Polaronic effect on a bound polaron

Feynman variational path-integral theory was used to obtain the ground-state energy of a polaron in a quantum well in the presence of a Coulomb potential for arbitrary values of the electron-phonon coupling constant α. Numerical and analytical results showed that the energy shift was more sensitive to α than to the Coulomb binding parameter (β) and increased with the decrease of effective quantum well widthl _Z. It was interesting that due to the electronic confinement in the quasi-2D (quantum well) structures, the lower bound of the strong coupling regime was shifted to smaller values of α. Comparison of the polaron in the quantum well with that in the quantum wire or dot showed that the polaronic effect strengthened with decrease of the confinement dimension. Project (No. 19804009) supported by the National Natural Science Foundation of China     

AgxZn1-x和AgxAl1-x双相合金超导体的超导态参数

A well-known pseudopotential is used to investigate the superconducting state parameters (SSP), viz., electronphonon coupling strength, Coulomb pseudopotential, transition temperature, isotope effect exponent and effective interaction strength for Ag _x Zn_{1 − x} and Ag _x Al_{1 − x} binary alloys theoretically for the first time. We have incorporated here five different types of the local field correction functions to show the effect of exchange and correlation on the aforesaid properties. Very strong influence of various exchange and correlation functions is concluded from the present study. Comparison with others such experimental values is encouraging, which confirms applicability of the model potential in explaining the superconducting state parameters of binary mixture.      

Hölder stability estimate for an inverse parabolic problem

This paper deals with a parabolic system in a multi-dimentional bounded domain Ω⊂R ⁿ with the smooth boundary δΩ. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ω⊂Ω at some time-interval. Our main result is the Holder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations. Supported by the Natural Science Foundation of Jiangxi Province Government (981102) and the Natural Science Foundation of Shanghai Municipal Commission (99ZA14030)     

Parthenolide inhibits proliferation of vascular smooth muscle cells through induction of G0/G1 phase cell cycle arrest

Objective  This study is to determine the effect of the natural product parthenolide, a sesquiterpene lactone isolated from extracts of the herb Tanacetum parthenium, on the proliferation of vascular smooth muscle cells (VSMCs). Methods  Rat aortic VSMCs were isolated and cultured in vitro, and treated with different concentrations of parthenolide (10, 20 and 30 μmol/L). [³H]thymidine incorporation was used as an index of cell proliferation. Cell cycle progression and distribution were determined by flow cytometric analysis. Furthermore, the expression of several regulatory proteins relevant to VSMC proliferation including IκBα, cyclooxygenase-2 (Cox-2), p21, and p27 was examined to investigate the potential molecular mechanism. Results  Treatment with parthenolide significantly decreased the [³H]thymidine incorporation into DNA by 30%∼56% relative to control values in a dose-dependent manner (P<0.05). Addition of parthenolide also increased cell population at G₀/G₁ phase by 19.2%∼65.7% (P<0.05) and decreased cell population at S phase by 50.7%∼84.8% (P<0.05), which is consistent with its stimulatory effects on p21 and p27. In addition, parthenolide also increased IκBα expression and reduced Cox-2 expression in a time-dependent manner. Conclusion  Our results show that parthenolide significantly inhibits the VSMC proliferation by inducing G₀/G₁ cell cycle arrest. IκBα and Cox-2 are likely involved in such inhibitory effect of parthenolide on VSMC proliferation. These findings warrant further investigation on potential therapeutic implications of parthenolide on VSMC proliferation in vivo. Project (No. 491020-W50315) supported by the Foundation of the Health Bureau of Zhejiang, China     

A rigidity theorem for submanifolds in S^n＋p with constant scalar curvature

Let M‘ be a closed submanifold isometrically immersed in a unit sphere S^n p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of M‘, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for M‘ immersed in S^n p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.     

Projectively flat Asanov Finsler metric

In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.     

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice d (d≥2) with partial ordering ≤, let {XK; K ∈ d } be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ d . Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε 0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).     

Infrared Absorption Spectra of Serpentine Cat＇s Eye from Sichuan Province of China

Infrared （IR） absorption spectra and X-ray powder diffraction （XRD） patterrns of sexpenfine cat＇s eye from Sichuan Province have been investigated, and infrared absorption bands of the serpentine have been assigned in this paper. The results indicate that the bands near 3 600 - 3 700 cm^-1 belong to the stretching absorption band VOH, the bands in 948 - 1 100 cm^-1 axe assigned to the stretching vibraling band Usvo, and the bands at 600 570 and 440 cm^-1 respectively belong to the bending vibration band VOH, δMg-O and δSi-O. The serpentine cat＇ s eye includes two types： chrysotile and antigorite. Chrysotile has a sharp and intensive band at 3 688 cm^-1 and a weak band at 3 643 cm^-1 , while antigorite has only one intensive band in the region. At vibration band VSi-O, chrysotile and antigorite have a similar feature at 1 071 cm^-1, but the band at 980 cm^-1 in anfigorite has been split into two bands in chrysotile - a strong one at 1 027 cm^-1 and a weak one at 949 cm^-1. In addition, antigorite has a characteristic bending vibrating band δMg-O at 570 cm^-1. Based on the analysis of the feature of crystal structure, their IR differences axe well explained.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

在n维赋范空间中单位球体积及其渐进性质

Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞.     

A general version of the Morse-Sard theorem

Let k,m,n be positive integers,and k≥2,α∈(0,1],0＜r＜min {m,n} an integer,d=r (m-r)/(k α),and iff∈ Ck,α(Rm,R″),A =Cr(f)= {x ∈ Rm ,rank(Df(x))≤r},thenf(A)is d-null.Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.     

混合流体完备方程组的局部解析解

With the straification theory we have proved the transversal layer s03,k(D) of complete equations for mixed fluid is not an empty set: s03,k(D)≠φfor all k(k≥1). Based on this conclusion and the "secondary equation" of s03,k(D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.     

Estimation method for mixed-effect coefficient semiparametric regression model

Consider the mixed-effect coefficient semiparametric regression modelZ=X'α+Y'β+g(T)+e, whereX, Y andT are random vectors onR ^p×R ^q×[0, 1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=Σ),g(.) is an unknown function on [0, 1], e is a random error with mean zero and variance σ², and (X, Y, T) and (β,e), β ande are mutually independent. We estimate α,b andg(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α,b have asymptotic normality and obtain the best convergence raten ^−1/3 for the estimation ofg(.). Project supported by the NSFC and the Natural Science Foundation of Zhejiang Province.     

L^p-estimates on a ratio involving a Bessel process

INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., …     

一类关于半正定规划的多项式原对偶内点算法

1 Introduction Interior-point methods (IPMs) for semidefinite opti-mization (SDO) have been studied intensively,due totheir polynomial complexity and practical efficiency.In the past decade , SDO has become a popular re-search area in mathematical programming when it be-came clear that the algorithm for linear opti mization(LO) can often be extended to the more general SDOcase. Other two factors are also responsible for thisincreasing interest in SDO. Firstly, SDO has a wideapplication…     

Regular-singular crossings on nonlinear systems with turning point

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From personal to conventional probabilities: from sample set to sample space

This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with learners’ initial ways of reasoning. We suggest a “desirable pedagogical approach” in which the solution builds on the set of outcomes as identified by learners and serves as a bridge towards mathematical convention. To explore prospective high school mathematics teachers’ ideas related to addressing a potential learner’s mistake and their reactions towards the suggested approach, we presented them with two tasks. In Task I, participants (n = 30) were asked to suggest a pedagogical remedy to a frequent mistake found in dealing with a standard probability problem, whereas in Task II, they were asked to solve a probabilistic problem, which they had not encountered previously. We discuss participants’ mathematical solutions to Task II in reference to their pedagogical approaches to Task I. The presented disparity serves in extending the convincing power of the suggested pedagogical approach.     

Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd+1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd+1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] + 1 q2d 33 1.     

Purification and some properties of a β-glucanase from a strain,Trichoderma reesei GXC

β-glucanase was purified from a solid-state culture ofTrichoderma reesei on wheat bran in three steps which comprised ammonium sulfate precipitation, Sephadex G-100 chromatography, and DEAE-Sephadex A-50 chromatography. The molecular mass was determined to be 35.21 kilodaltons by sodium dodecyl sulfate-12.5% polyacrylamide gel electrophoresis. The β-glucanase at low pHs was more stable than that at high pHs, and optimum pH was 5.0. The optimum temperature was 60°C, and β-glucanase was relatively stable at below 40°C for 60 min. TheK _m of the enzyme on β-glucan was 10.86 mg/ml, and theV _max on β-glucan was 14286 μmol of glucose equivalents per mg of the pure enzyme per min. The β-glucanase activity was significantly inhibited by Fe³⁺ ions, and was reduced in the presence of Cu²⁺ ions, Mn²⁺ ions and Mg²⁺ ions at 5 mmol/L and 10 mmol/L, respectively. The β-glucanase activity was stimulated by Co²⁺ ions, Ca²⁺ ions, Zn²⁺ ions, and Fe²⁺ ions at 1 mmol/L and 5 mmol/L, respectively. Project supported by Foundation for University Key Teacher of the State Ministry of Education, the National Natural Science Foundation of China (No. 30000118) and Zhejiang Provincial Natural Science Foundation of China (No. 399409).     

组成于平行机和批处理机的二阶段混合流水作业问题

A hybrid two-stage flowshop scheduling problem was considered which involves m identical parallel machines at Stage 1 and a burn-in processor M at Stage 2, and the makespan was taken as the minimization objective. This scheduling problem is NP-hard in general. We divide it into eight subcases. Except for the following two subcases： （1） b≥ an, max{m, B} 〈 n; （2） a1 ≤ b ≤ an, m ≤ B 〈 n, for all other subcases, their NP-hardness was proved or pointed out, corresponding approximation algorithms were conducted and their worst-case performances were estimated. In all these approximation algorithms, the Multifit and PTAS algorithms were respectively used, as the jobs were scheduled in m identical parallel machines.