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Cyclical functions and permutation matrices

โœ Scribed by Louis A. Pipes

Publisher
Elsevier Science
Year
1969
Tongue
English
Weight
610 KB
Volume
287
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

IBSTRBCT: Cyclical functions are an extension of the concept of hyperbolic functions. These fu,zctions have many interestkg and important properties. This paper develops the theory of these functions from a novel point of view by using the properties of permutation matrices. The connectiotz between cyclical functions and the matrix exponential function of the permutation matrix is demonstrated. The cyclical functions of the third and fourth orders are discussed in detail and th,e general theory of cyclical functions of order n is given. Applications of the fourth-order cyclical junctions to the vibrations of beams are considered.

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Primitivity of Permutation Groups, Coher
Primitivity of Permutation Groups, Coherent Algebras and Matrices
โœ Gareth A. Jones; Mikhail Klin; Yossi Moshe ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 114 KB

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give