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1.
2.
Anatol Odzijewicz 《Journal of Functional Analysis》2004,217(1):103-125
The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W∗-algebras is given particular attention. Semidirect products and the extension of the restricted Banach Lie-Poisson space by the Banach Lie-Poisson space of compact operators are given as examples. 相似文献
3.
For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I2(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G2, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in Bn-, Dn- and G2-bracket algebras, and as an application, discover a Pieri-type formula in the Bn-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary Bn-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid. 相似文献
4.
Anatol Odzijewicz 《Communications in Mathematical Physics》1988,114(4):577-597
Quantization of a mechanical system with the phase space a Kähler manifold is studied. It is shown that the calculation of the Feynman path integral for such a system is equivalent to finding the reproducing kernel function. The proposed approach is applied to a scalar massive conformal particle interacting with an external field which is described by deformation of a Hermitian line bundle structure. 相似文献
5.
Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system 总被引:1,自引:0,他引:1
Berenstein I Yang L Dolnik M Zhabotinsky AM Epstein IR 《The journal of physical chemistry. A》2005,109(24):5382-5387
We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay. 相似文献
6.
Anatol Odzijewicz 《Letters in Mathematical Physics》1984,8(4):329-335
Starting from conformal kinematics we show that the complex Minkowski space
as a model of time-space is as good as the real one. A holomorphic field theory is constructed on
and it is shown that real field theory is a linear approximation of the holomorphic one. 相似文献
7.
Zhabotinsky AM 《Chaos (Woodbury, N.Y.)》1991,1(4):379-386
The history of the discovery and study of chemical oscillations and waves is presented from the very first accidental observations up to the systematic design of chemical oscillators. Special emphasis is devoted to the long-term debate over the possibility of pure chemical oscillations, i.e., concentration oscillations in homogeneous closed systems. 相似文献
8.
Anatol Nowicki 《Fortschritte der Physik》1986,34(10):649-673
The hermitean oscillator-like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson-fermion oscillators are explicitely described. The assumption of positive definite metric in a Hilbert space of the oscillators states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp (N; 2M; R); the unitary compact superalgebra su (N; M); the unitary noncompact one SU(N; K, M); and the quaternionic unitary superalgebra uuα(N; M; H). 相似文献
9.
One investigates a generalization of difference calculus and applies it to solve the functional equations of second order.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.
This work is supported in part by KBN grant 2 PO3 A 012 19. 相似文献
10.
Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes 总被引:1,自引:0,他引:1
Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic. 相似文献