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91.
M. K. Bos. 《Mathematics of Computation》2003,72(244):2001-2012
In this paper, an algorithm for computing the principal character for affine Lie algebras is discussed and presented. The principal characters discovered using this program are given and/or proven. Results include level 2 and 3 character formulas in and the sole existence of the Rogers-Ramanujan products in , , , , , , . 相似文献
92.
In this paper we study the holomorphic K-theory of a projective variety. This K-theory is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory is built out of studying algebraic bundles over a variety up to algebraic equivalence. In this paper we will give calculations of this theory for flag like varieties which include projective spaces, Grassmannians, flag manifolds, and more general homogeneous spaces, and also give a complete calculation for symmetric products of projective spaces. Using the algebraic geometric definition of the Chern character studied by the authors we will show that there is a rational isomorphism of graded rings between holomorphic K-theory and the appropriate morphic cohomology groups, in terms of algebraic co-cycles in the variety. In so doing we describe a geometric model for rational morphic cohomology groups in terms of the homotopy type of the space of algebraic maps from the variety to the symmetrized loop group U(n)/
n
where the symmetric group
n
acts on U(n) via conjugation. This is equivalent to studying algebraic maps to the quotient of the infinite Grassmannians BU(k) by a similar symmetric group action. We then use the Chern character isomorphism to prove a conjecture of Friedlander and Walker stating that if one localizes holomorphic K-theory by inverting the Bott class, then rationally this is isomorphic to topological K-theory. Finally this will allows us to produce explicit obstructions to periodicity in holomorphic K-theory, and show that these obstructions vanish for generalized flag mani-folds. 相似文献
93.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
94.
Bhagat Singh 《Czechoslovak Mathematical Journal》2000,50(3):627-639
Qualitative comparison of the nonoscillatory behavior of the equations
and
is sought by way of finding different nonoscillation criteria for the above equations, L
n is a disconjugate operator of the form
Both canonical and noncanonical forms of L
n have been studied. 相似文献
95.
Let V be a module over a principal ideal domain. Then V = M N where M is divisible and N has no nonzero divisible submodules. In this paper we determine the forcing linearity number for V when N is a direct sum of cyclic modules. As a consequence, the forcing linearity numbers of several classes of Abelian groups are obtained. 相似文献
96.
FANG FUQUAN 《数学年刊B辑(英文版)》2000,(4)
1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th… 相似文献
97.
98.
Marco Castrillón López Jaime Muñz Masquó 《International Journal of Theoretical Physics》2007,46(4):1020-1026
It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing
in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent
with respect to the pairing.
PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc
Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13 相似文献
99.
The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented. 相似文献
100.
Daryl Geller Domenico Marinucci 《Journal of Mathematical Analysis and Applications》2011,375(2):610-630
The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008) [14], and Geller et al. (2008, 2009) [12] and [13]. Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications. 相似文献