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We derive some elementary formulas expressing the relation between the dihedral angles and edge lengths of a tetrahedron in hyperbolic space. 相似文献
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M. Kosti? 《Journal of Mathematical Analysis and Applications》2008,338(2):1224-1242
Convoluted C-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated C-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are obtained. Relations between convoluted C-cosine functions and analytic convoluted C-semigroups, introduced and investigated in this paper are given through the convoluted version of the abstract Weierstrass formula which is also proved in the paper. Ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups. Several examples of operators generating convoluted cosine functions, (analytic) convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors. As an application, it is proved that the polyharmonic operator Δn2, n∈N, acting on L2[0,π] with appropriate boundary conditions, generates an exponentially bounded Kn-convoluted cosine function, and consequently, an exponentially bounded analytic Kn+1-convoluted semigroup of angle , for suitable exponentially bounded kernels Kn and Kn+1. 相似文献
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利用Grassmann代数的理论与方法,给出了n维欧氏空间En中n维单形第二余弦定理一种简单的证明.然后利用第二余弦定理给出了n维单形正弦定理一种新的简单证明. 相似文献
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本文在更为广泛的权函数和边界函数的范围内,使用不高于独立列场合下的矩条件,讨论了NA列的一类小参数级数的极限状态及收敛速度.因此,本文的结果即使对独立列也是有意义的. 相似文献
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George Benke 《Journal of Mathematical Analysis and Applications》2003,284(2):647-655
Given N?1 and d?1, we show the existence of positive integers λkj for 1?k?N and 1?j?d such that
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