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Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 672-679页

作者： MA Jun 1,2, TANG Jun 2 , ZHANG AiHua 3 & JIA Ya 2 1 Department of Physics, lanzhou university of Technology, lanzhou 730050, china 2 Department of Physics, Central china normal university, Wuhan 430079, china 3 college of Electrical and information Engineering, lanzhou university of Technology, lanzhou 730050, china Department of Physics Lanzhou University of Technology Lanzhou China Department of Physics Central China Normal University Wuhan China college of Electrical and information Engineering Lanzhou University of Technology Lanzhou China

The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.

关键词： spiral wave factor of synchronization breakup multiplicative noise robustness

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Quantum nonlocality of generic family of four-qubit entangled pure states

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Chinese Physics B 2015年第7期24卷 83-87页

作者：丁东何英秋闫凤利高亭 college of Physics science and information Engineering Hebei Normal University Department of Basic Curriculum North China Institute of Science and Technology college of mathematics and information science Hebei Normal University

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states ｜Gabcd〉[Phys. Rev. A 65 052112（2002）] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called ＂four-qubit the maximally entangled state ｜Gm〉＂ and it is also violated by four-qubit W state and a special family of states ｜Gab00〉. Moreover, a useful entanglement-nonlocality relationship for the family of states ｜Gab00〉is derived. Finally, we present a scheme of preparation of the state ｜Gm〉with linear optics and cross-Kerr nonlinearities.

关键词： quantum nonlocality Bell-type inequality quantum entanglement

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An Iterative Process for a Finite Family of Pseudocontractive Mappings

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Acta Mathematica Sinica,English Series 2009年第2期25卷 293-298页

作者： Yi Sheng SONGcollege of mathematics and information science,He ’nan normal university,Xinxiang 453007,P. R. china college of mathematics and information science He’nan Normal University Xinxiang P. R. China

The purpose of this paper is to study the following implicit iteration scheme recentlyintroduced by Xu and Ori [Numer. Funct. Anal. Optim., 22, (2001) 767-773]:x= αx+ (1 -α)Tx, n≥1,and to prove several strongly and weakly convergent theorems of the iteration for a finite family ofpseudocontractive mappings under condition α∈ (0, b] (?) (0,1).

关键词： Pseudocontractive mappings strong and weak convergence implicit iteration process common fixed points

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Parametric instabilities in quantum plasmas with electron exchange-correlation effects

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Chinese Physics B 2013年第2期22卷 341-346页

作者：何彩霞薛具奎 Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province College of Physics and Electronics EngineeringNorthwest Normal University

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are *** using the quantum hydrodynamic equations with the electron exchange-correlation correction,we obtain an effective quantum Zaharov model,which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave *** influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in *** is shown that the electron exchange-correlation effects and quantum effects are strongly *** quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain *** electron exchange-correlation effects tend to enhance the parametric instabilities,while quantum effects suppress the instabilities.

关键词： parametric instabilities quantum Langmuir waves electron exchange-correlation

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Linear Maps Preserving Projections of Jordan Products on the Space of Self-Adjoint Operators

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Journal of Mathematical Research with Applications 2012年第2期32卷 235-240页

作者： Meifeng WANG,Guoxing JI college of mathematics and information science,Shaanxi normal university,Shaanxi 710062,china college of mathematics and information science Shaanxi Normal University Shaanxi 710062

Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ *** is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}.

关键词： self-adjoint operator Jordan product projection linear map.

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Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

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science china mathematics 2006年第10期49卷 1392-1404页

作者： XU Yichao,CHEN Minru & MA Songya Academy of mathematics and Systems science, Chinese Academy of sciences, Beijing 100080, china college of mathematics and information sciences, Henan university, Kaifeng 475001, china Academy of mathematics and Systems science Chinese Academy of Sciences Beijing China college of mathematics and information sciences Henan University Kaifeng China

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso (D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN,F)) and Iso (D(VN, F))(0), where G(0) is the unit connected component of the Lie group G.

关键词： holomorphic automorphism group, homogeneous Siegel domain, normal Siegel domain, complex homogeneous bounded domain.

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λ-fold indecomposable large sets of Steiner triple systems

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science china mathematics 2010年第11期53卷 2877-2888页

作者： JI LiJun1, TIAN ZiHong2, & KANG QingDe2 1Department of mathematics, Suzhou university, Suzhou 215006, china 2college of mathematics and information science, Hebei normal university, Shijiazhuang 050016, china Department of mathematics Suzhou University Suzhou China college of mathematics and information science Hebei Normal University Shijiazhuang China

A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).

关键词： Steiner triple system large set candelabra system indecomposable

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Optical pulse compression using a nonlinear optical loop mirror constructed from dispersion decreasing fiber

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science china(Technological sciences) 2004年第1期47卷 33-50页

作者： CAO Wenhua & LIU SonghaoSchool of information, Wuyi university, Jiangmen 529020, china School for information and Optoelectronic science and Engineering, South china normal university, Guangzhou 510631, china School of information Wuyi University Jiangmen China School for information and Optoelectronic science and Engineering South China Normal University Guangzhou China

A novel scheme to compress optical pulses is proposed and demonstrated numerically, which is based on a nonlinear optical loop mirror constructed from dispersion decreasing fiber (DDF). We show that, in contrast to the conventional soliton-effect pulse compression in which compressed pulses are always accompanied by pedestals and frequency chirps owning to nonlinear effects, the proposed scheme can completely suppress pulse pedestals and frequency chirps. Unlike the adiabatic compression technique in which DDF length must increase exponentially with input pulsewidth, the proposed scheme does not require adiabatic condition and therefore can be used to compress long pulses by using reasonable fiber lengths. For input pulses with peak powers higher than a threshold value, the compressed pulses can propagate like fundamental solitons. Furthermore, the scheme is fairly insensitive to small variations in the loop length and is more robust to higher-order nonlinear effects and initial frequency chirps than the adiabatic compression technique.

关键词： dispersion decreasing fiber (DDF), optical pulse compression, optical solitons.

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Analysis on crossover probability estimation using LDPC syndrome

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science china(information sciences) 2011年第9期54卷 1895-1904页

作者： FANG Yong college of information Engineering,northwest A&F university,Yangling 712100,china college of information Engineering Northwest A&F University Yangling China

Correlation estimation is a critical issue that impacts the application of Slepian-Wolf coding (SWC) in *** online correlation estimation is a type of newly-appearing approaches,in which the decoder estimates the virtual correlation channel between two correlated sources using both side information and the compressed SWC bitstream of the *** the compressed SWC bitstream usually contains partial information of the source,the emergence of dynamic online correlation estimation is helpful to solving the problem of correlation estimation in the SWC and further makes the SWC ***,the SWC is usually implemented by LDPC *** this case,the SWC bitstream is just the LDPC syndrome of the *** has been revealed that there are residual redundancies in LDPC syndromes,which can be used to estimate the crossover probability between two correlated binary ***,this algorithm has not been well justified *** paper makes use of the central limit theorem (CLT) to establish a mathematic model for analyzing the performance of this ***,for irregular LDPC codes,the optimization of weight vectors is discussed in *** experimental results are provided to validate the analysis.

关键词： distributed source coding Slepian-Wolf coding LDPC syndrome correlation estimation

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The best quadrature based on given Hermite information for the Sobolev class KW^r[a,b]

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science china mathematics 2006年第8期49卷 1146-1152页

作者： WANG Xinghua & YANG Shijun Department of mathematics, Zhejiang university, Hangzhou 310028, china Department of mathematics, Hangzhou normal college, Hangzhou 310036, china Department of mathematics Zhejiang University Hangzhou China Department of mathematics Hangzhou Normal College Hangzhou China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite *** work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, Hermite information, perfect spline, optimal recovery, best quadrature.

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