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R. Hettich E. Haaren M. Ries G. Still 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》1987,67(12):589-597
In earlier papers [3, 4] a defect-minimization method was proposed to compute approximate eigenfunctions of membranes by means of a parametric semi-infinite optimization problem. The method gives approximations and error bounds of eigenvalues and eigenfunctions. An algorithm based on this method has been implemented for the special case of elliptic membranes with variable eccentricity. In this paper we show that by this method we obtain very accurate results even for eccentricities near one. In addition the method is very appropriate to study the behavior of eigenfunctions. 相似文献
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This paper presents duality results between generalized and inexact linear programs and describes a special type of linear semi-infinite programs in connection with the programs above mentioned. In order to solve inexact linear programs a corresponding auxiliary problem can be formulated which is explicitly solvable. However, this auxiliary problem is a reformulation of the reduced semi-infinite problem. Therefore, all the numerical methods for solving semi-infinite linear programs can be used for the numerical treatment of inexact and generalized linear programs.
Zusammenfassung Die vorliegende Arbeit zeigt Dualitätsergebnisse zwischen verallgemeinerten und inexakten linearen Programmen auf und beschreibt einen speziellen Typ linear-semi-infiniter Programme in Zusammenhang mit den oben erwähnten Optimierungsaufgaben. Um inexakte lineare Programme zu lösen wird ein Hilfsproblem aufgestellt, das explizit lösbar ist. Dieses Hilfsproblem ist eine Reformulierung des reduzierten semi-infiniten Problems. Daher können alle numerischen Methoden zur Lösung semi-infiniter linearer Programme auch zur numerischen Behandlung von inexakten und verallgemeinerten lineraren Programmen herangezogen werden.相似文献
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Philippe Weis;Clarissa Hettich;Daniel Kratzert;Ingo Krossing; 《欧洲无机化学杂志》2019,2019(11-12):1657-1668
By reacting P4Se3 and As4S3 with Ag[Al(ORF)4] {–RF = –C(CF3)3 or –hfip [= –C(H)(CF3)2]} in suitable solvents, Ag(P4Se3)[Al(Ohfip)4] (1), Ag(P4Se3)2[Al(ORF)4] (2), Ag(P4Se3)3[Al(ORF)4] (3), Ag2(As4S3)3[Al(ORF)4]2 (4) and Ag(As4S3)2[Al(ORF)4] (5) were synthesized and characterized by SC-XRD, Mass spectrometry, Raman spectroscopy as well as solution NMR spectroscopy. When using stronger coordinating anions, only P4Se3 forms an isolable complex yielding 1 featuring a [Ag2(P4Se3)2]2+ core capped by anions acting as the first example of P4Se3 coordinating through selenium atoms. Upon using the weakly coordinating anion [Al{OC(CF3)3}4]–, the dimeric complexes 2 and 4 are accessible in dichloromethane or ortho-difluorobenzene (o-dfb), respectively. Complex 2 shows isolated [Ag2(P4Se3)4(CH2Cl2)2]2+ dications with a [Ag2(P4Se3)2]2+ core similar to 1. Complex 4 shows isolated [Ag2(As4S3)3]2+ dications featuring a weak argentophilic contact. All of these complexes include solvent molecules or anions in the coordination sphere of the metal. When switching to the polar yet non-coordinating solvent SO2, the coordination spheres are filled with additional ligands and compounds 3 and 5 form. Complex 3 shows condensed [Ag(P4Se3)3]+ units yielding a one dimensional chain and represents the first homoleptic metal(P4Se3) complex. Complex 5 shows a similar paddle wheel structure as in 4 with interconnecting As4S3 ligands and is the first known example of a homoleptic metal(As4S3) complex. 相似文献
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Hai-Feng Ji Robert L. Hettich Gilbert M. Brown Reza Dabestani 《Photochemistry and photobiology》1999,70(6):882-886
We have synthesized two derivatives of alkylanthracene covalently bonded to 1,3-alternate calix[4]aza-crown-6 at the nitrogen position to study the effect of alkali metal ion complexation on the emission properties of anthracene fluorophore. The mono- and dianthryl-substituted probes are weakly fluorescent because their emission is partially quenched by photoinduced electron transfer (PET) from the nitrogen lone pair to the excited singlet state of anthracene. Upon complexation of alkali metal ions (e.g. K+, Cs+) by the crown moiety, the nitrogen lone pair can no longer participate in the PET process causing an enhancement in the emission of anthracene fluorophore (fluorescent turn on). The maximum fluorescence enhancement observed upon complexation of cesium ions by mono- and dianthryl-substituted calix[4]aza-crown-6 relative to the uncomplexed form was 8.5- and 11.6-fold, respectively. 相似文献
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Hansen H Aichele T Hettich C Lodahl P Lvovsky AI Mlynek J Schiller S 《Optics letters》2001,26(21):1714-1716
A pulsed, balanced homodyne detector has been developed for precise measurement of the electric field quadratures of pulsed optical quantum states. A high level of common mode suppression (>85 dB) and low electronic noise (730 electrons per pulse) provide a signal-to-noise ratio of 14 dB for measurement of the quantum noise of individual pulses. Measurements at repetition rates as high as 1 MHz are possible. As a test, quantum tomography of the coherent state was performed, and the Wigner function and the density matrix were reconstructed with 99.5% fidelity. The detection system can be used for ultrarsensitive balanced detection in cw mode, e.g., for weak absorption measurements. 相似文献