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81.
Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z2, where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D4 is the Cherednik algebra of type C∨C1, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI. 相似文献
82.
Abull is the (self-complementary) graph with verticesa, b, c, d, e and edgesab, ac, bc, bd, ce; a graphG is calledBerge if neitherG not its complement contains a chordless cycle whose length is odd and at least five. We prove that bull-free Berge graphs are perfect; a part of our argument relies on a new property of minimal imperfect graphs.This work was done while both authors were at the School of Computer Science, McGill University; support by NSERC is gratefully acknowledged. 相似文献
83.
The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated
in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical
model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple
n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained
reaction heat.
Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May
2006. 相似文献
84.
A. Janušauskas 《Lithuanian Mathematical Journal》1996,36(1):22-31
Institute of Mathematics and Informatics. Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys.
Vol. 36, No. 1, pp. 27–38, January–March,. 1996. 相似文献
85.
86.
Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference
between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results.
Received April 2, 1996 / Revised version received July 30, 1990 相似文献
87.
JiŘí Kvapil Josef Kvapil Bohumil Perner Michal Košelja Helena Jelínková 《Czechoslovak Journal of Physics》1990,40(11):1283-1287
The methods of growing YAG:Nd crystals with a flat interface and YAP:Nd crystals with a sharp conical interface are described. The form of the interface was controlled by the He and H2O content in the reducing atmosphere composed mainly of Ar and H2 as well as by axial temperature gradient above the melt level. The crystals of 120–180 mm in length were machined to the high-quality slabs. 相似文献
88.
The present paper summarizes detailed investigations of Nd3+ fluorescence spectra in YAP:Nd laser crystal in the broad spectral range of 370–1100 nm at liquid nitrogen temperature. Especially, Nd3+ near UV and visible fluorescence spectra were studied for the first time in this crystal. The Nd3+ near UV and visible fluorescence spectra of this crystal consist of many narrow lines (up to 50). The Nd3+ near UV and visible fluorescence lines arise mainly from4D3/2 and2P3/2 Nd3+ terms (transitions from4D3/2,2P3/2 to lower lying Nd3+ levels are responsible for their appearance). At room temperature the fluorescence spectra consist of broad bands with narrow lines (mainly4D3/24F3/2,4F5/2 and2H9/2 transitions). 相似文献
89.
Z. Kožíšek 《Czechoslovak Journal of Physics》1990,40(6):592-604
The kinetic equation of the classical homogeneous nucleation theory is rewritten in dimensionless form and it is shown that the numerical computation of the dimensionless kinetic equation is approximately 20 times faster in comparison with the original kinetic equation. The results are compared with known analytical results and with previous numerical results in the case of the constant and variable temperature for the model Li2O.2 SiO2 melt. It is shown, e.g., that under non-isothermal conditions the nucleation rate is greater than the quasistationary nucleation rate and the cluster distribution function is greater than the corresponding quasiequilibrium cluster distribution function. 相似文献
90.
XPS spectra of YIG, YIG:Bi, YIG:Ca and YIG:Co(Ge, Ca) epitaxial garnet films were measured at room temperature. The positions of the main iron, yttrium, oxygen, bismuth, cobalt and lead spectral lines were determined and their changes with the surface treatments were investigated. It was found that divalent and trivalent states of iron and cobalt ions can be resolved, the chemical shifts being in oposite directions.The authors would like to thank Dr. J. imová for careful EPMA analysis of the samples. 相似文献