Searcharxiv⌕ Search

arXiv subjects

Fang Li

Publications and source records attributed to Fang Li.

At least 163 records · Page 9Linked to original sources
arXiv2017

Long-time behavior of the three dimensional globally modified Navier-Stokes equations

This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\mathcal{A}_0$ in $H$ and investigate the regularity of the global attractors by proving that $\mathcal{A}_0=\mathcal{A}$ established in \cite{ct}, which implies the asymptotic smoothing effect of solutions for the three dimensional globally modified Navier-Stokes equations in the sense that the solutions will eventually become more regular than the initial data. Furthermore, we construct an exponential attractor in $H$ by verifying the smooth property of the difference of two solutions, which entails the fractal dimension of the global attractor is finite.

math.DS↗
arXiv2017

On Exchange Spectra of Valued Cluster Quivers and Cluster Algebras

Inspirited by the importance of the spectral theory of graphs, we introduce the spectral theory of valued cluster quiver of a cluster algebra. Our aim is to characterize a cluster algebra via its spectrum so as to use the spectral theory as a tool. First, we give the relations between exchange spectrum of a valued cluster quiver and adjacency spectrum of its underlying valued graph, and between exchange spectra of a valued cluster quiver and its full valued subquivers. The key point is to find some invariants from the spectrum theory under mutations of cluster algebras, which is the second part we discuss. We give a sufficient and necessary condition for a cluster quiver and its mutation to be cospectral. Following this discussion, the so-called cospectral subalgebra of a cluster algebra is introduced. We study bounds of exchange spectrum radii of cluster quivers and give a characterization of $2$-maximal cluster quivers via the classification of oriented graphs of its mutation equivalence. Finally, as an application of this result, we obtain that the preprojective algebra of a cluster quiver of Dynkin type is representation-finite if and only if the cluster quiver is $2$-maximal.

math.RT↗
arXiv2017

Community detection based on significance optimization in complex networks

Community structure is an important structural property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, but analyzing the behaviors of the methods is also of interest in the theoretical research and real applications. Here, we focus on an important measure for community structure, significance [Sci. Rep. 3 (2013) 2930]. Specifically, we study the effect of various network parameters on this measure in detail, analyze the critical behaviors of it in partition transition, and analytically give the formula of the critical points and the phase diagrams. The results shows that the critical number of communities in partition transition increases dramatically with the difference between inter- and intra-community link densities, and thus significance optimization displays higher resolution in community detection than many other methods, but it is also easily to lead to the excessive splitting of communities. By Louvain algorithm for significance optimization, we confirmed the theoretical results on artificial and real-world networks, and give a series of comparisons with some classical methods.

physics.soc-ph↗
arXiv2016

Global attractor of the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain

This paper is concerned with the long-time behavior of solutions for the three dimensional primitive equations of large-scale ocean and atmosphere dynamics in an unbounded domain. Since the Sobolev embedding is no longer compact in an unbounded domain, we cannot obtain the asymptotical compactness of the semigroup generated by problem (2.4)-(2.6) by the Sobolev compactness embedding theorem even if we obtain the existence of an absorbing set in more regular phase space. To overcome this difficulty, we first prove the asymptotical compactness in a weak phase space of the semigroup generated by problem (2.4)-(2.6) by combining the tail-estimates and the energy methods. Thanks to the existence of an absorbing set in more regular phase space, we establish the existence of a global attractor of problem (2.4)-(2.6) by virtue of Sobolev interpolation inequality.

math.AP↗
arXiv2016

Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and $F$-polynomials

In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in \cite{fz3} which asks whether an acyclic sign-skew-symmetric matrix is always totally sign-skew-symmetric. As applications, the positivity for cluster algebras in acyclic sign-skew-symmetric case is given; further, the $F$-polynomials of cluster algebras are proved to have constant term 1 in acyclic sign-skew-symmetric case.

math.RT↗
arXiv2016

Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere. As a byproduct, we obtain the fractal dimension of the global attractor for the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere is finite, which is in consistent with the results in \cite{jn2,jn1}.

math-ph↗
arXiv2016

On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.

math.RA↗
arXiv2016

On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfaces

Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a rooted cluster algebra are corresponded one-by-one to the regular $\mathcal D$-classes of the semigroup consisting of partial seed endomorphisms of the initial seed. Moreover, for a rooted cluster algebra from a Riemannian surface, they are also corresponded to the isomorphism classes of the so-called paunched surfaces.

math.RA↗
arXiv2016

A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

math.OC↗
arXiv2015

Representations of Frobenius-type triangular matrix algebras

The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g. that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.

math.RA↗
arXiv2015

Global dynamics of competition models with nonlocal dispersals I: Symmetric kernels

In this paper, the global dynamics of two-species Lotka-Volterra competition models with nonlocal dispersals is studied. Under the assumption that dispersal kernels are symmetric, we prove that except for very special situations, local stability of semi-trivial steady states implies global stability, while when both semi-trivial steady states are locally unstable, the positive steady state exists and is globally stable. Moreover, our results cover the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.

math.AP↗
arXiv2015

On Mathematical Symbols in China

When studying the history of mathematical symbols, one finds that the development of mathematical symbols in China is a significant piece of Chinese history; however, between the beginning of mathematics and modern day mathematics in China, there exists a long blank period. Let us focus on the development of Chinese mathematical symbols, and find out the significance of their origin, evolution, rise and fall within Chinese mathematics.

math.HO↗
arXiv2015

Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: I. Spreading and Vanishing Dichotomy

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In this first part, we show that a spreading-vanishing dichotomy occurs for such free boundary problems, that is, the species either successfully spreads to all the new environment and stabilizes at a time almost periodic positive solution, or it fails to establish and dies out eventually. The results of this part extend the existing results on spreading-vanishing dichotomy for time and space independent, or time periodic and space independent, or time independent and space periodic diffusive KPP equations with free boundaries. The extension is nontrivial and is ever done for the first time.

math.DS↗
arXiv2015

Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: II. Spreading Speeds and Semi-Wave

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In the first part of the series, we showed that a spreading-vanishing dichotomy occurs for such free boundary problems (see [16]). In this second part of the series, we investigate the spreading speeds of such free boundary problems in the case that the spreading occurs. We first prove the existence of a unique time almost periodic semi-wave solution associated to such a free boundary problem. Using the semi-wave solution, we then prove that the free boundary problem has a unique spreading speed.

math.AP↗
arXiv2015

Determining phase-space properties of the IHEP RFQ output beam using the RMS beam widths from wire-scanners

A beam line is built after the IHEP RFQ for halo study. To determine transverse emittance and ellipse parameters of the RFQ output beam, beam size data obtained from the first two of 14 wire scanners are employed. By using the transfer matrix method and the least square method, a set of linear equations were set up and solved. The solutions were then applied as initial beam parameters in multi-particle simulations to check the method of calculation. It is shown that difference between the simulated RMS beam size and the measured one at the measurement location is less than 7%, which is acceptable in our experiments.

physics.acc-ph↗
arXiv2015

600-T Magnetic Fields due to Cold Electron Flow in a simple Cu-Coil irradiated by High Power Laser pulses

A new simple mechanism due to cold electron flow to produce strong magnetic field is proposed. A 600-T strong magnetic field is generated in the free space at the laser intensity of 5.7x10^15 Wcm^-2. Theoretical analysis indicates that the magnetic field strength is proportional to laser intensity. Such a strong magnetic field offers a new experimental test bed to study laser-plasma physics, in particular, fast-ignition laser fusion research and laboratory astrophysics.

physics.plasm-ph↗
arXiv2015

Experimental generation of 8.4 dB entangled state with an optical cavity involving a wedged type-II nonlinear crystal

Entangled state of light is one of the essential quantum resources in quantum information science and technology. Especially, when the fundamental principle experiments have been achieved in labs and the applications of continuous variable quantum information in the real world are considered, it is crucial to design and construct the generation devices of entangled states with high entanglement and compact configuration. We have designed and built an efficient and compact light source of entangled state, which is a non-degenerate optical parametric amplifier (NOPA) with the triple resonance of the pump and two subharmonic modes. A wedged type-II KTP crystal inside the NOPA is used for implementing frequency-down-conversion of the pump field to generate the optical entangled state and achieving the dispersion compensation between the pump and the subharmonic waves. The EPR entangled state of light with quantum correlations of 8.4 dB for both amplitude and phase quadratures are experimentally produced by a single NOPA under the pump power of 75 mW.

quant-ph↗