COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

1.IntroductionThispaperisdevotedtothecalculatiollofT,ranchesofHopfpointswhichemallatefromacertaillsingularPointofatwopar:lmeterII()nlinearsystemwhereXisarealHillersspac(},Aabifllrcationparallleter,oranadditionalcontrolparameter,alldgisasnlootllmapping.\Nreassllllle(HI)gisA--synlnletric:thereexistsalillearoperators:X-Xsatisfying(I:identicaloperatorillX)Itiswellknottrnthat(1.2)irldllcestilesplittillgl)Th.firstauthorhasbeedsupportedbyar(>searchgralltoftileV'Olkswagen-StiftungWesaythatxiss…     

函数的双参数平均的几个性质

对于函数 f(x) q的双参数平均 Mp,q(f;a,b) ,证明当 f(x)为单调函数时它是 a,b的单调函数 ;当f (x)不是常量时它是 p,的严格增函数     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

Dependence of calculated electron effective attenuation lengths on transport mean free paths obtained from two atomic potentials

We report changes in electron effective attenuation lengths (EALs) resulting from use of transport mean free paths (TMFPs) obtained from the Dirac–Hartree–Fock (DHF) potential instead of the Thomas–Fermi–Dirac (TFD) potential in an algorithm used in the National Institute of Standards and Technology (NIST) Electron Effective‐Attenuation‐Length Database (SRD 82). TMFPs from the former potential are believed to be more reliable than those obtained from the latter potential. We investigated changes in the EALs for selected photoelectron and Auger‐electron lines in four elemental solids (Si, Cu, Ag, and W), for Si 2p photoelectrons of varying energy in SiO₂, and for photoelectrons excited by Al Kα X rays in four candidate gate‐dielectric materials (HfO₂, ZrO₂, HfSiO₄, and ZrSiO₄). For each material, we computed the change in the average EAL for a range of overlayer‐film thicknesses from zero to a maximum value corresponding to attenuation of the substrate signal to 10% of its original value. This EAL change was a maximum for electrons emitted normally from the surface and decreased monotonically with increasing emission angle. The maximum EAL change varied between ?4.4% and 2.6% for the three groups of materials. We found that the maximum EAL change correlated mainly with the TMFP change. We found that TMFP changes in other solids could generally lead to maximum EAL changes between ?2.6% and 1.9% for electron energies between 500 and 2000 eV. For lower energies, the maximum EAL changes could be larger for some solids. Our revised EALs for Si 2p photoelectrons in SiO₂ excited by Mg and Al Kα X rays agree within 0.5% with values reported by Seah and Spencer from a detailed analysis of SiO₂ film‐thickness measurements by XPS and other techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

Chen’ s theorem in arithmetical progressions

LetN be a sufficiently large even integer and

On sequential procedures for the point estimation of the mean of a normal population

The sequential procedures developed by Starr (1966, Ann. Math. Statist., 37, 1173–1185) for estimating the mean of a normal population are further analyzed. Asymptotic properties of the regret and first two moments of the stopping rules are studied and second-order approximations are derived.     

西安地区成年健康人群血清中微量元素正常值研究

用随机抽样的方法对西安地区436名健康人血清中Zn、Fe、Cu、Mn、Pb、Cd、Cr、Ni、Mo和Se十种微量元素正常值进行石墨炉原子吸收光谱法测定，并用ST286型计算机进行多因素相关分析和统计处理．结果表明，血清Zn、Cu分布比较集中，其它元素变异度比较大；多数元素与年龄呈相关关系。其中Zn、Cu、Fe、Mn、Pb、Se与年龄呈正相关 而Mo则与年龄呈负相关；多数元素含量与地城环境中徽量元素的分布有明显的相似性．总之，不同地区不同性别和不同年龄段血清微量元素有显著的差异．     

Photoinduced electron transport process in electrochemical cell I. Phenomenological description

The process of electron transport plays an essential role in the fundamental phenomena of life like photosynthesis, respiration and vision as well as in photoelectronic devices. However, the molecular mechanisms of the electron way and factors governing the transport rate in such systems are still unclear. Several groups have reported theoretical approaches for searching the mechanisms by using statistical mechanics, coherent dynamics and quantum mechanics. The current density vector inside the semiconducting layer is determined. In this paper we consider the problem of transport of electron promoted in the electrochemical cell constructed of two electrodes with the dye molecules immersed in. We describe the process of electron promotion by refractive light wave on the vacuum–semiconductor boundary as well as on the semiconducting electrode and the dye molecule layer in terms of extended phenomenological electrodynamics formalism. The results of our theoretical model show that such a theoretical approach will give more information on the mechanism of electron transport and will give insight in the determination of some electric features of materials.