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1.
Peter G. Casazza Gitta Kutyniok Mark C. Lammers 《Journal of Fourier Analysis and Applications》2004,10(4):383-408
Duality principles in Gabor theory such as the Ron–Shen duality principle and the
Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this
article we present a general approach to derive duality principles in abstract frame theory. For
each sequence in a separable Hilbert space we define a corresponding sequence dependent only
on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms
of the associated one, which yields duality relations for the abstract frame setting. In the last part
we apply our results to Gabor systems. 相似文献
2.
Pete Johnson 《School science and mathematics》2007,107(7):279-292
Over one‐third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses. 相似文献
3.
Peter G. Casazza Ole Christensen Alexander M. Lindner Roman Vershynin 《Proceedings of the American Mathematical Society》2005,133(4):1025-1033
We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linearly independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences.
4.
Experimental Techniques - 相似文献
5.
Béla Pete 《Tetrahedron letters》2003,44(12):2537-2539
Valuable new synthetic intermediates, 4- or 6-chloromethyl-1H-indole-2-carboxylates, were prepared by the elimination of SO2 from 2-ethoxycarbonyl-1H-indole-4- or 6-methanesulfonic acids, respectively, which are easily accessible by Fischer-type indolization. 相似文献
6.
Nitrogen bridgehead compounds part 21. Preparation of new quaternary 2,3a,6a-triazaphenalenium salts
István Bitter Béla Pete István Hermecz Gábor Tóth Kálmán Simon Mátyás Czugler Zoltán Mészáros 《Tetrahedron letters》1982,23(28):2891-2894
The first representatives of a new ring system, the 2,3a,6a-triazaphenalenium quaternary salts are prepared by the cycloaddition of tetrahydro-4H-pyrido[1,2-a] pyrimidin-4-ones containing an α-chloroenamine moiety with azomethines. 相似文献
7.
The photochemical behaviour of 2-alkylamino 2-cyclohexenones is very sensitive to the nitrogen substituents. α-Ketoazetidines are produced by irradiation of 2-methanesulfonamido-2-cyclohexenones; however a desulfonation and aryl migration process can compete in the case of 2-arenesulfonamido-2-cyclohexenones. Furthermore divinylamine and photo-Fries rearrangements are the main reactions with 2-anilino 2-cyclohexnone and 2-benzoylamido 2-cyclohexenone respectively. 相似文献
8.
The first examples of sequential photocycloaddition-rearrangement reactions of naphthalene-tethered resorcinol ethers are described. Bichromophoric aromatic compounds with naphthalene and resorcinol ether moieties were irradiated in the presence/absence of a small amount of acid to give the corresponding cycloaddition-rearrangement products. From the determination of quantum yields, steady-state fluorescence spectral studies, and fluorescence lifetime measurements, the mechanism of this novel photoinduced multistep reaction was elucidated to involve the initial intramolecular exciplex formation, followed by the intramolecular [2 + 2] photocycloaddition between the two aromatic rings and the subsequent acid-catalyzed skeletal rearrangement of the resulting cyclobutane derivative leading to the final products. 相似文献
9.
The first example of fluorine elimination α to a carboxyl group is reported. The defluorination occurs when solution of perfluorocarboxylic esters in hexamethyl-phosphortriamide are irradiated with UV light (254 nm). Mechanistic and synthetic aspects of this new reaction are described. 相似文献
10.