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Showing papers on "Quintic function published in 1975"


Journal ArticleDOI

214 citations


Journal ArticleDOI
TL;DR: The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines to numerically solve two-point boundary-value problems.
Abstract: : The report is concerned with the use of collocation by splines to numerically solve two-point boundary-value problems. The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines. Consideration is given both to convergences as the mesh is refined and to the bandwidth of the matrices involved. Comparisons are made to a similar approach using the Galerkin method rather than collocation. (Author)

53 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the corresponding result can be obtained for any quintic nonresidue D(mod p) for any quadratic partition of p. Full details are given for D = 2, 3, 5.
Abstract: Let p be a prime=1 (mod 5). If 2 is a quintic nonresidue (mod p) then 2" s a (mod p) for some fifth root of unity α6 (^ 1) (mod p). Emma Lehmer has given an explicit expression for

11 citations


Book ChapterDOI
01 Jan 1975
TL;DR: In this paper, simple eigenvalue problems of vibrating string and the vibrating beam are treated by the method of finite elements using the different types of quadratic up to quintic elements.
Abstract: The simple eigenvalue problems of the vibrating string and the vibrating beam are treated by the method of finite elements using the different types of quadratic up to quintic elements. The resulting equations are interpreted as difference equations and their local truncation errors are analyzed and discussed. To solve the general algebraic eigenvalue problems the method of coordinate overrelaxation is applied. It is found that the asymptotic convergence of the algorithm depends in a substantial way on the type of the element. Finally, the condition numbers of the stiffness matrices for quartic and quintic elements behave amazingly.

2 citations


Journal ArticleDOI
TL;DR: In this article, the authors extended Segre's work to normal elliptic scrollar varieties of dimension k, defining and describing k most general types of such varieties, which they called simploids.
Abstract: In his classical memoir on the projective classification of elliptic ruled surfaces Corrado Segre described in particular two most general normal types, of even and odd order respectively, of which the former has precisely two minimum directrix curves, while the latter has an elliptic pencil of such curves. The present paper extends this work to normal elliptic scrollar varieties of dimension k, defining and describing k most general types of such varieties. Particular attention is paid to one of these types, which we call the simploid, in which the points of the variety correspond to the unordered sets of k values of an elliptic parameter (modulo its periods). The paper concludes with the identification of a series of self-dual « linked pairs » of such scrollar varieties, of which the simplest example is that of the elliptic quintic ruled surface and the elliptic quintic scrollar threefold in four-dimensional space.