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1.
Germund Dahlquist 《BIT Numerical Mathematics》1993,33(1):85-112
An algorithm for accurate numerical inversion of slowly convergent Fourier and Laplace Transforms is studied. It makes use of several equidistant grids with the same number of points, covering different symmetric intervals of the time and frequency axes. Typically, the number of operations per computed function value is about twice as large as for an ordinary FFT. The distribution of points is, however, for many applications much more adequate because, globally, the union of the grids is an approximately equidistant point set on a logarithmic scale.Dedicated to Gene H. Golub on the occasion of his 60'th birthday 相似文献
2.
By Richardson extrapolation from 2h andh toh/2 the results of computations with coarse grids are used for the construction of an initial approximation on finer grid. After a rather small number of iterations high accuracy is obtained. Numerical results are given for the two-dimensional Laplace equation. 相似文献
3.
Germund Hjer 《International journal of quantum chemistry》1979,15(4):389-401
It is found that ordinary STO s fall off too fast in the atomic region in many cases. A new type of basis set, which is more adaptable to the rather different requirements of the various atomic orbitals in an atom, is developed. The suggested functional form χ(r) = Nrn-1 exp{?α[(βr + 1)1/2 ? 1]} contains the STO s as a limiting case. Calculations on a series of atoms from H to Zn show that the new basis gives better results than STO s for equal basis set size. The necessary integrals do not present any problem to evaluate. 相似文献
4.
The theoretical justification of the model potential method is studied in some detail. The correct equations within the framework of Roothaan's open-shell scheme are derived and the approximations necessary to get a workable method are discussed. Analysis of the local part of the model potential suggests a new analytical form for it. The new expression is theoretically more consistent than the original one, and it can be determined in a more straightforward way. A basis set approximation, which is particularly suitable for approximate evaluation of two-electron integrals when only valence orbitals are involved, is discussed and tested with encouraging results. The ideas are tested on the Fe and I atoms. 相似文献
5.
Norah Barba-Behrens America Vázquez-Olmos Silvia E. Castillo-Blum Germund Höjer Sara Meza-Höjer Rosa María Hernández María de Jesús Rosales-Hoz Ramón Vicente Albert Escuer 《Transition Metal Chemistry》1996,21(1):31-37
Summary The following coordination compounds derived from 2-guanidinobenzimidazole (2GB) (1); [Ni(2GB)2]Cl2· H2O, (2); [Ni(2GB)2]Br2·3H2O, (3); [Ni(2GB)2-(NO3)2, (4); [Ni(2GB)2](OAc)2, (5); [Cu(2GB)Cl2], (6); [Cu(2GB)Br2], (7); [Cu(2GB)2]Br2·2H2O, (8); [Cu(2GB)2](NO3)2·H2O, (9); [Cu(2GB)2](OAc)2· H2O, (10); [Zn(2GB)Cl2]·H2O, (11); [Zn(2GB)Br2]·H2O, (12); [Co(2GB)Cl2(H2O)2]·5H2O, (13); [Co-(2GB)2Cl2]·3H2O, (14); [Co(2GB)2(H2O)2](NO3)2· 4H2O, (15); and [Co(2GB)2(H2O)2](OAc)2, (16) have been synthesized and characterized by i.r. and electronic spectroscopy. In addition (6)–(10) were analysed by e.p.r. The X-ray diffraction structure of compound (4) was obtained. It crystallizes in the monoclinic system, C2/c (a = 22.511(7), b = 6.735(6) and c= 15.345(5)Å, =115.31(3)°, Z = 4, final R = 0.0360 and R
w = 0.0388 for 1167 observed independent reflections). The nickel(II) atom coordinates two ligands in a square-planar geometry through the imidazolic N(3) and the guanidino N(12).The probable ligand isomers involved in the coordination were determined by theoretical calculations, and the possible structures of the coordination compounds were investigated in order to verify that the experimentally proposed structures were stable. Two different types of coordination compounds were found. One, where the ligand is chelating through the imidazolic N(3) and the guanidino N(12), which is the case for most of the complexes [(2)–(13)]. With only one ligand in the coordination sphere, the structure was either tetrahedral (copper and zinc chloride and bromide complexes) or octahedral (cobalt). With two chelating 2GB units a square-planar geometry was stabilized [(2)–(5) and (8)–(10)]. The second type of coordination behaviour was observed in the cobalt compounds [(14)–(16)]. Here the ligand coordinates monodentate through the imidazolic N(3); the structure is tetrahedral. 相似文献
6.
A special stability problem for linear multistep methods 总被引:7,自引:0,他引:7
Germund G. Dahlquist 《BIT Numerical Mathematics》1963,3(1):27-43
The trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. For this method error bounds are derived which are valid under rather general conditions. In order to make sure that the error remains bounded ast , even though the product of the Lipschitz constant and the step-size is quite large, one needs not to assume much more than that the integral curve is uniformly asymptotically stable in the sense of Liapunov.The preparation of this paper was partly sponsored by the Office of Naval Research and the US Army Research Office (Durham). Reproduction in whole or in part is permitted for any purpose of the US Government. 相似文献
7.
A method for making secret programs for automatic identity checking with very high demands for security, is described. The consistency of the sequence of digits, which identifies the person, is tested by a sequence of transformations, chosen by means of a stored secret random table. The method has been implemented for a system of unattended cash dispenser terminals, equipped with microprocessors. 相似文献
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9.
Germund Dahlquist 《BIT Numerical Mathematics》1997,37(4):804-832
This part contains Chapter 3 (of 5), which is mainly concerned with the derivation, analysis and applications of a summation formula, due to Lindelöf, for alternating series and complex power series, including ill-conditioned power series. An appendix is devoted to complete monotonicity and related questions. The reader is referred to Part I (in this volume of BIT) for the abstract, the contents and the bibliography of the whole work. A short list of references for this part is at the end of this part. 相似文献
10.
Ins Nicols Martha Vilchis Nidia Aragn Ren Miranda Germund Hojer Miguel Castro 《International journal of quantum chemistry》2003,93(6):411-421
The structural and electronic parameters of the horminone molecule, an abietan diterpene quinone, were studied by means of all‐electron calculations using Hartree–Fock and density functional theory‐based methods, as implemented in the Gaussian98 program. The 6‐31G orbital basis sets were used for the C, H, O, and Mg atoms. The results allow the identification of the negative site of horminone (HM) most favorable for its binding to the Mg2+ ion. The HM–Mg2+ complex is assumed to play a significant role in the antibacterial activity. First, it penetrates the membrane cell. Then, through its interaction with rRNA, it inhibits the protein synthesis in several types of bacteria. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 411–421, 2003 相似文献