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51.
Masaaki Sugihara 《Numerische Mathematik》1997,75(3):379-395
Summary. In the light of the functional analysis theory we establish the optimality of the double exponential formula. The argument
consists of the following three ingredients: (1) introduction of a number of spaces of functions analytic in a strip region
about the real axis, each space being characterized by the decay rate of their elements (functions) in the neighborhood of
the infinity; (2) proof of the (near-) optimality of the trapezoidal formula in each space introduced in (1) by showing the
(near-) equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum
error norm of quadratures; (3) nonexistence theorem for the spaces, the characterizing decay rate of which is more rapid than
the double exponential.
Received September 15, 1995 / Accepted December 14, 1995 相似文献
52.
We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP
n
. For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish
a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP
n
and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of
the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by
congruence classes or if distances π/2 are allowed. Finally we do the same
kind of investigation also for the complex hyperbolic space ℂH
n
. Most of the results are completely analogous, however, there are also some interesting differences.
Received: 15 January 1996 相似文献
53.
54.
Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and
[16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized
by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which
an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement
indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results.
Received May 15, 1995 / Revised version received April 17, 1996 相似文献
55.
56.
Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are
presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods
are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods.
Received December 19, 1994 / Revised version received January 18, 1996 相似文献
57.
提出用溶胶粒子表面修饰方法,结合溶胶凝胶技术制备无机催化膜.该方法的基本原理是利用合适的金属配合物在胶粒表面的吸附作用,经溶胶凝胶过程,将活性组分结合到无机膜中.实验测定结果表明:(NiEDTA)2-,VO-3,MoO2-4,(Pd(NH3)4)2+,PdCl2-4,PtCl2-6和RhCl3-6可用来修饰AlOOH溶胶.以Pd/γAl2O3催化膜的制备为例,经三次溶胶凝胶过程,可制得无裂缺的厚度为9μm的Pd/γAl2O3催化膜,膜材料的平均孔直径为6nm,Pd被均匀地分布在膜的顶层,其平均粒径为23nm. 相似文献
58.
Addition of functionalized zinc-copper reagents to the title complexes proceeds in a highly diastereoselective fashion to afford dienol complexes. The relative configurations of adducts 3d were determined by single X-ray diffraction analysis. 相似文献
59.
The characterization of the clusters formed on alkaline hydrolysis of [PdCl4]2– was performed using17O,23Na,35Cl,133Cs NMR and UV spectroscopy. The chemical composition of the clusters was found to be [Pd(OH)2]
n
·nNaCl. No mononuclear oxo- or hydroxocomplexes were detected. The spatial structure of the clusters is stabilized by alkali metal cations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 675–679, April, 1993. 相似文献
60.
The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data. 相似文献