Long—Range Effects on the Pyroelectric Coefficient of Ferroelectric Superlattice

Long-range effects on the pyroelectric coefficient of a ferroelectric superlattice consisting of two different ferroelectric materials are investigated based on the transverse Ising model.The effects of the interfacial coupling and the thickness of one period on the pyroelectric coefficient of the ferroelectric superlattics are studied by taking into account the long-range interaction.It is found that with the increase of the strength of the long-range interaction,the pyroelectric coefficient decreases when the temperature is lower than the phase transition temperature;the mumber of the pyroelectric peaks decreases gradually and the phase transition temperature increases,It is also found that with the decrease of the interfacial coupling and the thickness of one period.the phase transition temperature and the number of the pyroelectric peaks decrease.     

Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let −Dω(·,z)D+q be a differential operator in L²(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form

     

Dynamics of a general non-autonomous stochastic Lotka-Volterra model with delays

In this paper, a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. For this model, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The influences of the stochastic noises to the properties of the stochastic model are discussed. The property permanence for the model is preserved with the sufficiently small noise and sufficiently large noise may cause extinction of the model. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.     

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM (Ⅱ):DOUBLE■-l

1991MRSubjectionClassification81R05,20C351IntroductionIiiapreviouspaper['].wit11avediscussedhowtoconstructthewavefllucti()llsofL-S(\011piing,single-lferlllionsystelll.Alldthecoefficientsoffi.actiollalparentage(CFP)withfixs(1seniorityharebeedcalclllatedbyarecurrentformula.Practically,withthe11alpoftileoperatorsofferrxlionpairsthegeneralwavefunctionsofmanyfermionswithsixlgle-lcouldbeobtainedfi.omthewavefullctionswithoutfermionpairs.Asaresult,therecurrentforlllulaofdeterrxliningCFPissimplif…     

单纯形上Bernstein多项式的一些性质

设Ｂ_m（ｆ，·）为函数ｆ在ｄ维单纯形σ上的ｎ阶Ｂｅｒｎｓｔｅｉｎ多项式，本文对ｆ∈Ｃ^ｒ（σ）及ｆ∈Ｃ^r+2（σ）给出了ｆ的各阶编导数用Ｂ_n（ｆ，·）相应偏导数逼近的误差估计．同时也考虑了整系数Ｂｅｒｎｓｔｅｉｎ多项式的Ｌ_p模估计     

A projection method of estimation for a subfamily of exponential families

Summary This paper is concerned with estimation for a subfamily of exponential-type, which is a parametric model with sufficient statistics. The family is associated with a surface in the domain of a sufficient statistic. A new estimator, termed a projection estimator, is introduced. The key idea of its derivation is to look for a one-to-one transformation of the sufficient statistic so that the subfamily can be associated with a flat subset in the transformed domain. The estimator is defined by the orthogonal projection of the transformed statistic onto the flat surface. Here the orthogonality is introduced by the inverse of the estimated variance matrix of the statistic on the analogy of Mahalanobis's notion (1936,Proc. Nat. Inst. Sci. Ind.,2, 49–55). Thus the projection estimator has an explicit representation with no iterations. On the other hand, the MLE and classical estimators have to be sought as numerical solutions by some algorithm with a choice of an initial value and a stopping rule. It is shown that the projection estimator is first-order efficient. The second-order property is also discussed. Some examples are presented to show the utility of the estimator.     

Ballistic transmission through quasi-periodic shape barrier resonant tunneling structures

A theoretical model is proposed to study the ballistic electron transport for a quasi-periodic multibarrier structure where two different barrier shapes are arranged according to the Thue–Morse sequence. Important tunneling features are revealed form such arrangements. It is noted that the tunneling band spectrum could be fragmented by tailoring the shape of the barriers in the structure. Results for the transmission coefficients and the current densities are compared with the corresponding periodic and single shape barrier arrangements. The quasi-periodic structure consisting of the rectangular and triangular barrier shapes is suggested to be more suitable for the electronic and opto-electronic devices due to its high negative differential conducting effect.     

Asymptotic properties of a stochastic chemostat including species death rate

This paper deals with a stochastic system which models the population dynamics of a chemostat including species death rate. On the basis of the theory on Markov semigroup, we demonstrate that the probability densities of the distributions for the solutions are absolutely continuous. The densities will convergence in L¹ to an invariant density or weakly convergence to a singular measure under appropriate conditions. We also give the sufficient criteria for extinction exponentially of the species. To be specific, when D₁>D and the strength of perturbation is relatively small, we derive a precise threshold for the species survival.     

Degrees of stretched Kostka coefficients

Given a partition λ and a composition β, the stretched Kostka coefficient is the map n ↦ K _{n λ,n β} sending each positive integer n to the Kostka coefficient indexed by n λ and n β. Kirillov and Reshetikhin (J. Soviet Math. 41(2), 925–955, 1988) have shown that stretched Kostka coefficients are polynomial functions of n. King, Tollu, and Toumazet have conjectured that these polynomials always have nonnegative coefficients (CRM Proc. Lecture Notes 34, 99–112, 2004), and they have given a conjectural expression for their degrees (Séminaire Lotharingien de Combinatoire 54A, 2006). We prove the values conjectured by King, Tollu, and Toumazet for the degrees of stretched Kostka coefficients. Our proof depends upon the polyhedral geometry of Gelfand–Tsetlin polytopes and uses tilings of GT-patterns, a combinatorial structure introduced in De Loera and McAllister, (Discret. Comput. Geom. 32(4), 459–470, 2004). Research supported by NSF VIGRE Grant No. DMS-0135345 and by NWO Mathematics Cluster DIAMANT.     

拉脱法测液体表面张力系数的误差分析

对拉脱法测量液体表面张力系数实验的原理和仪器做了简要的介绍,并着重对该实验误差的来源进行了分析探讨。