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51.
52.
Christian Bär 《Communications in Mathematical Physics》1997,188(3):709-721
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension
2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that
the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface
and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold
has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal.
Received: 28 October 1996 / Accepted: 3 March 1997 相似文献
53.
The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl2 is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl. 相似文献
54.
P. Thomsen-Schmidt K. Hasche G. Ulm K. Herrmann M. Krumrey G. Ade J. Stümpel I. Busch S. Schädlich A. Schindler W. Frank D. Hirsch M. Procop U. Beck 《Applied Physics A: Materials Science & Processing》2004,78(5):645-649
High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO2 on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh 相似文献
55.
The separation of the toxicologically important aldehyde acrolein from other carbonyl compounds by high performance liquid chromatography after derivatization to 2,4-dinitrophenylhydrazones is critically discussed on the basis of a selection of published methods. A method is proposed whereby the compounds acrolein, acetone, and propanal may be reproducibly separated to baseline by a reversed phase HPLC procedure employing a ternary mixture of methanol, water, and acetonitrile as mobile phase. 相似文献
56.
Christian Hill 《Journal of Molecular Spectroscopy》2007,241(1):15-17
Recently-formulated centrifugal distortion corrections to the spin-spin Hamiltonian have been used to analyse the first excited triplet state (ã3A2) of deuterated selenoformaldehyde. By including six spin-spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required. 相似文献
57.
58.
Christian Wolf 《Journal of statistical physics》2006,122(6):1111-1138
In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical
physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform
a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete
theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification
for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss
possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence
of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques
from smooth ergodic theory including the thermodynamic formalism.
2000
Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30 相似文献
59.
Björn Wängler Carmen Beck Esther Schirrmacher Frank Rösch Michael Eisenhut 《Tetrahedron letters》2006,47(33):5985-5988
The synthesis of tris-allyl-DOTA starting from cyclen and its application in the preparation of DOTA-peptide conjugates is reported. Clinically important conjugates such as DOTA-Tyr3-octreotide (DOTA-TOC), DOTA-Tyr3-octreotate (DOTA-TATE) as well as a DOTA-RGD peptide were synthesized in high yields with Fmoc solid phase peptide synthesis. The final, extremely reliable de-allylation was achieved on solid phase by different methods identifying morpholine/Pd(0) as the most suitable one obtaining all DOTA peptide conjugates in high yields. All DOTA-peptides were purified by reversed phase HPLC and structural identity was proved using MALDI-TOF mass spectrometry. 相似文献
60.
Oscillatory change of pH occurs during the chromate-catalyzed decomposition of hydrogen peroxide in a weakly acidic medium at elevated temperature and at high initial concentration of hydrogen peroxide. In a closed system, there are only two or three periods, but sustained oscillation occurs in a CSTR. In a CSTR bistability is also found. In closed systems the temperature exhibits a great maximum (up to 15°C increase), in a CSTR sustained oscillation occurs at a constant stationary temperature. 相似文献