Rate of Convergence for the Empirical Distribution Function and the Empirical Characteristic Function of Mixing Processes

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Application of B-splines finite basis sets to relativistic two-photon decay rates of level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies. Received: 6 January 1998 / Accepted: 31 March 1998     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.     

Projection conditions on the vorticity in viscous incompressible flows

The problem of establishing appropriate conditions for the vorticity transport equation is considered. It is shown that, in viscous incompressible flows, the boundary conditions on the velocity imply conditions of an integral type on the vorticity. These conditions determine a projection of the vorticity field on the linear manifold of the harmonic vector fields. Some computational consequences of the above result in two-dimensional calculations by means of the nonprimitive variables, stream function and vorticity, are examined. As an example of the application of the discrete analogue of the projection conditions, numerical solutions of the driven cavity problem are reported.     

Haar wavelets of higher order on fractals and regularity of functions

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329-340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in or a cube in . It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets.     

Estimation of heavy-tailed probability density function with application to Web data

Summary  Common non-parametric estimators of a probability density function (PDF) show bad performance for heavy-tailed PDFs. Using a parametric approximation of the true cumulative distribution function (CDF), the transformation-retransformation of the data is explored here as a useful tool for the reliable PDF prediction. The PDF estimators are compared by their capacity to solve a classification problem. Simulation results and an application to Web data analysis are presented, too.     

“最小键级原理”的从头算证实———苯和苯胺类硝基衍生物

感度是爆炸物对外界刺激的敏感程度 ,是火药、炸药和起爆药的基本属性 .在外界撞击作用下炸药发生爆炸的难易程度即该炸药的撞击感度 .感度通常依靠实测 ,从理论上加以判别是人们追求的目标 ,故研究炸药感度与结构的关系一直是该领域的热点 .根据撞击引起热解、热解引起爆炸、撞击感度主要与热解引发步骤相关联等思想 ,我们建议了“最小键级原理 (PSBO)”[1- 4] :对系列结构相似爆炸物 ,其热解引发键键级 (或重叠布居 )越小 ,则撞击感度越大 ;热解引发键键级越大 ,则撞击感度越小 .该判据已在多系列炸药中获得证实和应用[1- 4] .“热解引…     

Uniform convexity of ψ-direct sums of Banach spaces

Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕_ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕_ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?_p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?_p,q is the Lorentz sequence space. These results extend the well-known fact for the ?_p-sum . Some other examples are also presented.     

Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

Effects of Cs treatment on field emission properties of capped carbon nanotubes

Within the methodology [M. Khazaei, A.A. Farajian, Y. Kawazoe, Phys. Rev. Lett. 95 (2005) 177602] based on first-principles electronic structure calculations, the effects of Cs treatment on current emissions and emission patterns of capped carbon nanotubes are considered at low deposition densities when the nanotubes are under an electric field 0.2 V/Å. The results show that the current emission from the cap with one adsorbed Cs is 3.4 times larger than the cap without any Cs. It is 9.6 times larger in the cap with two adsorbed Cs atoms. After Cs deposition the emission patterns become asymmetric (current emission from the carbon atoms located at the topmost pentagon ring close to Cs atoms is larger than the other atomic sites). There are very few localized states on Cs atoms. Hence, although the tunneling probability of electron emission from Cs atoms is significant, there is no current from Cs atoms. In addition, the effect of Cs on work function reduction of nanotubes is explained in terms of Cs deposition densities and the surface dipole moments.