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1.
Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are
presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods
are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods.
Received December 19, 1994 / Revised version received January 18, 1996 相似文献
2.
Lancaster G.P.T. Häffner H. Wilson M.A. Becher C. Eschner J. Schmidt-Kaler F. Blatt R. 《Applied physics. B, Lasers and optics》2003,76(8):805-808
We present a scheme for employing a violet extended-cavity diode laser in experiments with single, trapped ions. For this the grating-stabilised laser is spatially and spectrally filtered and referenced to a Fabry–Pérot cavity. We measure an upper limit to the line width by observing a 305-kHz FWHM beat note with the second harmonic of a titanium sapphire laser. The laser is subsequently used to optically cool a single 40Ca+ ion close to the Doppler limit. PACS 03.67.Lx; 32.80.Pj; 42.55.Px 相似文献
3.
4.
Pennington DA Coles SJ Hursthouse MB Bochmann M Lancaster SJ 《Chemical communications (Cambridge, England)》2005,(25):3150-3152
The mono(salicylaldiminato) complexes Ti{3-tBu-2-(O)C6H3CH=N(R)}Cl3(THF)(where R = C6H5, C6F5) react with the metallated pyrrolylaldiminato ligand, K[2-(C6H5NCH)C4H3N], to afford the first examples of hybrid salicylaldiminato-ligated octahedral titanium complexes; the pre-catalysts give from very high to extremely high ethene polymerisation productivities when activated with MAO. 相似文献
5.
Bolei Yan Simon W. Lewis Paul J. Worsfold J.Steven Lancaster Anthony Gachanja 《Analytica chimica acta》1991
An overview of liquid phase chemiluminescence (CL) processes is presented and the potential for CL detection in liquid chromatography (LC) is discussed, with particular reference to the luminol and peroxyoxalate reactions. Post column ion displacement from a solid phase reagent [a cation exchange resin in the copper(II) form] followed by catalysis of the luminol reaction is used for the quantification of mixtures of weak acids after separation by ion-exclusion chromatography. Polyaromatic hydrocarbons (PAHs) released during the combustion of biomass fuels are separated by reversed-phase chromatography and quantified by their sensitizing effect on the peroxyoxalate reaction. This procedure is also used for the determination of carboxylic acids in non-aqueous media after selective pre-column derivatization with a fluorescent label (9-anthracenemethanol). 相似文献
6.
Battle PD Blundell SJ Brooks ML Hervieu M Kapusta C Lancaster T Nair SP Oates CJ Pratt FL Rosseinsky MJ Ruiz-Bustos R Sikora M Steer CA 《Journal of the American Chemical Society》2004,126(39):12517-12527
The temperature dependence of the crystal structure and electronic properties of brownmillerite-like Ca(2.5)Sr(0.5)GaMn(2)O(8) has been studied by neutron powder diffraction and muSR spectroscopy. The results show that short-range 2D magnetic order begins to develop within the perovskite-like bilayers of MnO(6) octahedra approximately 50 K above the 3D Néel temperature of approximately 150 K. The bilayers show a structural response to the onset of magnetism throughout this temperature range whereas the GaO(4) layers that separate the bilayers only respond below the 3D ordering temperature. XANES spectroscopy shows that the sample contains Mn(3+) and Mn(4+) cations in a 1:1 ratio, and the behavior in the region of the Néel transition is interpreted as a local charge ordering. Electron diffraction and high-resolution electron microscopy have been used to show that the local microstructure is more complex than the average structure revealed by neutron diffraction, and that microdomains exist in which the GaO(4) tetrahedra show different orientations. It is argued that the bonding requirements of diamagnetic gallium control the electronic behavior within the perovskite-like bilayers. 相似文献
7.
Adams MR Aïd S Anthony PL Averill DA Baker MD Baller BR Banerjee A Bhatti AA Bratzler U Braun HM Breidung H Busza W Carroll TJ Clark HL Conrad JM Davisson R Derado I Dhawan SK Dietrich FS Dougherty W Dreyer T Eckardt V Ecker U Erdmann M Faller F Fang GY Figiel J Finlay RW Gebauer HJ Geesaman DF Griffioen KA Guo RS Haas J Halliwell C Hantke D Hicks KH Hughes VW Jackson HE Jancso G Jansen DM Jin Z Kaufman S Kennedy RD Kinney ER Kirk T Kobrak HG Kotwal AV Kunori S Lancaster S Lord JJ Lubatti HJ 《Physical review letters》1995,74(9):1525-1529
8.
9.
LoSecco JM Bionta RM Biewitt G Bratton CB Casper D Chrysicopoulou P Claus R Cortez BG Errede S Foster GW Gajewski W Ganezer KS Goldhaber M Haines TJ Jones TW Kielczewska D Kropp WR Learned JG Lehmann E Park HS Reines F Schultz J Seidel S Shumard E Sinclair D Sobel HW Stone JL Sulak L Svoboda R van der Velde JC Wuest C 《Physical review letters》1985,54(21):2299-2301
10.
Pennington DA Clegg W Coles SJ Harrington RW Hursthouse MB Hughes DL Light ME Schormann M Bochmann M Lancaster SJ 《Dalton transactions (Cambridge, England : 2003)》2005,(3):561-571
The silyl ethers 3-But-2-(OSiMe3)C6H3CH=NR (2a-e) have been prepared by deprotonation of the known iminophenols (1a-e) and treatment with SiClMe3 (a, R = C6H5; b, R = 2,6-Pri2C6H3; c, R = 2,4,6-Me3C6H2; d, R = 2-C6H5C6H4; e, R = C6F5). 2a-c react with TiCl4 in hydrocarbon solvents to give the binuclear complexes [Ti{3-But-2-(O)C6H3CH=N(R)}Cl(mu-Cl3)TiCl3] (3a-c). The pentafluorophenyl species 2e reacts with TiCl4 to give the known complex Ti{3-But-2-(O)C6H3CH=N(R)}2Cl2. The mononuclear five-coordinate complex, Ti{3-But-2-(O)C6H3CH=N(2,4,6-Me3C6H2)}Cl3 (4c), was isolated after repeated recrystallisation of 3c. Performing the dehalosilylation reaction in the presence of tetrahydrofuran yields the octahedral, mononuclear complexes Ti{3-But-2-(O)C6H3CH=N(R)}Cl3(THF) (5a-e). The reaction with ZrCl4(THF)2 proceeds similarly to give complexes Zr{3-But-2-(O)C6H3CH=N(R)}Cl3(THF) (6b-e). The crystal structures of 3b, 4c, 5a, 5c, 5e, 6b, 6d, 6e and the salicylaldehyde titanium complex Ti{3-But-2-(O)C6H3CH=O}Cl3(THF) (7) have been determined. Activation of complexes 5a-e and 6b-e with MAO in an ethene saturated toluene solution gives polyethylene with at best high activity depending on the imine substituent. 相似文献