The best quadrature formula based on Hermite information for the class KW~2[a,b]

The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.     

Determination of cosmological parameters: An introduction for non-specialists

I start by defining the cosmological parameters H ₀, Θ _m and Θ_A. Then I show how the age of the universe depends on them, followed by the evolution of the scale parameter of the universe for various values of the density parameters. Then I define strategies for measuring them, and show the results for the recent determination of these parameters from measurements on supernovas of type 1a. Implications for particle physics is briefly discussed at the end.     

Transient Heat and Moisture Flow Around Heat Source Buried in an Unsaturated Half Space

This article presents solutions for the transient heat and moisture transport due to both disk heat source and cylindrical heat source buried in an unsaturated half space. The solutions are presented in Hankel–Laplace transform domain and in dimensionless style. Coupled effect of thermally driven moisture transport is especially investigated because of its importance to alter the flow field in low-permeability medium. Parametric study has been performed to assess the effects of five independent dimensionless parameters on flow field. The stability and accuracy of the present solutions are demonstrated from the comparison between the results obtained from these solutions and those by using a well-established finite element code CODE_BRIGHT. Despite the simplified assumptions required in order to obtain analytical solutions in Hankel–Laplace transform domain, the results incorporate the main mechanisms involved in the coupled thermo-hydraulic (T-H) problem, and they may be eventually used for validation purposes.     

Edgeworth expansions for stochastic approximation theory

To estimate the root ϑ of an unknown regression function f: ℝ → ℝ the iterative Robbins-Monro method X _n+1 = X _n − a/nY _n with noisy observations Y _n = f(X _n ) + V _n of f(X _n ) can be used. It is well known that X _n − ϑ can be approximated by a weighted sum of the observation errors V _n . As recently shown this approximation can be improved by adding quadratic and cubic forms in the observation errors. This paper presents valid Edgeworth expansions of the distribution function of the approximating sequence up to a remainder term of order o(1/√n) or even o(1/n).      

Measurement of excitation spectra for highly ionized sulphur

The excitation spectra in the wavelength range of 19—40 nm for highly ionized sulphur ions were measured by using the beam-foil method at the Heavy lon Research Facility in Lanzhou. In this experiment, more than 30 spectral lines were observed, which belonged to the transitions of the excitation energy levels for highly ionized SX—SXV ions, and 5 new lines were determined. The experimental results were compared with those from other experiments and theoretical calculations.     

拟似然非线性模型的某些渐近推断:几何方法

Abstract. A modified Bates and Watts geometric framework is proposed for quasi-likelihoodnonlinear models in Euclidean inner product space. Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi-likelihood nonlinear models is stud-ied. Several previous results for nonlinear regression models and exponential family nonlinearmodels etc. are extended to quasi-likelihood nonlinear models.     

A new approach to the busy period of the M/M/1 queue

In this paper, we provide a new approach to the computation of the Laplace transform of the length of the busy period of the M/M/1 queue with constrained workload (finite dam), without the use of complex analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Linear quantum Enskog equation. I. Homogeneous quantum fluids

The quantum-statistical generalization of the well-known classical, linear revised Enskog equation is derived for spatially uniform systems. This new quantum kinetic equation allows the study of equilibrium time correlation functions and their associated transport coefficients of normal quantum fluids where static correlations and degeneracy effects due to particle statistics (both are treated exactly) are important. Furthermore, we derive the quantum-statistical analog of the classical ring operator. These microscopic and systematic derivations are based on a recently developed superoperator formalism (including cluster expansion techniques) that, as a main feature, allows a clear distinction between static and dynamic correlations, which is crucial in the discussion of the Enskog approximation.     

Local times of continuous N-parameter strong martingales

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. By extending Itô-type formulas for M to a function whose 2Nth derivative is Dirac's δ-distribution, Tanaka-type formulas for M are obtained. They represent local time of M with respect to occupation time scaled by the N-fold product of the Stieltjes measure defined by the quadratic variation of M and its kth derivatives in space, where k ≤ N − 1. Applications of Doob's and Burkholder's inequalities give continuity properties: space time continuity for local time, space continuity for the derivatives. In case N is even, for the continuity of the (N − 1)st derivative an additional condition on M is needed which may have a relation to the existence of local times of M w.r.t. different occupation time scales.     

Lattice parameter and thermal expansion of CsCl and CsBr by x-ray powder diffraction. II. Thermal expansion of CsBr from room temperature to 78.2 °K

The lattice parameters of CsBr at eight different temperatures from room temperature to 78.2 °K were measured and the true lattice parameters were obtained by the least squares method using the Nelson-Riley extrapolation function. Using these parameters the thermal expansion coefficients of CsBr were estimated at each temperature by fitting them into a cubic polynomial involving temperatureT. Theα _T thus obtained were compared with the values of earlier workers who used an interferometric technique and the agreement was found to be good.