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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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 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

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

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.

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

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

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

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.

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 $$ A_n^{(\alpha)}(x)=\sum_{k=0}^n\binom{n}{k}^{\alpha}\binom{n+k}{k}^{\alpha}x^k.$$

Lehmer's type congruences for lacunary harmonic sumsMay 07 2009Oct 10 2009In this paper, we study the Lehmer's type congruences for lacunary harmonic sums.

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.

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

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

q-Analogue of Gauss' Divisibility TheoremApr 05 2008We give a q-analogue of Gauss' divisibility theorem

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

Calculating Vacuum Energy as a Possible Explanation of the Dark EnergyJan 20 2011Jun 15 2011We carried out a study of the properties of the $\lambda \phi^4$ field solutions. By constructing Gaussian wave packets to calculate the $S$ matrix, we show that the probability of the vacuum unbroken state transfers to the broken state is about $10^{-52}$. ... More

Meson Mass Spectrum of Heavy-Light Quarks Combinations with Dirac EquationJun 15 2011Nov 23 2011We use the Dirac equation to study the mass spectrum of mesons with heavy-light quark combinations. First we study the Dirac equation with spherically symmetry and funnel potential, and apply them on the hydrogen-like atom problem to check the correctness ... More

Propagation of Delayed Lattice Differential Equations without Local QuasimonotonicityMay 06 2014This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice ... More

Collaborative Recommendation with Auxiliary Data: A Transfer Learning ViewJul 09 2014Intelligent recommendation technology has been playing an increasingly important role in various industry applications such as e-commerce product promotion and Internet advertisement display. Besides users' feedbacks (e.g., numerical ratings) on items ... More

The redshift and geometrical aspect of photonsApr 09 2007The cosmological redshift phenomenon can be described by the dark matter field fluid model, the results deduced from this model agree very well with the observations. The observed cosmological redshift of light depends on both the speed of the emitter ... More

On consecutive happy numbersJul 08 2006Jul 27 2006Let e>=1 and b>=2 be integers. For a positive integer n=\sum_{j=0}^ka_jb^j with 0<=a_j<b, define T_{e,b}(n)=\sum_{j=0}^ka_j^e. n is called (e,b)-happy if T_{e,b}^r(n)=1 for some r>=0, where T_{e,b}^r is the r-th iteration of T_{e,b}. In this paper, we ... More

A q-analogue of Lehmer's congruenceJul 25 2005Aug 17 2005We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.

jQuery.Feyn: Drawing Feynman Diagrams with SVGNov 26 2013jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external graphics, ... More

Robust Spectral Detection of Global Structures in the Data by Learning a RegularizationSep 09 2016Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or ... More

Rational homotopy theory and nonnegative curvatureJun 29 2001In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds ... More

Regularity of Solution to Axis-symmetric Navier-Stokes Equations with a Slightly Supercritical ConditionOct 23 2014Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of Chen-Strain-Tsai-Yau, ... More

Regularity and geometric character of solution of a degenerate parabolic equationApr 07 2015This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $u_{t}=\Delta{}u^{m}$. Our main objective is to improve the H$\ddot{o}$lder estimate obtained by pioneers and then, to ... 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

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

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

On the number of distinct prime factors of $nj+a^hk$Jul 12 2009Aug 06 2009Let $\omega(n)$ denote the number of distinct prime factors of $n$. Then for any given $K\geq 2$, small $\epsilon>0$ and sufficiently large (only depending on $K$ and $\epsilon$) $x$, there exist at least $x^{1-\epsilon}$ integers $n\in[x,(1+K^{-1})x]$ ... More

On the integers not of the form $p+2^a+2^b$May 25 2009Jul 07 2009We prove that |{1<=y<=x: y is odd and not of the form p+2^a+2^b}|>>x^{1-\epsilon} for any \epsilon>0, where the implied constant only depends on \epsilon.

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

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

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

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.

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.

On simultaneous conjugation of permutationsOct 21 2018In this paper we give an affirmative answer to a conjecture proposed by Danny Neftin, that is, if the commutator of two permutations has at least n-4 fixed points where two permutations are in degree n symmetric group, then there exists a permutation ... More

A Nonlinear Singular Diffusion Equation with SourceApr 06 2015In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which depends on initial ... 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

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

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.

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

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

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 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 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

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

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

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

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