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Horst Bingmann Lothar Knothe Dieter Hunkler Horst Prinzbach 《Tetrahedron letters》1979,20(42):4053-4056
The vinylogous heptafulvalene (“heptafulvadiene”) (5) cleanly undergoes the antarafacial 16-electron electrocyclisation to (11) upon thermal activation (benzene, Ea = 22.1 kcal/mol; log A = 10.8). 相似文献
994.
Benzylic C-C bonds in diarylmethanes and diarylethanes (Ar = phenyl, naphthyl) are cleaved by potassium in dimethoxyethane/octaglyme. 相似文献
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This paper discusses an application of partial tensor Golub–Kahan bidiagonalization to the solution of large-scale linear discrete ill-posed problems based on the t-product formalism for third-order tensors proposed by Kilmer and Martin (M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl., 435 (2011), pp. 641-658). The solution methods presented first reduce a given (large-scale) problem to a problem of small size by application of a few steps of tensor Golub–Kahan bidiagonalization and then regularize the reduced problem by Tikhonov's method. The regularization operator is a third-order tensor, and the data may be represented by a matrix, that is, a tensor slice, or by a general third-order tensor. A regularization parameter is determined by the discrepancy principle. This results in fully automatic solution methods that neither require a user to choose the number of bidiagonalization steps nor the regularization parameter. The methods presented extend available methods for the solution for linear discrete ill-posed problems defined by a matrix operator to linear discrete ill-posed problems defined by a third-order tensor operator. An interlacing property of singular tubes for third-order tensors is shown and applied. Several algorithms are presented. Computed examples illustrate the advantage of the tensor t-product approach, in comparison with solution methods that are based on matricization of the tensor equation. 相似文献
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Caterina Fenu Lothar Reichel Giuseppe Rodriguez 《Numerical Linear Algebra with Applications》2016,23(3):467-484
Generalized cross validation is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small‐scale problems, but prohibitively expensive to compute for large‐scale ones. This paper describes a novel method, based on Gauss‐type quadrature, for determining upper and lower bounds for the desired expression. These bounds are used to determine the regularization parameter for large‐scale problems. Computed examples illustrate the performance of the proposed method and demonstrate its competitiveness. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Lothar Heinrich 《Applications of Mathematics》2016,61(4):443-461
First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function C(x, y) defining an α-determinantal point process (DPP). Assuming absolute integrability of the function C0(x) = C(o, x), we show that a stationary α-DPP with kernel function C0(x) is “strongly” Brillinger-mixing, implying, among others, that its tail-σ-field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications to statistical second-order analysis of α-DPPs. 相似文献
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Absolute Configuration from Different Multifragmentation Pathways in Light‐Induced Coulomb Explosion Imaging 下载免费PDF全文
Dr. Martin Pitzer Gregor Kastirke Dr. Maksim Kunitski Dr. Till Jahnke Dr. Tobias Bauer Christoph Goihl Florian Trinter Carl Schober Kevin Henrichs Jasper Becht Stefan Zeller Helena Gassert Markus Waitz Andreas Kuhlins Hendrik Sann Felix Sturm Florian Wiegandt Dr. Robert Wallauer Dr. Lothar Ph. H. Schmidt Allan S. Johnson Manuel Mazenauer Benjamin Spenger Sabrina Marquardt Sebastian Marquardt Prof. Dr. Horst Schmidt‐Böcking Prof. Dr. Jürgen Stohner Prof. Dr. Reinhard Dörner Dr. Markus Schöffler Prof. Dr. Robert Berger 《Chemphyschem》2016,17(16):2465-2472
The absolute configuration of individual small molecules in the gas phase can be determined directly by light‐induced Coulomb explosion imaging (CEI). Herein, this approach is demonstrated for ionization with a single X‐ray photon from a synchrotron light source, leading to enhanced efficiency and faster fragmentation as compared to previous experiments with a femtosecond laser. In addition, it is shown that even incomplete fragmentation pathways of individual molecules from a racemic CHBrClF sample can give access to the absolute configuration in CEI. This leads to a significant increase of the applicability of the method as compared to the previously reported complete break‐up into atomic ions and can pave the way for routine stereochemical analysis of larger chiral molecules by light‐induced CEI. 相似文献