac number.

Rational Normal Curves on Low Degree Complete IntersectionsOct 13 2013May 24 2016This is the second in a sequence of papers on the geometry of spaces of rational normal curves on smooth complete intersections. For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli ... More

The fractional Brownian motion and the halo mass functionOct 16 2006The fractional Brownian motion with index $\alpha$ is introduced to construct the fractional excursion set model. A new mass function with single parameter $\alpha$ is derived within the formalism, of which the Press-Schechter mass function (PS) is a ... More

Equivariant Phantom mapsJun 29 2001A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of ... More

Having the H-space structure is not a generic propertyJun 29 2001In this note, we answer in negative a question posed by McGibbon about the generic property of H-space structure. In fact we verify the conjecture of Roitberg. Incidentally, the same example also answers in negative the open problem 10 in McGibbon.

The Very Basics of Higher-Spin TheoryFeb 13 2017These notes are based on two lectures given at the Twelfth Modave Summer School in Mathematical Physics 2016. The Fronsdal equation and action for both Minkowski and (A)dS backgrounds are discussed in detail.

Triviality and Split of Vector Bundles on Rationally Connected VarietiesOct 22 2013Feb 07 2014In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and only if the restrictions of the vector bundle to Schubert lines are trivial. ... More

p-adic deformation of graph cyclesOct 12 2016Mar 23 2017In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex projective manifolds. ... More

Remarks on 1-D Euler Equations with Time-Decayed DampingOct 27 2015We study the 1-d isentropic Euler equations with time-decayed damping \begin{equation} \left\{ \begin{aligned} &\partial_t \rho+\partial_x(\rho u)=0, \\ &\partial_t(\rho u)+ \partial_x(\rho u^2)+\partial_xp(\rho)=-\frac{\mu}{1+t}\rho u,\\ &\rho|_{t=0}=1+\varepsilon\rho_0(x),u|_{t=0}=\varepsilon ... More

Geometry of Rational Curves on Low degree Complete IntersectionsOct 13 2013Jan 15 2017For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli space \bar{M}_{0,m}(X,m)\rightarrow X^m and the forgetful functor F : \mathbb{F} \rightarrow \bar{M}_{0,m}. We prove that a general ... More

The Multiple Permutation Problem and Some ConjecturesJul 27 2010In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel approaches to ... More

On finite marked length spectral rigidity of hyperbolic cone surfaces and the Thurston metricMar 06 2017We study the geometry of hyperbolic cone surfaces, possibly with cusps or geodesic boundaries. We prove that any hyperbolic cone structure on a surface of non-exceptional type is determined up to isotopy by the geodesic lengths of a finite specific homotopy ... More

Arithmetic properties of q-Fibonacci numbers and q-Pell numbersAug 27 2005Aug 31 2005We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

Affine equivalence and saddle connection graphs of translation surfacesSep 14 2018To every translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the underlying translation surfaces. ... More