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Showing papers on "Biorthogonal system published in 1980"


Journal ArticleDOI
TL;DR: In this article, a method for measuring the degree to which one biological outline form lies in between two others is presented, based on the cosine of a non- Euclidean angle between the tensors.
Abstract: SYNOPSIS. This essay presents a method for measuring the degree to which one biological outline form lies in between two others. The procedure does not measure forms separately, but rather compares pairs of tensors expressing D'Arcy Thompson's “Cartesian transformations” according to the biorthogonal formalism of Bookstein. In analogy with conventional methods, betweenness is computed as a similarity score, the cosine of a non- Euclidean angle between the tensors. The new quantities, size-betweenness and shapebetweenness, enable comparisons of form series against a priori orderings intra- and interspecifically

26 citations


Journal ArticleDOI
TL;DR: In this article, a biorthogonal series expansion and a numerical finite difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques.
Abstract: A biorthogonal series expansion and a numerical finite-difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques. For this problem the method of biorthogonal series is faster, cheaper, and more accurate.

6 citations


Journal ArticleDOI
01 Jan 1980

2 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that extremal functions associated with a general functional form a set of biorthogonal and doubly orthogonal functions, and that the extremal function associated with the general functional can be found in the E and H plane strip source antennas.
Abstract: It is shown that the extremal functions associated with a general functional form a set of biorthogonal and doubly orthogonal functions. The theory is applied to antenna theory to find the doubly orthogonal functions of the E and H plane strip source antennas.

2 citations


01 Mar 1980
TL;DR: The method can be used to decompose superpositions of signatures as well as for improving separation of measured parameters for pattern recognition and to suppress interferences from the background when it is included in the given set of signatures.
Abstract: : A mathematical method is developed for generating a set of filter functions from a given set of signatures. The filter function set of functions is biorthogonal to the set of signature functions; therefore, any one filter function gives a perfect response to one signature, and a response to all other given signatures is completely suppressed. The method can be used to decompose superpositions of signatures as well as for improving separation of measured parameters for pattern recognition. It can also be used to suppress interferences from the background when it is included in the given set of signatures. A method of adding new filter functions to an existing set without complete recomputation (adaptive learning) is discussed. (Author)

1 citations


Book ChapterDOI
M. Geradin1
01 Jan 1980
TL;DR: A variant of the method is proposed in which biorthogonality is maintained between displacements and the associated inertia loads, using elementary hermitian transformations.
Abstract: The biorthogonal Lanczos algoritm is discussed as a very economical method for extracting the lower frequency spectrum of the generalized eigenvalue problem A variant of the method is proposed in which biorthogonality is maintained between displacements and the associated inertia loads , using elementary hermitian transformations. Numerical applications of the method to some bench mark cases demonstrate its computational efficiency.