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91.
92.
Summary In the present work we extent the results in [RS] on CHIP, i.e. Cardinal Hermite Interpolation by the span of translates of directional derivatives of a box spline. These directional derivatives are that ones which define the type of the Hermite Interpolation. We admit here several (linearly independent) directions with multiplicities instead of one direction as in [RS]. Under the same assumptions on the smoothness of the box spline and its defining matrixT we can prove as in [RS]: CHIP has a system of fundamental solutions which are inL
L
2 together with its directional derivatives mentioned above. Moreover, for data sequences inl
p
(
d
), 1p2, there is a spline function inL
p, 1/p+1/p=1, which solves CHIP.Research supported in part by NSERC Canada under Grant # A7687. This research was completed while this author was supported by a grant from the Deutscher Akademischer Austauschdienst 相似文献
93.
Wolfgang Rother 《manuscripta mathematica》1989,65(4):413-426
We consider the semilinear eigenvalue problem
on N (N 2) (N2) and investigate the question under which conditions on the radially symmetric function q, =0 is a bifurcation point for this equation in H1, In H2 and in Lp for 2p+. 相似文献
94.
For smooth nonlinear systems
相似文献
95.
Wolfgang Rother 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1988,39(3):334-350
Summary Following a suggestion of J. Goodisman, we substitute the therm
by
in the Thomas-Fermi-von Weizsäcker energy functional for atoms.f
z3 [0,1] is a function depending on the nuclear chargez.We establish conditions for the functionsf
z
such that the ratio of this modified TFW-energyE
kz
/TFWG
(z) (kz is the total number of electrons) and the exact quantum mechanical energy converges to 1 asz. Moreover, we prove thatE
kz
/TFWG
(z)=E
kz
/TFW
(z)+Dz
2+o(z
2) (z) and determineD. Here,E
kz
/TFW
(z) is the unmodified TFW energy.
Zusammenfassung Einem Vorschlag J. Goodismans folgend, ersetzen wir in dem Thomas-Fermi-von Weizsäcker Energiefunktional für Atome den Term durch .f z3 [0,1] ist hierbei eine Funktion, die von der Kernladungszahlz abhängt.Wir geben dann Bedingungen für die Funktionenf z an, unter denen der Quotient der so modifizierten TFW-energieE kz /TFWG (z) (kz=Anzahl der Elektronen) und der exakten quantenmechanischen Energie fürz gegen 1 konvergiert. Darüber hinaus beweisen wir, daßE kz /TFWG (z)=E kz /TFW (z)+D·o(itz) 2 (z) gilt und bestimmmenD. E kz /TFW (z) ist hierbei die nicht-modifizierte TFW-Energie.相似文献 96.
A. Türler H. W. Gäggeler D. T. Jost P. Armbruster W. Brüchle H. Folger F. P. Heßberger S. Hofmann G. Münzenberg V. Ninov M. Schädel K. Sümmerer J. V. Kratz U. Scherer 《Zeitschrift für Physik A Hadrons and Nuclei》1988,331(3):363-364
The isotope254No was produced in the fusion reaction48Ca +208Pb. Using the velocity filter SHIP and radiochemical techniques it was found that the nuclide254No with a half-life of 55 s decays byα, EC, and spontaneous-fission. Deduced partial half-lives are (61±2) s forα-decay, (550 ?160 +370 ) s for EC and [2.2 ?1.0 +2.0 ]×104 s for spontaneous fission. 相似文献
97.
98.
Dirk Lützenkirchen‐Hecht Kay Rohrmann Thomas Stöcker Wolfgang Thiel 《Surface and interface analysis : SIA》2007,39(11):845-851
Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
99.
Naumann W 《The Journal of chemical physics》2005,123(6):64505
Fluorescence quenching by excimer formation is studied on the assumption that the excimer formation and dissociation can be modeled as overdamped motion in an attractive potential (classical potential models). An approach to the zeroth-order, concentration-independent quenching constants is proposed which starts from a mean reaction-time ansatz and reduces the calculation essentially to the solution of the eigenvalue problem for the Smoluchowski operator which describes the excimer equilibration. For a square-well potential model it is shown that a quenching constant expansion in terms of relaxation modes, truncated at the kinetic level, gives a satisfactory approximation of the recently obtained exact zeroth-order result under defined conditions. It is demonstrated how this two-mode approach can be applied for a quenching constant estimation if the excimer formation and dissociation are modeled by more realistic interaction potentials, as for instance, Morse- or Gaussian-type ones. 相似文献
100.
Wolfgang Werner 《Fresenius' Journal of Analytical Chemistry》1992,342(10):783-786
Summary Systematic quality assurance, e.g. in accordance with the provisions of ISO 9000, requires not only the targeted use of quality as a management tool, but also a revised attitude to operational procedures. Although sophisticated checking of the final results of a procedure (e.g. results of analyses, sales products, reports) meets the legal requirements and often also the customers' requirements, this misses the chance of being able to influence the quality of a final result at the earliest possible stage. It is then only possible subsequently to take the uneconomic decision as to whether the result of the work is useable or must be discarded or the object reworked. Within quality assurance, all operations are to be considered as processes with the aim of arriving at a statistically controlled process. The advantages of statistical process control are explained by way of examples from analytical procedures and production. The status of internal audits is explained as it interrelates with process control. 相似文献
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