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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.
13.
Stanis aw Urban Maria Massalska-Arod
Albert Wü rflinger Roman D browski 《Liquid crystals》2003,30(3):313-318
The pressure-temperature ( p - T ) phase diagrams for four smectogenic members of the 4'-alkyl-4-cyanobiphenyl homologous series ( n CB, n =9, 10, 11 and 12) over the temperature range 320-410 K and pressure range 0.1-300 MPa (3 kbar) were constructed using DTA. At 1 atm 9CB exhibits nematic and smectic A d phases, while the other members show only the smectic A d phase. However, at elevated pressures the clearing line splits in the case of 10CB and 11CB which indicates the induction of a nematic phase. It was found that the triple point, where the isotropic, nematic and smectic phases coexist, is strongly shifted to higher pressures with increasing chain length. This was interpreted as being caused by a loss of the rod-like shape of the molecules containing longer alkyl tails which explore a range of conformations. The slope of the clearing line, d T /d p , depends strongly on the length of the alkyl chain for the n CB series, but does not show a step-wise change between the nematogenic and smectogenic members. 相似文献
14.
Roman N. Karasev 《Discrete and Computational Geometry》2005,34(1):25-45
Three theorems of this paper generalize previous results of the author
on conjectures of A. Bezdek and V.V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescribed measures of parts. Then we prove a corollary on the existence of a possibly nonconvex polytope with a given set of vertices, containing given points in its interior. We also consider problems of the following type: find an assignment of vectors from a given set to the parts of a given convex partition of ℝn so that the shifts of the parts by their corresponding vectors either do not intersect by interior points or cover ℝn 相似文献
15.
Grega Cigler Roman Drnovšek Damjana Kokol-Bukovšek Matja? Omladi? Thomas J. Laffey Heydar Radjavi Peter Rosenthal 《Journal of Functional Analysis》1998,160(2):245
T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable. 相似文献
16.
We discuss general questions about the choice of optimization criteria for the stressed state of thermoelastic shells taking account of the functional measures of the space-time variability of its characteristics. The efficiency of the proposed approach is illustrated using the example of the solution of a problem for an axisymmetrically heated cylindrical shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 11–18. 相似文献
17.
Alexei A. Belik Andrei V. Mironov Roman V. Shpanchenko Eiji Takayama‐Muromachi 《Acta Crystallographica. Section C, Structural Chemistry》2007,63(7):i37-i39
The crystal structure of a new high‐pressure modification of cadmium divanadium hexaoxide, CdV2O6, was refined from X‐ray single‐crystal data. It contains zigzag chains of edge‐sharing VO6 octahedra. Octahedra in adjacent chains share corners and form corrugated layers. Octahedrally coordinated Cd atoms, which lie on twofold axes, are situated between the layers. The columbite‐like structure results in a strong distortion of the CdO6 octahedra which may be stabilized only at high pressure. 相似文献
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The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH2)2C6H3OH (LH) revealed compounds L3Al ( 1 ) and L2AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe2 ( 3 ), rather 2 together with Me3Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, 1H and 13C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph3SnOH, giving LSnPh3 ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, 1H, 13C and 119Sn NMR spectroscopy and 1H, 119Sn HMBC experiments. The system 2 and B(C6F5)3 in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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