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991.
Thomas H Pate 《Journal of Differential Equations》1979,34(2):261-272
If m and n are positive integers then let S(m, n) denote the linear space over R whose elements are the real-valued symmetric n-linear functions on Em with operations defined in the usual way. If is a function from some sphere S in Em to R then let (i)(x) denote the ith Frechet derivative of at x. In general (i)(x)∈S(m,i). In the paper “An Iterative Method for Solving Nonlinear Partial Differential Equations” [Advances in Math. 19 (1976), 245–265] Neuberger presents an iterative procedure for solving a partial differential equation of the form , where k > n, is the unknown from some sphere in Em to R, A is a linear functional on S(m, n), and F is analytic. The defect in the theory presented there was that in order to prove that the iterates converged to a solution the condition was needed. In this paper an iteration procedure that is a slight variation on Neuberger's procedure is considered. Although the condition cannot as yet be eliminated, it is shown that in a broad class of cases depending upon the nature of the functional A the restriction may be replaced by the restriction . 相似文献
992.
Ludwig Arnold 《Linear algebra and its applications》1976,13(3):185-199
It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let An=(aij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ(n)}1?k?n its eigenvalues, and {uk(n)}1?k?n the corresponding (orthonormalized column) eigenvectors. Let , put (bookeeping function for the length of the projections of the new row v1n of An onto the eigenvectors of the preceding matrix An?1), and let finally (empirical distribution function of the eigenvalues of . Suppose (i) , (ii) limnXn(t)=Ct(0<C<∞,0?t?1). Then ,where W is absolutely continuous with (semicircle) density 相似文献
993.
Levels of138Ce and140Nd have been studied using the138Ba(α,4nγ)138Ce and140Ce(α, 4nγ)140Nd reactions. Singleγ-ray spectra,γ-γ coincidence spectra, angular and time distributions with respect to the beam bursts have been measured. A number of higher excited states with excitation energies up to about 5 MeV and with spin value up to 12 are populated in both nuclei. The lower states with spins and parities 7?, 5?, 6? and 10+ can be explained by two-quasiparticle neutron configurations of the types (h 11/2 ?1 ,d 3/2 ?1 ) 7? , (h 11/2 ?1 ,S 1/2 ?1 ) 5?, 6? and (h 11/2 ?2 ) 10+. Several high-spin states observed in138Ce and140Nd can be explained qualitatively as four-quasiparticle states with two-proton-two-neutron configurations. The 3? state at an energy of 2,137.4 keV is observed in138Ce. The evidence for the existence of the low-lying 3? states in140Nd at 2,124.0 keV is discussed. Beside the known 9.6 ms (7?) isomeric state in138Ce another state at 3,538.5keV (10+) with a half life of about 200 ns has been observed. The observed levels in the138Ce and140Nd nuclei are compared with theoretical predictions using delta force interaction. 相似文献
994.
995.
Arnold Kirsch 《ZDM》2014,46(4):691-695
The paper wants to show how it is possible to develop based on an adequate basic idea (so-called “Grundvorstellung”) of the derivative a visual understanding of the (first) Fundamental theorem of Calculus. 相似文献
996.
997.
Iwan Jerjen Vincent Revol Andreas J. Brunner Philipp Schuetz Christian Kottler Rolf Kaufmann Thomas Luethi Giovanni Nicoletti Claus Urban Urs Sennhauser 《Polymer Testing》2013
The processing of thermoplastics can induce a wide range of defects such as stress whitening, cavitation and porosity, which can adversely affect the reliability of the final products. Hence, fast and effective non-destructive detection methods for such defects are highly important for quality assurance on production lines. In this paper, X-ray dark field imaging is presented as a new non-destructive testing method that allows the visualization of stress whitening or cavitation efficiently. The performance of the method is demonstrated for the case of an injection-moulded polyvinylidene fluoride part that exhibits stress whitening. Whereas the stress whitening could not be detected by conventional X-ray imaging, it was localized by an X-ray dark field image acquired within a few minutes. Once the precise location of the stress whitening was known, it was possible to verify the result by local micro X-ray computed tomography and by a micro section image. 相似文献
998.
Mark P. Waller Thomas Dresselhaus Jack Yang 《Journal of computational chemistry》2013,34(16):1420-1428
Here, we present just a collection of beans (JACOB): an integrated batch‐based framework designed for the rapid development of computational chemistry applications. The framework expedites developer productivity by handling the generic infrastructure tier, and can be easily extended by user‐specific scientific code. Paradigms from enterprise software engineering were rigorously applied to create a scalable, testable, secure, and robust framework. A centralized web application is used to configure and control the operation of the framework. The application‐programming interface provides a set of generic tools for processing large‐scale noninteractive jobs (e.g., systematic studies), or for coordinating systems integration (e.g., complex workflows). The code for the JACOB framework is open sourced and is available at: www.wallerlab.org/jacob . © 2013 Wiley Periodicals, Inc. 相似文献
999.
1000.
Dr. Joice Thomas Dr. Liliana Dobrzańska Prof. Luc Van Meervelt Prof. Mario Alfredo Quevedo Prof. Krzysztof Woźniak Marcin Stachowicz Prof. Mario Smet Prof. Wouter Maes Prof. Wim Dehaen 《Chemistry (Weinheim an der Bergstrasse, Germany)》2016,22(3):979-987
A synthetic route towards homodiselenacalix[4]arene macrocycles is presented, based on the dynamic covalent chemistry of diselenides. The calixarene inner rim is decorated with either alkoxy or tert‐butyl ester groups. Single‐crystal X‐ray analysis of two THF solvates with methoxy and ethoxy substituents reveals the high similarity of their molecular structures and alterations on the supramolecular level. In both crystal structures, solvent channels are present and differ in both shape and capacity. Furthermore, the methoxy‐substituted macrocycle undergoes a single‐crystal‐to‐single‐crystal transformation during which the molecular structure changes its conformation from 1,3‐alternate (loaded with THF/water) to 1,2‐alternate (apohost form). Molecular modelling techniques were applied to explore the conformational and energetic behaviour of the macrocycles. 相似文献