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Simple (abstract algebra)
About: Simple (abstract algebra) is a research topic. Over the lifetime, 22861 publications have been published within this topic receiving 341569 citations.
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TL;DR: For the molecules Be2, F2, and P2 of Table I, the unrestricted Hartree-Fock solution breaks the singlet spin symmetry, even though the density functional solutions do not.
Abstract: For the molecules Be2, F2, and P2 of Table I, the unrestricted Hartree-Fock solution breaks the singlet spin symmetry, even though the density-functional solutions do not. For these broken-symmetry solutions, the UHF atomization energies become 17, 220, and 141 kcalymol, respectively, and the mean absolute error of all the UHF atomization energies becomes 69.8 kcalymol. The PBE correlation energy of the two-electron ions of nuclear charge Z ! ` should be corrected to 20.0479 hartree, consistent with the PBE value v 0.046644 stated in the Letter. The quoted value 20.0482 hartree was obtained from the more refined v 0.046920 of G. G. Hoffman, Phys. Rev. B 45, 8730 (1992). Reference [6] should have been “A. C. Scheiner, J. Baker, and J. W. Andzelm, J. Comput. Chem. (to be published)”.
11,883 citations
TL;DR: In this article, the applicability of statistics to a wide field of problems is discussed, and examples of simple and complex distributions are given, as well as a discussion of the application of statistics in a wide range of problems.
Abstract: This paper discusses the applicability of statistics to a wide field of problems. Examples of simple and complex distributions are given.
9,091 citations
TL;DR: Kernel methods are of flexible form and can be used where simple parametric models are found to be inappropriate or difficult to specify and give alternative approaches to the Anderson (1982) Fourier transform methods.
Abstract: In this paper kernel methods for the nonparametric estimation of the utilization distribution from a random sample of locational observations made on an animal in its home range are described. They are of flexible form, thus can be used where simple parametric models are found to be inappropriate or difficult to specify. Two examples are given to illustrate the fixed and adaptive kernel approaches in data analysis and to compare the methods. Various choices for the smoothing parameter used in kernel methods are discussed. Since kernel methods give alternative approaches to the Anderson (1982) Fourier transform methods, some comparisons are made.
3,949 citations
01 Jan 1995
2,821 citations