A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations

After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.

     

Smoothness in Bayesian Non-parametric Regression with Wavelets

Consider the classical nonparametric regression problem y_i = f(t_i) + _ii = 1,...,n where t_i = i/n, and _i are i.i.d. zero mean normal with variance ². The aim is to estimate the true function f which is assumed to belong to the smoothness class described by the Besov space B _pq ^q . These are functions belonging to L_p with derivatives up to order s, in L_p sense. The parameter q controls a further finer degree of smoothness. In a Bayesian setting, a prior on B _pq ^q is chosen following Abramovich, Sapatinas and Silverman (1998). We show that the optimal Bayesian estimator of f is then also a.s. in B _pq ^q if the loss function is chosen to be the Besov norm of B _pq ^q . Because it is impossible to compute this optimal Bayesian estimator analytically, we propose a stochastic algorithm based on an approximation of the Bayesian risk and simulated annealing. Some simulations are presented to show that the algorithm performs well and that the new estimator is competitive when compared to the more standard posterior mean.     

Preparation of 20-hydroxyecdysone-22-benzoate

20-Hydroxyecdysone-22-benzoate was for the first time synthesized from 20-hydroxyecdysone.Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 401–403, September–October, 2004.     

Hydrogen adsorption on Mo1−xRex(110) (x=0–0.25) surfaces

The effects of adsorbed H on the Mo_1−xRe_x(110), x=0, 0.05, 0.15, and 0.25, surfaces have been investigated using low-energy electron diffraction (LEED) and high-resolution electron energy loss spectroscopy (HREELS). For the x=0.15 alloy only, a c(2×2) LEED pattern is observed at a coverage Θ0.25 ML. A (2×2) pattern is observed for H coverages around Θ0.5 ML from surfaces with x=0, 0.05, and 0.15. Both c(2×2) and (2×2) patterns are attributed to reconstruction of the substrate. At higher coverages, a (1×1) pattern is observed. For the alloy surface with x=0.25, only a (1×1) pattern is obtained for all H coverages. Two H vibrations are observed in HREELS spectra for all Re concentrations, which shift to higher energies at intermediate coverages. Both peaks exhibit an isotopic shift, confirming their assignment to hydrogen. For Re concentrations of x=0.15 and higher, a third HREELS peak appears at 50 meV as H (D) coverage approaches saturation. This peak does not shift in energy with isotopic substitution, yet cannot be explained by contamination. The intrinsic width of the loss peaks depends on the Re concentration in the surface region and becomes broader with increasing x. This broadening can be attributed to surface inhomogeneity, but may also reflect increased delocalization of the adsorbed hydrogen atom.     

Small-Mass Behavior of Quantum Gibbs States for Lattice Models with Unbounded Spins

We construct the distribution of the infinite-dimensional Markov process associated with a finite-temperature Gibbs state for a quantum mechanical anharmonic crystal. The corresponding state is constructed via a cluster expansion technique for an arbitrary fixed temperature and, correspondingly, small enough masses of particles.     

About the definition of mass in (Machian) classical mechanics

We want in this note to clarify some aspects of the Machian foundation of the concept of mass in classical mechanics; specifically, we show how the relations of transitivity for the mass-ratios, necessary for a well grounded definition of mass, can be derived from Machian postulates.     

Reduction of AC losses applying novel resistive interfilamentary carbonate barriers in multifilamentary Bi(2223) tapes

Hysteresis losses and coupling losses, a main component of the AC losses in Bi(2223) tapes, can effectively be reduced by enhancing the resistivity of the matrix material between the filaments and applying a filament twist. Since through alloying the sheath, as using AgAu(8 wt.%), the resistivity can only be raised by a factor <10 (77 K), a new conductor configuration with a quite novel composite matrix having resistive SrCO₃ barriers inside the Ag matrix between the filaments was developed. These new barriers, a cheap and commercial material, withstand the tape annealing, do not react with the superconductor, sinter dense and have a good bonding to Ag. Applying two different preparation techniques for 19 filament prototype tapes, critical current densities up to 20.7 kA cm⁻² were achieved. We report on tape preparation, the effect on the phase texture and the superconducting properties of such barrier tapes.     

Retrocrural masses of extramedullary hemopoiesis in beta-thalassemia

A case of extramedullary hemopoiesis in an 18-yr-old girl suffering from beta-thalassemia is reported. Extramedullary hemopoietic masses were localized apart from the paraspinal region in the retrocrural areas as well as the presacral region associated with massive destruction of the sacrum. The importance of recognition of hemopoietic masses in these regions in conditions other than hereditary hemolytic anaemias is briefly discussed.     

预平衡裂变

实验证明,重离子熔合裂变与入射道的质量不对称有关,说明对于某些反应体系,熔合形成的复合体系,裂变时未忘记其形成的历史.在实验观察的基础上,我们提出了预平衡裂变模型,解释了重离子垒下熔合裂变碎片角分布各向异性异常.     

Shrinkage estimators of the location parameter for certain spherically symmetric distributions

We consider estimation of a location vector for particular subclasses of spherically symmetric distributions in the presence of a known or unknown scale parameter. Specifically, for these spherically symmetric distributions we obtain slightly more general conditions and larger classes of estimators than Brandwein and Strawderman (1991,Ann. Statist.,19, 1639–1650) under which estimators of the formX +ag(X) dominateX for quadratic loss, concave functions of quadratic loss and general quadratic loss.Research supported by NSF grant DMS-88-22622