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121.
Within Archimedean -groups, and with an infinite cardinal or , we consider X-hulls where X stands for any of the following classes of -groups: -projectable; laterally -complete; boundedly laterally -complete; conditionally -complete; combinations of the preceding, together with divisibility and/or relative uniform completeness. All these hulls exist, and may be obtained by iterated adjunction of the required extra elements, within the essential hull. When the -groups is relatively -complemented one step in the iteration suffices for several crucial properties. We derive from the above a considerable number of equations involving combinations of these hull operators. 相似文献
122.
George E. Andrews Anne Schilling S. Ole Warnaar 《Journal of the American Mathematical Society》1999,12(3):677-702
Using new -functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A version of the classical Bailey lemma. We apply our result, which is distinct from the A Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W algebra.
123.
We conclude the construction of the algebraic complex, consisting of spaces of differentials of Euclidean metric values, for four-dimensional piecewise-linear manifolds. Assuming that the complex is acyclic, we investigate how its torsion changes under rebuildings of the manifold triangulation. We first write formulas for moves 33 and 24 based on the results in our two previous works and then study moves 15 in detail. Based on this, we obtain the formula for a four-dimensional manifold invariant. As an example, we present a detailed calculation of our invariant for the sphere S
4; in particular, the complex does turn out to be acyclic. 相似文献
124.
In a recent letter, new representations were proposed for the pair of sequences (,), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers and k and a partition , whose parts do not exceed N – 1. Our results give rise to what we call a higher level Bailey lemma. As an application it is shown how this lemma can be applied to yield general q-series identities, which generalize some well-known results of Andrews and Bressoud. 相似文献
125.
利用第一、二类高阶Bernoulli数和二类Stirling数S1(n,k),S2(n,k)的定义.研究了二类高阶Bernoulli数母函数的幂级数展开,揭示了二类高阶Bernoulli数之间以及与第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间的内在联系,得到了几个关于二类高阶Bernoulli数和第一类Stirling数S1(n,k)、第二类Stirling数S2(n,k)之间有趣的恒等式. 相似文献
126.
基于相空间Green函数的生成泛函,导出了非定域变换下正则形式的Ward恒等式.用于非AbelChern-Simons(CS)理论,得到了正规项角间的一些关系式.这里给出的形式的显著优点在于匆需作出相空间生成泛函中对正则动量的路径积分.在非AbelCS理论中的非定域变换下,仅要求和不变,即可导出正规顶角间的一些关系式. 相似文献
127.
We prove an identity for Hall–Littlewood symmetric functions labelled by the Lie algebra A2. Through specialization this yields a simple proof of the A2 Rogers–Ramanujan identities of Andrews, Schilling and the author. 相似文献
128.
The join A ∨ B of two semigroup varieties A and B is investigated. The latrine of subvarieties of A ∨ B is completely described, It is shown that this lattice is finite and non-modular and that all varieties in it are finitely based and finitely generated. 相似文献
129.
Manuel Kauers 《Discrete Mathematics》2006,306(17):2073-2083
We provide a new algorithm for indefinite nested summation which is applicable to summands involving unspecified sequences x(n). More than that, we show how to extend Karr's algorithm to a general summation framework by which additional types of summand expressions can be handled. Our treatment of unspecified sequences can be seen as a first illustrative application of this approach. 相似文献
130.
Kung-Yu Chen 《Journal of Mathematical Analysis and Applications》2005,311(2):582-599
The authors investigate several families of double-series identities as well as their (known or new) consequences involving various hypergeometric functions in one and two variables. A number of associated generating-function relationships, involving certain classes of hypergeometric polynomials, are also considered. 相似文献