total 2813took 0.16s

A Neural Network Prediction Based Adaptive Mode Selection Scheme in Full-Duplex Cognitive NetworksApr 12 2019We propose a neural network (NN) predictor and an adaptive mode selection scheme for the purpose of both improving secondary user's (SU's) throughput and reducing collision probability to the primary user (PU) in full-duplex (FD) cognitive networks. SUs ... More

Transmission Capacity of Full-Duplex MIMO Ad-Hoc Network with Limited Self-Interference CancellationApr 29 2018Sep 09 2018In this paper, we propose a joint transceiver beamforming design to simultaneously mitigate self-interference (SI) and partial inter-node interference for full-duplex multiple-input and multiple-output ad-hoc network, and then derive the transmission ... More

Energy-Efficient Data Collection and Wireless Power Transfer Using A MIMO Full-Duplex UAVNov 22 2018In this paper, we propose a novel energy-efficient data collection and wireless power transfer (WPT) framework for internet of things (IoT) applications, via a multiple-input multiple-output (MIMO) full-duplex (FD) unmanned aerial vehicle (UAV). To exploit ... More

Energy Efficient Resource Allocation for Mobile-Edge Computation Networks with NOMASep 04 2018Feb 14 2019This paper investigates an uplink non-orthogonal multiple access (NOMA)-based mobile-edge computing (MEC) network. Our objective is to minimize the total energy consumption of all users including transmission energy and local computation energy subject ... More

Resource Allocation in Full-Duplex Mobile-Edge Computing Systems with NOMA and Energy HarvestingJul 31 2018This paper considers a full-duplex (FD) mobile-edge computing (MEC) system with non-orthogonal multiple access (NOMA) and energy harvesting (EH), where one group of users simultaneously offload task data to the base station (BS) via NOMA and the BS simultaneously ... More

Multi-Antenna Assisted Virtual Full-Duplex Relaying with Reliability-Aware Iterative DecodingJul 13 2017Oct 18 2017In this paper, a multi-antenna assisted virtual full-duplex (FD) relaying with reliability-aware iterative decoding at destination node is proposed to improve system spectral efficiency and reliability. This scheme enables two half-duplex relay nodes, ... More

Square Deviation Based Symbol-Level Selection for Virtual Full-Duplex Relaying NetworksJul 14 2017Nov 02 2017In this paper, a symbol-level selective transmission for virtual full-duplex (FD) relaying networks is proposed, which aims to mitigate error propagation effects and improve system spectral efficiency. The idea is to allow two half-duplex relays, mimicked ... More

Symbol-Level Selective Full-Duplex Relaying with Power and Location OptimizationDec 20 2017Jun 02 2018In this paper, a symbol-level selective transmission for full-duplex (FD) relaying networks is proposed to mitigate error propagation effects and improve system spectral efficiency. The idea is to allow the FD relay node to predict the correctly decoded ... More

On the Weak Solutions to Mixed Navier-Stokes-Darcy ModelAug 15 2016In this paper, an a priori estimate of weak solutions to the mixed Navier-Stokes-Darcy model with Beaver-Joseph-Saffman's interface condition is established. Based on this result, the existence and global uniqueness of the weak solution is obtained. Then ... More

On Transformations of Load-Store Maurer Instruction Set ArchitectureAug 19 2008Jan 20 2009In this paper, we study how certain conditions can affect the transformations on the states of the memory of a strict load-store Maurer ISA, when half of the data memory serves as the part of the operating unit.

Acyclic edge coloring of sparse graphsFeb 28 2012A proper edge coloring of a graph $G$ is called acyclic if there is no bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by $\chi'_a(G)$, is the least number of colors $k$ such that $G$ has an acyclic edge $k$-coloring. The maximum ... More

Agnostic Lane DetectionMay 02 2019Lane detection is an important yet challenging task in autonomous driving, which is affected by many factors, e.g., light conditions, occlusions caused by other vehicles, irrelevant markings on the road and the inherent long and thin property of lanes. ... More

A Deterministic Algorithm for Bridging Anaphora ResolutionNov 14 2018Previous work on bridging anaphora resolution (Poesio et al., 2004; Hou et al., 2013b) use syntactic preposition patterns to calculate word relatedness. However, such patterns only consider NPs' head nouns and hence do not fully capture the semantics ... More

On smooth moduli space of Riemann surfacesOct 10 2016Oct 14 2016In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $\mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$ The main theorem ... More

Quantified Differential Temporal Dynamic Logic for Verifying Properties of Distributed Hybrid SystemsJul 11 2012We combine quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with temporal logic for reasoning about the temporal behavior during their operation. Our logic supports verification of temporal ... More

On the canonical volume of 3-folds of general type with $P_{12}\geq 2$Jul 30 2014Let $V$ be a nonsingular projective 3-fold of general type. When the pluricanonical section index $\delta(V)>12$, Chen-Chen \cite{Chen3} has a complete list of the possibility for the weighted basket ${\mathbb B}(V)$. However the possibility of ${\mathbb ... More

Measuring Knowledge for Recognition and Knowledge EntropyNov 15 2018People employ their knowledge to recognize things. This paper is concerned with how to measure people's knowledge for recognition and how it changes. The discussion is based on three assumptions. Firstly, we construct two evolution process equations, ... More

On the minimal speed and asymptotics of the wave solutions for the lotka volterra systemFeb 15 2010e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave solutions are ... More

Construction of Arakelov-modular Lattices over Totally Definite Quaternion AlgebrasApr 11 2016Sep 13 2016We study ideal lattices constructed from totally definite quaternion algebras over totally real number fields, and generalize the definition of Arakelov-modular lattices over number fields. In particular, we prove for the case where the totally real number ... More

Asymptotic stability of the rarefaction wave for the non-viscous and heat-conductive ideal gas in half spaceMay 28 2018This paper is concerned with the impermeable wall problem for an ideal polytropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof ... More

Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifoldsFeb 25 2016In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. ... More

Eigenvalues under the Ricci flow of model geometriesFeb 15 2016In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized Ricci flow of model geometries. In every Bianchi class, we estimate the derivative of the eigenvalue. Then we construct monotonic ... More

All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groupsJul 10 2013Oct 08 2016This is the second part of the works on Hausdorff dimensions of Schottky groups. It has been conjectured that the Hausdorff dimensions of nonclassical Schottky groups are strictly bounded from below. In this second part of our works we provide a resolution ... More

The classification of Kleinian groups of Hausdorff dimensions at most oneOct 10 2016In this paper we provide the complete classification of Kleinian groups of Hausdorff dimensions less than $1.$ In particular, we prove that every purely loxodromic Kleinian groups of Hausdorff dimension $<1$ is a classical Schottky group. This upper bound ... More

On smooth moduli space of Riemann surfacesOct 10 2016In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $\mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$ The main theorem ... More

On hypercomplexifying real forms of arbitrary rankSep 28 2002For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, ... More

A theoretical and numerical study of gravity driven coating flow on cylinder and sphere: fingering instabilityAug 11 2017To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave equation and ... More

A theoretical and numerical study of gravity driven coating flow on cylinder and sphere: two-dimensional and axisymmetric capillary wavesJul 31 2017The theoretical and numerical models for gravity driven coating flow on upper cylinder and sphere are formulated. Using a perturbation method, the governing equations which depend on one Bond number $Bo$ are derived for a liquid film flow down the outside ... More

Global Attractor in Competitive Lotka-Volterra SystemsNov 21 2007For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species ... More

Optimal Error Estimates of A Decoupled Scheme Based on Two-Grid Finite Element for Mixed Stokes-Darcy ModelSep 08 2015Oct 26 2015Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get the optimal ... More

Thermodynamic cycle in a cavity optomechanical systemFeb 16 2014A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its ... More

Quasi-lattice chains and multipartite entanglement in a cavityJun 12 2013Nov 12 2014Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission ... More

Construction of Arakelov-modular Lattices from Number FieldsSep 11 2016An Arakelov-modular lattice of level $\ell$, where $\ell$ is a positive integer, is an $\ell-$modular lattice constructed from a fractional ideal of a CM field such that the lattice can be obtained from its dual by multiplication of an element with norm ... More

Abrikosov String in N=2 Supersymmetric QEDMay 12 2000May 23 2000We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with N=2-preserving superpotential, in which case the Abrikosov string is found to be 1/2-BPS saturated. Adding a quadratic small perturbation in the superpotential breaks N=2 supersymmetry ... More

Complex Hessian Equation on Kähler ManifoldDec 24 2008In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was proved.

The classification of Kleinian groups of Hausdorff dimensions at most oneOct 10 2016Dec 16 2017In this paper we provide the complete classification of Kleinian groups of Hausdorff dimensions less than $1.$ In particular, we prove that every purely loxodromic Kleinian groups of Hausdorff dimension $<1$ is a classical Schottky group. This upper bound ... More

Permanence criteria for Kolmogorov systems with delaysMar 07 2013In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result (J. Math. Biol. Vol. 25 (1987) 411-422) for autonomous replicator and Lotka-Volterra ... More

Quasi-convergence of the Ricci flow on locally homogeneous closed 4-manifoldsJan 05 2015We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equivalence class under certain conditions.

Shear viscosity of hot QCD from transport theory and thermal field theory in real time formalismJan 31 2005We study shear viscosity in weakly coupled hot pure gauge field QCD theory basing on transport theory and the Kubo formula using the closed time path formalism (CTP) of real time finite temperature field theory. We show that the viscosity can be obtained ... More

Atom-driven multistability in an optomechanical cavity under broken PT-symmetryDec 07 2015An optical field inside a Fabry-Perot cavity would exhibit multistability either when an atomic medium, acting as a classical dielectric, is filled into the cavity or when the cavity becomes optomechanical where one reflecting end becomes movable. An ... More

Convexity of Hessian Integrals and Poincare Type InequalitiesMay 11 2009May 25 2009In this paper, we studied integrals involving both real and complex Hessian operators over bounded domain. Poincare type inequalities were proved in both cases which generalized a early results of Trudinger and Wang.

Mutual Conversion Between Preference Maps And Cook-Seiford VectorsDec 09 2018In group decision making, the preference map and Cook-Seiford vector are two concepts as ways of describing ties-permitted ordinal rankings. This paper shows that they are equivalent for representing ties-permitted ordinal rankings. Transformation formulas ... More

Analysis of a model arising from invasion by precursor and differentiated cellsJan 16 2013We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equals a certain number, and below which there is no monotonic wave ... More

On smooth moduli space of Riemann surfacesOct 10 2016Nov 15 2016In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $\mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$ The main theorem ... More

Image Annotation Incorporating Low-Rankness, Tag and Visual Correlation and Inhomogeneous ErrorsAug 29 2015Aug 08 2016Tag-based image retrieval (TBIR) has drawn much attention in recent years due to the explosive amount of digital images and crowdsourcing tags. However, TBIR is still suffering from the incomplete and inaccurate tags provided by users, posing a great ... More

Kleinian groups of small Hausdorff dimension are classical Schottky groups IOct 15 2006Jun 30 2013In this paper we prove that there exists a positive number $\lambda>0$, such that any 2-generated Kleinian groups with limit set of Hausdorff dimension $<\lambda$ are classical Schottky groups.

Enhanced Word Representations for Bridging Anaphora ResolutionMar 13 2018Apr 13 2018Most current models of word representations(e.g.,GloVe) have successfully captured fine-grained semantics. However, semantic similarity exhibited in these word embeddings is not suitable for resolving bridging anaphora, which requires the knowledge of ... More

All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groupsJul 10 2013Dec 16 2017This is the second part of the works on Hausdorff dimensions of Schottky groups. It has been conjectured that the Hausdorff dimensions of nonclassical Schottky groups are strictly bounded from below. In this second part of our works we provide a resolution ... More

Quasiconformal Rigidity of Negatively Curved Three ManifoldsNov 28 2002In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature $-b^2\le K\le -1$ and finitely generated fundamental group. In-particular, we generalize the Sullivan's quasi-conformal rigidity for finitely generated fundamental ... More

Asymptotic Symmetries of the Null Infinity and the Isolated HorizonApr 19 2017Jul 24 2017The common intrinsic geometry shared by all the null hypersurfaces gives rise to the asymptotic symmetries found on the null infinities $\mathscr I^\pm$ and the isolated horizons $\Delta$. In this work, the properties of a null hypersurface are reviewed ... More

Some Analysis of the Knockoff Filter and its VariantsJun 11 2017In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables and determine which variables are truly associated with the response. In 2015, Barber and Candes ... More

A Pseudo Knockoff Filter for Correlated FeaturesAug 30 2017Sep 19 2017In 2015, Barber and Candes introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and prove that this method achieves exact FDR control. Inspired by the work of Barber and Candes (2015), we propose ... More

Dyson's Partition Ranks and their Multiplicative ExtensionsJul 13 2016We study the Dyson rank function $N(r,3;n)$, the number of partitions of $n$ with rank $\equiv r \pmod 3$. We investigate the convexity of these functions. We extend $N(r,3;n)$ multiplicatively to the set of partitions, and we determine the maximum value ... More

Remarks on GJMS operator of order sixMay 08 2016We study the sixth order GJMS operator $P_g^6$ in analytic aspects. Under conformal normal coordinates around some point, the expansion formulae of Green's function of $P_g^6$ with pole at the same point are presented. As a starting point of the study ... More

On robust pricing-hedging duality in continuous timeMar 10 2015Jul 06 2015We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, ... More

Completeness for a First-order Abstract Separation LogicAug 24 2016Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which completeness is not ... More

Ab Initio Study on Electronic Structure of ZrB12 under High Hydrostatic PressureJul 07 2006Using projector augmented wave approach within the generalized gradient approximation, we have studied the structural property and electronic structure of ZrB12. The calculated lattice constants and bulk modulus are in good agreement with the available ... More

Strong Equivalence Principle and Gravitational Wave Polarizations in Horndeski TheoryOct 01 2018The relative acceleration between two nearby particles moving along accelerated trajectories is studied, which generalizes the geodesic deviation equation. The polarization content of the gravitational wave in Horndeski theory is investigated by examining ... More

Three-Point Spectral Functions in $φ^3_6$ Theory at Finite TemperatureApr 24 1997Jul 07 1997We derive a set of relations among the thermal components of the 3-point function and its spectral representations at finite temperature in the real-time formalism. We then use these to explicitly calculate the 3-point spectral densities for $\phi^3_6$ ... More

Global smooth axisymmetric solutions to 2D compressible Euler equations of Chaplygin gases with non-zero vorticityOct 27 2018For 2D compressible isentropic Euler equations of polytropic gases, when the rotationally invariant data are a perturbation of size $\ve>0$ of a rest state, S.~Alinhac in \cite{Alinhac92} and \cite{Alinhac93} establishes that the smooth solution blows ... More

Like Sign Top Pair Production via $e^+e^-\to h^0A^0 \to tt\bar c\bar c$Apr 26 1996We discuss the possibility and likelihood that one may observe {\it like sign} top quark pair production at the Linear Collider. In general two Higgs models, flavor changing couplings involving top quark could be quite sizable. Exotic neutral Higgs bosons ... More

Search for TeV Scale Physics in Heavy Flavour DecaysAug 14 2008The subject of heavy flavour decays as probes for physics at and beyond the TeV scale is covered from the experimental perspective. Emphasis is placed on the more traditional Beyond the Standard Model topics that have potential for impact in the early ... More

What Can We Learn from Charmless Rare B Decays - the Past/Next 3 YearsSep 19 2000A personal perspective is given on physics of charmless rare B decays: 1997 -- 2003.

New Physics and Enhanced Gluonic PenguinDec 23 1997We discuss the historical development of the gluonic B-penguin, its sensitivity to $H^+$ effects, and $\bsg\sim$ 10--15% as a possible solution to the $\Bsl$ and $n_C$ problems. The latter and the connection of the gluonic penguin to inclusive $B\to \eta^\prime+ ... More

The Case for a Vector GlueballJul 31 1997Aug 02 1997We argue that the $1^{--}$ glueball $O$ is much cleaner than other glueball candidates. Anomalously large $J/\psi \to \rho\pi, K^*\bar K$ decays and the scalar glueball mass scale suggest that $m_{O} \simeq m_{J/\psi}$.

Possible Solution to $R_b$ -- $R_c$ ProblemApr 26 1996We investigate the $R_b$--$R_c$ problem, starting from the more diffcult $R_c$. Introducing an isosinglet charge 2/3 quark $Q$ moves both $R_c$ and $R_b$ in the right direction. If one allows for large $c$-$Q$ {\it and} $t$-$Q$ mixings, then $R_c$ could ... More

An ionization sensor scheme for ultra-low voltage operation using one-dimensional nanostructuresDec 03 2012The one-dimensional nanostructures have been used as the electrode to decrease the operation voltage where strong electric field is needed to function the device in the gaseous electronics. In this letter, a novel electrode scheme is proposed to generate ... More

Delay induced bifurcation of dominant transition pathwaysApr 15 2011Sep 18 2012We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability analysis of the {"on-axis"} ... More

Flexibility Induced Motion Transition of Active Filament: Rotation without Long-range Hydrodynamic InteractionOct 23 2012We investigate the motion of active semiflexible filament with shape kinematics and hydrodynamic interaction including. Three types of filament motion are found: Translation, snaking and rotation. Change of flexibility will induce instability of shape ... More

Incident Light Frequency-based Image Defogging AlgorithmMar 03 2017Considering the problem of color distortion caused by the defogging algorithm based on dark channel prior, an improved algorithm was proposed to calculate the transmittance of all channels respectively. First, incident light frequency's effect on the ... More

Enumeration of ${\rm AGL}(\frac m3, {\Bbb F}_{p^3})$-Invariant Extended Cyclic CodesMay 26 2009Let $p$ be a prime and let $r, e, m$ be positive integers such that $r|e$ and $e|m$. The enumeration of linear codes of length $p^m$ over ${\Bbb F}_{p^r}$ which are invariant under the affine linear group ${\rm AGL}(\frac me, {\Bbb F}_{p^e})$ is equivalent ... More

Entanglement detection beyond the CCNR criterion for infinite-dimensionsApr 07 2012Jun 16 2012In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion ... More

Study of Active Brownian Particle Diffusion in Polymer SolutionsJan 10 2018The diffusion behavior of an active Brownian particle (ABP) in polymer solutions is studied using Langevin dynamics simulations. We find that the long time diffusion coefficient $D$ can show a non-monotonic dependence on the particle size $R$ if the active ... More

A Nash Type result for Divergence Parabolic Equation related to Hormander's vector fieldsMay 17 2017In this paper we consider the divergence parabolic equation with bounded and measurable coefficients related to Hormander's vector fields and establish a Nash type result, i.e., the local Holder regularity for weak solutions. After deriving the parabolic ... More

Decoherence-free propagation and ramification of a solitary pulseNov 13 2018Using a microscopic master equation to account for the environmental effects, we compute the decoherence culminated on a two-level qubit when scattered by a narrow pulse. It is shown that the decoherence vanish when the pulse adopts a soliton shape of ... More

Topological charge of Skyrmions in Fe$_{0.5}$Co$_{0.5}$Si-Like Quasi-Two-Dimensional FerromagnetsJul 11 2018In a continuous system, magnetic skyrmions are characterized by an integer-valued topological index, often referred to as the topological charge. However, this topological concept is not applicable to the energetically stabilized magnetic structures of ... More

Maps preserving peripheral spectrum of generalized products of operatorsMay 30 2013Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be standard operator algebras on complex Banach spaces $X_1$ and $X_2$, respectively. For $k\geq2$, let $(i_1,...,i_m)$ be a sequence with terms chosen from $\{1,\ldots,k\}$, and assume that at least one of the ... More

Image Tag Completion and Refinement by Subspace Clustering and Matrix CompletionJun 10 2015Aug 08 2016Tag-based image retrieval (TBIR) has drawn much attention in recent years due to the explosive amount of digital images and crowdsourcing tags. However, the TBIR applications still suffer from the deficient and inaccurate tags provided by users. Inspired ... More

Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchyJun 24 2014This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Camassa-Holm Dym (CHD2) hierarchy. Our main tools include the polynomial recursive formalism, the hyperelliptic ... More

Determination of a Type of Permutation Trinomials over Finite Fields, IIApr 07 2014Let $q$ be a prime power. We determine all permutation trinomials of $\Bbb F_{q^2}$ of the form $ax+bx^q+x^{2q-1}\in\Bbb F_{q^2}[x]$. The subclass of such permutation trinomials of $\Bbb F_{q^2}$ with $a,b\in\Bbb F_q$ was determined in a recent paper ... More

Determination of a Type of Permutation Trinomials over Finite FieldsSep 13 2013Let $f=a{\tt x} +b{\tt x}^q+{\tt x}^{2q-1}\in\Bbb F_q[{\tt x}]$. We find explicit conditions on $a$ and $b$ that are necessary and sufficient for $f$ to be a permutation polynomial of $\Bbb F_{q^2}$. This result allows us to solve a related problem. Let ... More

A Class of Permutation Binomials over Finite FieldsOct 02 2012Let $q>2$ be a prime power and $f={\tt x}^{q-2}+t{\tt x}^{q^2-q-1}$, where $t\in\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\equiv 1\pmod 4$; (ii) ... More

Proof of a Conjecture on Permutation Polynomials over Finite FieldsApr 08 2013Let $k$ be a positive integer and $S_{2k}={\tt x}+{\tt x}^4+...+{\tt x}^{4^{2k-1}}\in\Bbb F_2[{\tt x}]$. It was recently conjectured that ${\tt x}+S_{2k}^{4^{2k}}+S_{2k}^{4^k+3}$ is a permutation polynomial of $\Bbb F_{4^{3k}}$. In this note, the conjecture ... More

On a Class of Permutation Trinomials in Characteristic 2Mar 12 2018Recently, Tu, Zeng, Li, and Helleseth considered trinomials of the form $f(X)=X+aX^{q(q-1)+1}+bX^{2(q-1)+1}\in\Bbb F_{q^2}[X]$, where $q$ is even and $a,b\in\Bbb F_{q^2}^*$. They found sufficient conditions on $a,b$ for $f$ to be a permutation polynomial ... More

Polynomials Meeting Ax's BoundDec 15 2015Let $f\in\Bbb F_q[X_1,\dots,X_n]$ with $\deg f=d>0$ and let $Z(f)=\{(x_1,\dots,x_n)\in \Bbb F_q^n: f(x_1,\dots,x_n)=0\}$. Ax's theorem states that $|Z(f)|\equiv 0\pmod {q^{\lceil n/d\rceil-1}}$, that is, $\nu_p(|Z(f)|)\ge m(\lceil n/d\rceil-1)$, where ... More

Permutation Polynomials of $\Bbb F_{q^2}$ of the form $a{\tt X}+{\tt X}^{r(q-1)+1}$Oct 01 2015Let $q$ be a prime power, $2\le r\le q$, and $f=a{\tt X}+{\tt X}^{r(q-1)+1}\in\Bbb F_{q^2}[{\tt X}]$, where $a\ne 0$. The conditions on $r,q,a$ that are necessary and sufficient for $f$ to be a permutation polynomial (PP) of ${\Bbb F}_{q^2}$ are not known. ... More

Stability Analysis of Linear Uncertain Systems via Checking Positivity of Forms on SimplicesMar 16 2010In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions of uncertain ... More

Limits of J-class operatorsOct 17 2010The purpose of the present work is to answer an open problem which is raised by G.Costakis and A.Manoussos in their paper "J-class operators and hypercyclicity " accepted by J. Operator Theory. More precisely, we give the spectral description of the closure ... More

On Global $\mathcal P$-FormsMay 19 2014Let $\Bbb F_q$ be a finite field with $\text{char}\,\Bbb F_q=p$ and $n>0$ an integer with $\text{gcd}(n, \log_pq)=1$. Let $(\ )^*:\Bbb F_q({\tt x}_0,\dots,{\tt x}_{n-1})\to\Bbb F_q({\tt x}_0,\dots,{\tt x}_{n-1})$ be the $\Bbb F_q$-monomorphism defined ... More

Linear maps preserving separability of pure statesOct 08 2012Apr 03 2013Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a characterization ... More

Criteria of positivity for linear maps constructed from permutation pairsFeb 01 2013Apr 15 2013In this paper, we show that a $D$-type map $\Phi_D:M_n\rightarrow M_n$ with $D=(n-2)I_n+P_{\pi_1}+P_{\pi_2}$ induced by a pair $\{\pi_1,\pi_2\}$ of permutations of $(1,2,..., n)$ is positive if $\{\pi_1,\pi_2\}$ has property (C). The property (C) is characterized ... More

Additive Lie ($ξ$-Lie) Derivations and Generalized Lie ($ξ$-Lie) Derivations on Prime AlgebrasApr 10 2010The additive (generalized) $\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) ... More

The spectral radius of graphs without long cyclesJul 16 2017Nikiforov conjectured that for a given integer $k\ge 2$, any graph $G$ of sufficiently large order $n$ with spectral radius $\mu(G)\geq \mu(S_{n,k})$ (or $\mu(G)\ge \mu(S_{n,k}^+))$ contains $C_{2k+1}$ or $C_{2k+2}$(or $C_{2k+2}$), unless $G=S_{n,k}$ ... More

The Polarizations of Gravitational WavesJun 11 2018The direct detection of gravitational waves by LIGO/Virgo opened the possibility to test General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General ... More

Gravitational waves in Einstein-Æther theory and generalized TeVeS theory after GW170817Jun 07 2018Aug 02 2018In this paper, the polarization contents of Einstein-\ae ther theory and the generalized TeVeS theory are studied. The Einstein-\ae ther theory has five polarizations, while the generalized TeVeS theory has six. In particular, transverse and longitudinal ... More

On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending dampingJun 29 2016In this paper, we are concerned with the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping \begin{equation*} \partial_t\rho+\operatorname{div}(\rho u)=0, \quad \partial_t(\rho ... More

Affine A^{(1)}_{3} N=2 monopole as the D module and affine ADHMN sheafDec 19 2006Jun 22 2007A Higgs-Yang Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual \alpha plane fields are holomorphic, but the right outgoing SD \beta plane fields are antiholomorphic, meanwhile the diffeomorphism ... More

Cooperativity of two cavity-coupled qubits: a multi-partite-entanglement approachJun 23 2016Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic cooperativity among the atoms and propose a time-resolved ... More

Effects of Dzyaloshinsky-Moriya Interaction on magnetism in NanodisksJul 28 2015We give a theoretical study on the magnetic properties of monolayer nanodisks with both Heisenberg exchange and Dzyaloshinsky-Moriya (DM) interactions. In particular, we survey the magnetic effects caused by anisotropy, external magnetic field, and disk ... More

A self-consistent approach to the one-dimensional chain models for the ferro- and antiferro-magnetism of nanotubesSep 23 2015We employ a self-consistent simulation approach based on quantum theory to investigate the physical properties of a pair of ferromagnetic and antiferromagnetic nanotubes. It was observed that under the given conditions, no matter the external magnetic ... More