Removable singularities of CR functions on singular boundaries

The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature of singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied. Received: 8 December 2000; in final form: 24 June 2001/Published online: 1 February 2002     

自由基-分子反应:F+Propene(CH2CHCH3)的从头算研究

采用从头算CCSD(T)/6-311 G(2d,2p)//B3LYP/6-311G(d,p)方法,研究了自由基-分子反应F CH2CHCH3的各种不同的反应通道．该反应主要是通过复合物形成机制进行,即F分别加到碳碳双键的两端形成自由基复合物1和2．这两种亚稳态自由基会解离成三种产物:H C3H5F、CH3 C2H3F和HF C3H5．理论计算结果表明,生成CH3 C2H3F是反应的主要通道,而生成H C3H5F和HF C3H5对产物也有一定的贡献．这一结果和实验符合得很好．     

Tchebychev acceleration technique for large scale nonsymmetric matrices

Summary The acceleration by Tchebychev iteration for solving nonsymmetric eigenvalue problems is dicussed. A simple algorithm is derived to obtain the optimal ellipse which passes through two eigenvalues in a complex plane relative to a reference complex eigenvalue. New criteria are established to identify the optimal ellipse of the eigenspectrum. The algorithm is fast, reliable and does not require a search for all possible ellipses which enclose the spectrum. The procedure is applicable to nonsymmetric linear systems as well.     

Optical characterization of thin thermal oxide films on copper by ellipsometry

A complete optical characterization in the visible region of thin copper oxide films has been performed by ellipsometry. Copper oxide films of various thicknesses were grown on thick copper films by low temperature thermal oxidation at 125 °C in air for different time intervals. The thickness and optical constants of the copper oxide films were determined in the visible region by ellipsometric measurements. It was found that a linear time law is valid for the oxide growth in air at 125 °C. The spectral behaviour of the optical constants and the value of the band gap in the oxide films determined by ellipsometry in this study are in agreement with the behaviour of those of Cu₂O, which have been obtained elsewhere through reflectance and transmittance methods. The band gap of copper oxide, determined from the spectral behaviour of the absorption coefficient was about 2 eV, which is the generally accepted value for Cu₂O. It was therefore concluded that the oxide composition of the surface film grown on copper is in the form of Cu₂O (cuprous oxide). It was also shown that the reflectance spectra of the copper oxide–copper structures exhibit behaviour expected from a single layer antireflection coating of Cu₂O on Cu. Received: 19 July 2001 / Accepted: 27 July 2001 / Published online: 17 October 2001     

Estimating the largest singular values of large sparse matrices via modified moments

We describe a procedure for determining a few of the largest singular values of a large sparse matrix. The method by Golub and Kent which uses the method of modified moments for estimating the eigenvalues of operators used in iterative methods for the solution of linear systems of equations is appropriately modified in order to generate a sequence of bidiagonal matrices whose singular values approximate those of the original sparse matrix. A simple Lanczos recursion is proposed for determining the corresponding left and right singular vectors. The potential asynchronous computation of the bidiagonal matrices using modified moments with the iterations of an adapted Chebyshev semi-iterative (CSI) method is an attractive feature for parallel computers. Comparisons in efficiency and accuracy with an appropriate Lanczos algorithm (with selective re-orthogonalization) are presented on large sparse (rectangular) matrices arising from applications such as information retrieval and seismic reflection tomography. This procedure is essentially motivated by the theory of moments and Gauss quadrature.This author's work was supported by the National Science Foundation under grants NSF CCR-8717492 and CCR-910000N (NCSA), the U.S. Department of Energy under grant DOE DE-FG02-85ER25001, and the Air Force Office of Scientific Research under grant AFOSR-90-0044 while at the University of Illinois at Urbana-Champaign Center for Supercomputing Research and Development.This author's work was supported by the U.S. Army Research Office under grant DAAL03-90-G-0105, and the National Science Foundation under grant NSF DCR-8412314.     

The existence of smooth densities for the prediction filtering and smoothing problems

The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.Work supported by NSF Grant No. DCR81-14726.Work supported by NSF Grant No. DMS87-01895.     

The dual of a finitely generated multiplication module

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in 1986.     

On the augmented system approach to sparse least-squares problems

Summary We study the augmented system approach for the solution of sparse linear least-squares problems. It is well known that this method has better numerical properties than the method based on the normal equations. We use recent work by Arioli et al. (1988) to introduce error bounds and estimates for the components of the solution of the augmented system. In particular, we find that, using iterative refinement, we obtain a very robust algorithm and our estimates of the error are accurate and cheap to compute. The final error and all our error estimates are much better than the classical or Skeel's error analysis (1979) indicates. Moreover, we prove that our error estimates are independent of the row scaling of the augmented system and we analyze the influence of the Björck scaling (1967) on these estimates. We illustrate this with runs both on large-scale practical problems and contrived examples, comparing the numerical behaviour of the augmented systems approach with a code using the normal equations. These experiments show that while the augmented system approach with iterative refinement can sometimes be less efficient than the normal equations approach, it is comparable or better when the least-squares matrix has a full row, and is, in any case, much more stable and robust.This author was visiting Harwell and was funded by a grant from the Italian National Council of Research (CNR), Istituto di Elaborazione dell'Informazione-CNR, via S. Maria 46, I-56100 Pisa, ItalyThis author was visiting Harwell from Faculty of Mathematics and Computer Science of the University of Amsterdam     

增算子的不动点和耦合不动点

Under some general continuous and compact conditions, the existence problems of fiked points andd coupled fixed points for increasing operators are studied. an application, we utilize the results obtained to study the existence of solutions for differential inclusions in Banach spaces.     

Asymptotic expansions in sequential estimation for the first-order random coefficient autoregressive model: Regenerative approach

Edgeworth expansions for the distribution of a sequential least squares estimator in the random coefficient autoregressive (RCA) model are derived. The regenerative approach to second-order asymptotic analysis of Markov-type statistical models is developed.