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91.
The racemic cis-anti-trans-steroids 9 to 11 have been synthesized in a highly stereoselective manner starting from 4-methoxybenzocyclobutene carboxylic acid via the key step 8 → 9 . (cf. Scheme 2). 相似文献
92.
93.
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96.
R. J. Schilling 《纯数学与应用数学通讯》1987,40(4):455-522
The following observation, due to E. Trubowitz, illustrates an intimate relationship between spectral theory and Hamiltonian mechanics in the presence of constraints. Let q(s) be a real periodic function such that the Hill operator, has only a finite number gR of simple eigenvalues. There exist gR + 1 periodic eigenfunctions x1,…, x and corresponding eigenvalues a1,…, a of L such that where yr = dxr/ds. The equations Lxr = arxr, r = 1,…,gR+1, make up the classical Neumann system, a system of harmonic oscillators constrained to the unit sphere. H. Flaschka obtained similar results about the Neumann system from a more general point of view. His assumption, that there exists an operator of odd order that commutes with L, leads to algebraic curve theory by the method of Krichever and from there to the Neumann formulas above. The familiar Lax pairs, the constants of motion and the quadrics of the Neumann system emerge as consequences of the Riemann-Roch theoreni. The existence of isospectral deformations of L, the Korteweg de-Vries hierarchy of the soliton equations, underlies the complete integrability of the Neumann system. This paper extends Flaschka's techniques, replacing L by an operator of order n 2 2. Higher Neumann systems are defined in a way that leads naturally to interesting symplectic manifolds, Lax pairs and integrals of motion. C. Tomei, using scattering theory, obtained some of our n = 3 formulas. 相似文献
97.
We construct for each n2 an isometric C-imbedding HnE6n–6 of the n-dim. hyperbolic space into the Euclidean space E6n–6 whose image is the graph of a C-map RnR5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2). 相似文献
98.
Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits. 相似文献
99.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》1986,102(1):27-58
Very general hypersurfaces in 4 contain r
2+(4/9) integer points in any ball of radiusr>1. As a consequence, an irreducible algebraic hypersurface in
n
(wheren4) which is not a cylinder and is of degreed, contains c(d, n)r
n–1–(5/9) integer points in a ball of radiusr. This improves on the known boundc(d, n)r
n–(3/2).Meinem verehrten Lehrer Professor E. Hlawka zum siebzigsten Geburtstag gewidmetWritten with partial support from NSF-MCS-8211461. 相似文献
100.
The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer. 相似文献