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61.
62.
If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥1 denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and
the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality.
Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 47A63, 15A60 相似文献
63.
Bruzón M. S. Gandarias M. L. Muriel C. Ramírez J. Saez S. Romero F. R. 《Theoretical and Mathematical Physics》2003,137(1):1367-1377
We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior. 相似文献
64.
65.
José M. Arrieta Neus Cónsul Anibal Rodríguez-Bernal 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,23(2):1-14
We prove the existence of nonconstant stable stationary
solutions of
an evolution problem with a nonlinear reaction acting on the
boundary. These solutions present layers at certain points of the
boundary. We also study the behavior of these solutions as the small
parameter appearing in the equation approaches zero and show some
stability properties of the profiles given by these equilibrium
solutions. 相似文献
66.
67.
Summary A new gas chromatographic method using an automatic purge-and-trap system coupled to a GC with mass selective detection to analyze styrene at the parts-per-trillions (ng kg–1) level is described. The method shows a good sensitivity and the detection limit is 10 ng kg–1 with a relative standard deviation (RSD) of 4.7% for 164 ng kg–1 styrene in olive oil. This analytical method has been successfully applied to the analysis of styrene in extra-virgin olive oil from the European market. 相似文献
68.
Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses. 相似文献
69.
B. Vizoso I. R. Matías M. López-Amo M. A. Muriel J. M. López-Higuera 《Optical and Quantum Electronics》1995,27(10):847-857
The design of a double-parallel amplified recirculating optical delay line utilizing an erbium-doped fibre amplifier for a fibre optical bus is described. This structure is used for amplifying, equalizing and filtering multicarrier signals coming from optoelectronic units attached to fibre couplers. The use of this structure for a hybrid multimode-singlemode fibre bus that includes optoelectronic units for sensors is also demonstrated. 相似文献
70.
Miroslav Menšík 《Czechoslovak Journal of Physics》1998,48(4):469-475
A time solution of the excimer-ion pair system is presented here with a special attention to the time asymptote.
Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic,
26–30 May 1997.
This work was supported by the grant No. C 1050601 of the Grant Agency of the Academy of Sciences of the Czech Republic. 相似文献