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Karl Gustafson 《Numerical Linear Algebra with Applications》2004,11(7):649-659
Given the operator product BA in which both A and B are symmetric positive‐definite operators, for which symmetric positive‐definite operators C is BA symmetric positive‐definite in the C inner product 〈x, y〉C? This question arises naturally in preconditioned iterative solution methods, and will be answered completely here. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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The structure, harmonic frequencies, and nonresonance Raman intensities for porphin, tetraazaporphin (TAP), and three of its isotopomers are calculated by the density-functional theory of B3LYP/6-31G(d). Scaling of force constants for porphin in nonredundant natural coordinates is performed. The scaling factors obtained were used to predict the force field and normal modes of TAP and three of its isotopomers. Two alternative methods are used to carry out reliable assignment of the TAP frequencies: wavenumber-linear scaling method and frequency-shift method. There is good agreement between the frequencies predicted within the framework of the three methods used. The conservativeness of the out-of-plane B
2g
- and B
3g
-modes for porphin and TAP is examined. The Raman spectrum for TAP is simulated. A refinement of the assignment of the experimental frequencies for TAP of even symmetry types on the basis of the calculations performed is made. 相似文献
15.
We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove
that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY. 相似文献
16.
HUYUDA MENGZHIQING 《高校应用数学学报(英文版)》1998,13(4):473-477
In this paper, the existence theorem of the cone-weak subdiflerential of set-valued mapping in locally convex topological vector space is proved. 相似文献
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当产品质量指标服从二元正态分时,可用T2控制图与Λ控制图联合判断产品生产的过程是否处于受控状态。本文利用T2统计量与F统计量、Λ统计量与F统计量之间的关系,得到了两指标情形下两类基于F分布统计量的统计过程控制图,简称双F统计过程控制图,并给出了控制图应用实例。 相似文献
19.
This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results. 相似文献
20.
The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L *(π 1(Y) → π 1(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π 1(X) ? π 1(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP * for manifold pairs and splitting obstruction groups LS *. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds. 相似文献