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91.
In this paper we introduce a kind of “noncommutative neighbourhood” of a semiclassical parameter corresponding to the Planck
constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed
by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a “distortion”
of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical
shadow. 相似文献
92.
Sławomir Prucnal Marcin Turek Andrzej Drozdziel Krzysztof Pyszniak Artur Wójtowicz Sheng-Qiang Zhou Alohe Kanjilal Artem Shalimov Wolfgang Skorupa Jerzy Zuk 《Central European Journal of Physics》2011,9(2):338-343
The InAs quantum structures were formed in silicon by sequential ion implantation and subsequent thermal annealing. Two kinds of crystalline InAs nanostructures were successfully synthesized: nanodots (NDs) and nanopyramids (NPs). The peaks at 215 and 235 cm?1, corresponding to the transverse optical (TO) and longitudinal optical (LO) InAs single-phonon modes, respectively, are clearly visible in the Raman spectra. Moreover, the PL band at around 1.3 µm, due to light emission from InAs NDs with an average diameter 7±2 nm, was observed. The InAs NPs were found only in samples annealed for 20 ms at temperatures ranging from 1000 up to 1200°C. The crystallinity and pyramidal shape of InAs quantum structures were confirmed by HRTEM and XRD techniques. The average size of the NPs is 50 nm base and 50 nm height, and they are oriented parallel to the Si (001) planes. The lattice parameter of the NPs increases from 6.051 to 6.055 Å with the annealing temperature increasing from 1100 to 1200°C, due to lattice relaxation. Energy dispersive spectroscopy (EDS) shows almost stoichiometric composition of the InAs NPs. 相似文献
93.
94.
We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X. 相似文献
95.
We consider the generalized Stäckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Stäckel transforms. 相似文献
96.
97.
98.
Artur Winternitz 《Monatshefte für Mathematik》1920,30(1):123-128
Ohne Zusammenfassung 相似文献
99.
Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation 总被引:1,自引:0,他引:1
Eduardo Uchoa Ricardo Fukasawa Jens Lysgaard Artur Pessoa Marcus Poggi de Aragão Diogo Andrade 《Mathematical Programming》2008,112(2):443-472
This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The
variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make
it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used.
Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables
are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational
results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open
instances could be solved to optimality. 相似文献
100.
Artur Winternitz 《Mathematische Zeitschrift》1927,26(1):165-169
Ohne Zusammenfassung 相似文献