arXiv subjects

Fang Li

Publications and source records attributed to Fang Li.

At least 181 records · Page 10Linked to original sources

arXiv2014

Status of CSNS H- ion source

A new H^- ion source has been installed successfully and will be used to serve the China Spallation Neutron Source (CSNS). In this paper, we report various components of the ion source, including discharge chamber, temperature, cooling system, extraction electrodes, analyzing magnet, remote control system and so on. Compared to the previous experimental ion source, some improvements have been made to make the ion source more compact and convenient. In the present arrangement, the Penning field is generated by a pair of pole tip extensions on the analyzing magnet instead of by a separate circuit. For the remote control system, F3RP61-2L is applied to the accelerator online control system for the first time. In the running of the ion source, a stable pulse H- beam with a current of 50 mA at an energy of 50 keV is produced. The extraction frequency and pulse width is 25 Hz and 500microsecond, respectively. Furthermore, an emittance scanner has been installed and measurements are in progress.

physics.acc-ph↗

arXiv2014

Finite time blowup of the stochastic shadow Gierer-Meinhardt System

By choosing some special (random) initial data, we prove that with probability $1$, the stochastic shadow Gierer-Meinhardt system blows up pointwisely in finite time. We also give a (random) upper bound for the blowup time and some estimates about this bound. By increasing the amplitude of the initial data, we can get the blowup in any short time with positive probability.

math.PR↗

arXiv2014

The natural quiver of an artinian algebra

The motivation of this paper is to study the natural quiver of an artinian algebra, a new kind of quivers, as a tool independing upon the associated basic algebra. In \cite{Li}, the notion of the natural quiver of an artinian algebra was introduced and then was used to generalize the Gabriel theorem for non-basic artinian algebras splitting over radicals and non-basic finite dimensional algebras with 2-nilpotent radicals via pseudo path algebras and generalized path algebras respectively. In this paper, firstly we consider the relationship between the natural quiver and the ordinary quiver of a finite dimensional algebra. Secondly, the generalized Gabriel theorem is obtained for radical-graded artinian algebras. Moreover, Gabriel-type algebras are introduced to outline those artinian algebras satisfying the generalized Gabriel theorem here and in \cite{Li}. For such algebras, the uniqueness of the related generalized path algebra and quiver holds up to isomorphism in the case when the ideal is admissible. For an artinian algebra, there are two basic algebras, the first is that associated to the algebra itself; the second is that associated to the correspondent generalized path algebra. In the final part, it is shown that for a Gabriel-type artinian algebra, the first basic algebra is a quotient of the second basic algebra. In the end, we give an example of a skew group algebra in which the relation between the natural quiver and the ordinary quiver is discussed.

math.RT↗

arXiv2014

Representations of skew group algebras induced from isomorphically invariant modules over path algebras

Suppose that $Q$ is a connected quiver without oriented cycles and $σ$ is an automorphism of $Q$. Let $k$ be an algebraically closed field whose characteristic does not divide the order of the cyclic group $\langleσ\rangle$. The aim of this paper is to investigate the relationship between indecomposable $kQ$-modules and indecomposable $kQ\#k\langleσ\rangle$-modules. It has been shown by Hubery that any $kQ\#k\langleσ\rangle$-module is an isomorphically invariant $kQ$-module, i.e., ii-module (in this paper, we call it $\langleσ\rangle$-equivalent $kQ$-module), and conversely any $\langleσ\rangle$-equivalent $kQ$-module induces a $kQ\#k\langleσ\rangle$-module. In this paper, the authors prove that a $kQ\#k\langleσ\rangle$-module is indecomposable if and only if it is an indecomposable $\langleσ\rangle$-equivalent $kQ$-module. Namely, a method is given in order to induce all indecomposable $kQ\#k\langleσ\rangle$-modules from all indecomposable $\langleσ\rangle$-equivalent $kQ$-modules. The number of non-isomorphic indecomposable $kQ\#k\langleσ\rangle$-modules induced from the same indecomposable $\langleσ\rangle$-equivalent $kQ$-module is given. In particular, the authors give the relationship between indecomposable $kQ\#k\langleσ\rangle$-modules and indecomposable $kQ$-modules in the cases of indecomposable simple, projective and injective modules.

math.RT↗

arXiv2014

On the first Hochschild cohomology of admissible algebras

Our aim in this paper is to investigate the first Hochschild cohomology of {\em admissible algebras} which can be seen as a generalization of basic algebras. For this purpose, we study differential operators on an admissible algebra. Firstly, differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the $k$-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field $k$ of characteristic $0$.

math.RA↗

arXiv2014

Genuses of cluster quivers of finite mutation type

In this paper, we study the distribution of the genuses of cluster quivers of finite mutation type. First, we prove that in the $11$ exceptional cases, the distribution of genuses is $0$ or $1$. Next, we consider the relationship between the genus of an oriented surface and that of cluster quivers from this surface. It is verified that the genus of an oriented surface is an upper bound for the genuses of cluster quivers from this surface. Furthermore, for any non-negative integer $n$ and a closed oriented surface of genus $n$, we show that there always exist a set of punctures and a triangulation of this surface such that the corresponding cluster quiver from this triangulation is exactly of genus $n$.

math.RT↗

arXiv2014

On representation rings in the context of monoidal categories

In general, representation rings are well-known as Green rings from module categories of Hopf algebras. In this paper, we study Green rings in the context of monoidal categories such that representations of Hopf algebras can be investigated through Green rings of various levels from module categories to derived categories in the unified view-point. Firstly, as analogue of representation rings of Hopf algebras, we set up the so-called Green rings of monoidal categories, and then list some such categories including module categories, complex categories, homotopy categories, derived categories and (derived) shift categories, etc. and the relationship among their corresponding Green rings. The main part of this paper is to characterize representation rings and derived rings of a class of inite dimensional Hopf algebras constructed from the Nakayama truncated algebras $KZ_{n}/J^{d}$ with certain constraints. For the representation ring $r(KZ_{n}/J^{d})$, we completely determine its generators and the relations of generators via the method of Pascal triangle. For the derived ring $dr(KZ_{n}/J^{2})$(i.e., $d=2$), we determine its generators and give the relations of generators. In these two aspects, the polynomial characterizations of the representation ring and the derived ring are both given.

math.RT↗

arXiv2014

Modulation and natural valued quiver of an algebra

The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural valued quiver}, of an artinian algebra so as to correspond to its valued Ext-quiver when this algebra is not $k$-splitting over the field $k$. Moreover, we illustrate the relation between the valued Ext-quiver and the natural valued quiver. The interesting fact we find is that the representation categories of a pseudo-modulation and of a pre-modulation are equivalent respectively to that of a tensor algebra of $\mathcal A$-path type and of a generalized path algebra. Their examples are given respectively from two kinds of artinian hereditary algebras. Furthermore, the isomorphism theorem is given for normal generalized path algebras with finite (acyclic) quivers and normal pre-modulations. Four examples of pseudo-modulations are given: (i) group species in mutation theory as a semi-normal generalized modulation; (ii) viewing a path algebra with loops as a pre-modulation with valued quiver which has not loops; (iii) differential pseudo-modulation and its relation with differential tensor algebras; (iv) a pseudo-modulation is considered as a free graded category.

math.RT↗

arXiv2014

Positive definite matrices in the view-points of planar networks and cluster subalgebras

As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of positive definite matrices via the planar networks and the so-called cluster subalgebra respectively, introduced here originally. This work firstly gives a combinatorial realization of all matrices through planar network, and then sets up a test method for positive definite matrices by $LDU$-decompositions and the horizontal weightings of all lines in their planar networks. On the other hand, mainly the relationship is built between positive definite matrices and cluster subalgebras.

math.RA↗

arXiv2014

Far-field Imaging beyond the Diffraction Limit Using a Single Radar

Far-field imaging beyond the diffraction limit is a long sought-after goal in various imaging applications, which requires usually an array of antennas or mechanical scanning. Here, we present an alternative and novel concept for this challenging problem: a single radar system consisting of a spatial-temporal resonant aperture antenna (referred to as the slavery antenna) and a broadband horn antenna (termed the master antenna). We theoretically demonstrate that such resonant aperture antenna is responsible for converting parts of the evanescent waves into propagating waves, and delivering them to the far-field. We also demonstrate that there are three basic requirements on the proposed subwavelength imaging strategy: the strong spatial-temporal dispersive aperture, the near-field coupling, and the temporal (or broadband) illumination. Such imaging concept of a single radar provides unique ability to produce real-time data when an object is illuminated by broadband electromagnetic waves, which lifts up the harsh requirements such as near-field scanning, mechanical scanning or antenna arrays remarkably. We expect that this imaging methodology will make breakthroughs in super-resolution imaging in the microwave, terahertz, optical, and ultrasound regimes.

physics.optics↗

arXiv2014

Theory of the far-field imaging beyond the Rayleigh limit based on the super-resonant lens

Essentially, the idea of improving the resolution of a given imaging system is to enhance its information capacity represented usually by the temporal-bandwidth (or, spatial-spectrum) product. This letter introduces the concept of super-resonant lens, and demonstrates theoretically that the information capacity of a far-field imaging system can be efficiently driven up when three basic requirements are satisfied: the super-resonance, the near-field coupling between imaged objects and the used super-resonant lens, and the broadband illumination, which leads to the subwavelength image of imaged objects from far-field measurements. Furthermore, a single-view imaging scheme is proposed and examined for the far-field imaging beyond the diffraction limit. This new approach will be a breakthrough in nanolithography, detection, sensing or sub-wavelength imaging in the near future.

physics.optics↗

arXiv2014

Far-field subwavelength imaging from a single broadband antenna in combined with strongly disordered medium

The far-field subwavlength imaging is a challenging issue. In this letter we demonstrate numerically that the far-field subwavelength imaging of weakly scattering objects can be obtained by processing the data acquired by a single antenna, which benefits from the use of the strongly disordered medium. A mathematical model has been proposed for solving such problem based on the idea of sparse reconstruction. Moreover, this study leads to an important conclusion that the strongly disordered medium can serves as an efficient apparatus for the single-antenna compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

physics.optics↗

arXiv2014

Subwavelength imaging of sparse broadband sources surrounded by an open disordered medium from a single antenna

In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea of sparse reconstruction. We show that the strongly disordered medium can serves as an efficient apparatus for compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

physics.optics↗

arXiv2013

Beat the Rayleigh limit: OAM based super-resolution diffraction tomography

This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). It is well accepted that the orbital angular momentum (OAM) provides additional electromagnetic degrees of freedom. This concept has been widely applied in science and technology. In this letter we revisit the DT problem extended with OAM, demonstrate theoretically and numerically that there is no physical limits on imaging resolution in principle by the OAM-DT. This super-resolution OAM-DT imaging paradigm, has no requirement for evanescent fields, subtle focusing lens, complicated post-processing, etc., thus provides a new approach to realize the wavefield imaging of universal objects with sub-wavelength resolution.

physics.optics↗

arXiv2013

Analysis of Uq(sl(m+1))-symmetries on quantum n-spaces

In this paper, the module-algebra structures of $U_q(sl(m+1))$ on the quantum $n$-space $A_q(n)$ are studied. We characterize all module-algebra structures of $U_q(sl(m+1))$ on $A_q(2)$ and $A_q(3)$ when $m\geq 2$. The module-algebra structures of $U_q(sl(m+1))$ on $A_q(n)$ are also considered for any $n\geq 4$.

math.QA↗

arXiv2013

Boltje-Maisch resolutions of Specht modules

In \cite{21}, Boltje and Maisch found a permutation complex of Specht modules in representation theory of Hecke algebras, which is the same as the Boltje-Hartmann complex appeared in the representation theory of symmetric groups and general linear groups. In this paper we prove the exactness of Boltje-Maisch complex in the dominant weight case.

math.RT↗

arXiv2013

A Basis of the $q$-Schur Module

In this paper, we construct the $q$-Schur modules as left principle ideals of the cyclotomic $q$-Schur algebras, and prove that they are isomorphic to those cell modules defined in \cite{8} and \cite{15} at any level $r$. Then we prove that these $q$-Schur modules are free modules and construct their bases. This result gives us new versions of several results about the standard basis and the branching theorem. With the help of such realizations and the new bases, we re-prove the Branch rule of Weyl modules which was first discovered and proved by Wada in \cite{23}.

math.RT↗

arXiv2013

Characterization Of Left Artinian Algebras Through Pseudo Path Algebras

In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field $k$ when it is splitting over its radical, in particular, when the dimension of the quotient algebra decided by the $n$'th Hochschild cohomology is less than 2 (for example, $k$ is finite or char$k=0$). Using generalized path algebras, the generalized Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebras are introduced as a new generalization of path algebras, which can cover generalized path algebras (see Fact 2.5). The main result is that (i) for a left Artinian $k$-algebra $A$ and $r=r(A)$ the radical of $A$, when the quotient algebra $A/r$ can be lifted, it holds that $A\cong PSE_k(Δ,\mathcal{A},ρ)$ with $J^{s}\subset<ρ>\subset J$ for some $s$ (Theorem 3.2); (ii) for a finite dimensional $k$-algebra $A$ with $r=r(A)$ 2-nilpotent radical, when the quotient algebra $A/r$ can be lifted, it holds that $A\cong k(Δ,\mathcal{A},ρ)$ with $\widetilde J^{2}\subset<ρ>\subset\widetilde J^{2}+\widetilde J\cap$ \textrm{Ker}$\widetildeφ$ (Theorem 4.3), where $Δ$ is the quiver of $A$ and $ρ$ is a set of relations. Meantime, the uniqueness of the quivers and generalized path algebra/pseudo path algebras satisfying the isomorphism relations is obtained in the case when the ideals generated by the relations are admissible (see Theorem 3.5 and 4.4).

math.RA↗