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581.
We study the transport and mixing properties of flows in a variety of settings, connecting the classical geometrical approach via invariant manifolds with a probabilistic approach via transfer operators. For non-divergent fluid-like flows, we demonstrate that eigenvectors of numerical transfer operators efficiently decompose the domain into invariant regions. For dissipative chaotic flows such a decomposition into invariant regions does not exist; instead, the transfer operator approach detects almost-invariant sets. We demonstrate numerically that the boundaries of these almost-invariant regions are predominantly comprised of segments of co-dimension 1 invariant manifolds. For a mixing periodically driven fluid-like flow we show that while sets bounded by stable and unstable manifolds are almost-invariant, the transfer operator approach can identify almost-invariant sets with smaller mass leakage. Thus the transport mechanism of lobe dynamics need not correspond to minimal transport.The transfer operator approach is purely probabilistic; it directly determines those regions that minimally mix with their surroundings. The almost-invariant regions are identified via eigenvectors of a transfer operator and are ranked by the corresponding eigenvalues in the order of the sets’ invariance or “leakiness”. While we demonstrate that the almost-invariant sets are often bounded by segments of invariant manifolds, without such a ranking it is not at all clear which intersections of invariant manifolds form the major barriers to mixing. Furthermore, in some cases invariant manifolds do not bound sets of minimal leakage.Our transfer operator constructions are very simple and fast to implement; they require a sample of short trajectories, followed by eigenvector calculations of a sparse matrix. 相似文献
582.
Susanne V. Mayer Anton Murnauer Marie‐Kristin von Wrisberg Marie‐Lena Jokisch Kathrin Lang 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2019,131(44):16023-16029
Inverse electron‐demand Diels–Alder cycloadditions (iEDDAC) between tetrazines and strained alkenes/alkynes have emerged as essential tools for studying and manipulating biomolecules. A light‐triggered version of iEDDAC (photo‐iEDDAC) is presented that confers spatio‐temporal control to bioorthogonal labeling in vitro and in cellulo. A cyclopropenone‐caged dibenzoannulated bicyclo[6.1.0]nonyne probe (photo‐DMBO) was designed that is unreactive towards tetrazines before light‐activation, but engages in iEDDAC after irradiation at 365 nm. Aminoacyl tRNA synthetase/tRNA pairs were discovered for efficient site‐specific incorporation of tetrazine‐containing amino acids into proteins in living cells. In situ light activation of photo‐DMBO conjugates allows labeling of tetrazine‐modified proteins in living E. coli. This allows proteins in living cells to be modified in a spatio‐temporally controlled manner and may be extended to photo‐induced and site‐specific protein labeling in animals. 相似文献
583.
Stefan Burle Thorsten Blume Emmanuel Leroy Anne Mengel Christian Parchmann Kathrin Schmidt Werner Skuballa 《Tetrahedron letters》2004,45(52):9569-9571
Ring enlargement of ansa-steroids leads to a variety of novel templates which are suitable for the preparation of diverse libraries of natural product derivatives. Key steps for the synthesis of these highly functionalized templates were either an ozonolysis-derivatization-ring closing metathesis-sequence or a macrolactonization. 相似文献
584.
K. Kratzl G. Billek E. Klein K. Buchtela 《Monatshefte für Chemie / Chemical Monthly》1957,88(5):721-734
Zusammenfassung Coniferin-(3-14C) wurde in verholzendes Fichtengewebe implantiert. Nach Extraktion geringer löslicher Anteile wurde das Holzpulver einer Äthanolyse unterworfen, wobei aktives Vanilloylacetyl-(3-14C) isoliert werden konnte. Die Lokalisierung der Aktivität in der Seitenkette des Vanilloylacetyls wird beschrieben.Die Aktivität aller Äthanolyseprodukte wurde gemessen, einzelne oxydativ zu Vanillin, Vanillinsäure und Oxalsäure abgebaut. Durch Vergleich der molaren spezifischen Aktivität der isolierten Reinsubstanzen mit der Aktivität des eingesetzten Coniferins konnten Verdünnungsgrade errechnet werden, die das Ausmaß der Umwandlung des Coniferins in die einzelnen Fraktionen wiedergeben.Herrn Prof.F. Wessely zum 60. Geburtstag in Verehrung gewidmet. 相似文献
585.
Friedrich W. Vierhapper Erich Tengler Prof. Dr. Karl Kratzl 《Monatshefte für Chemie / Chemical Monthly》1975,106(5):1191-1201
Creosol (1), bicreosol (4) and other monomeric and dimeric creosols are oxidized in 0.25M-NaOH (5 equivalents base per phenolic hydroxyl group) by molecular oxygen at 70°C. Creosol is fragmented under these conditions to low molecular weight products without previous dimerization. The importance of fragmentation processes without cleavage of the C?C-bond between the oxygen substituted ring atoms in the case of bicreosol, and its considerable stability against oxidation compared with other compounds investigated can be explained by the ability of the monoanion of4 to exist in a conformation allowing hydrogen bonding between the phenolic oxygens of the two rings. 相似文献
586.
Dellnitz M Junge O Lo MW Marsden JE Padberg K Preis R Ross SD Thiere B 《Physical review letters》2005,94(23):231102
We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near the 3:2 Hilda resonance into the realm of orbits crossing Mars' orbit are computed. In contrast to common numerical approaches, our technique does not depend on single long term simulations of the underlying model. Thus, our statistical results are particularly reliable since they are not affected by a dynamical behavior which is almost nonergodic (i.e., dominated by strongly almost invariant sets). 相似文献
587.
588.
Karl Kratzl 《Mikrochimica acta》1956,44(1-3):159-170
Ohne Zusammenfassung 相似文献
589.
Kathrin Bringmann 《The Ramanujan Journal》2006,12(2):257-266
We use Rademacher’s method to obtain asymptotic expressions for some restricted partition functions. For fixed positive integers
m > 1 and l, we consider the number p
m
(n) of partitions of n into summands not divisible by m, and the number p
m
l
(n) of partitons of n with the further restriction that any integer occurs at most l times as a summand.
2000 Mathematics Subject Classification Primary—11P82; Secondary—11P83 相似文献
590.
P. Claus E. Klein W. Grosch H. Bertl K. Kratzl 《Monatshefte für Chemie / Chemical Monthly》1966,97(1):271-280
Zusammenfassung Es wird die Synthese von N-Hydroxymethylamiden choleretisch wirksamer Phenolcarbonsäuren sowie von Alkoxymethyläthern mykostatisch wirksamer Phenolcarbonsäureester beschrieben.
Meinem Lehrer, Herrn Prof.A. v. Wacek, zum 70. Geburtstag gewidmet. 相似文献
The preparation of N-hydroxymethylamides of phenolic carboxylic acids with choleretic activity and of alkoxymethyl ethers of phenolic ethyl benzoates with mycostatic activity is described.
Meinem Lehrer, Herrn Prof.A. v. Wacek, zum 70. Geburtstag gewidmet. 相似文献