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APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS
Bulletin of the Australian Mathematical Society, 2020 A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms.
Nokhodkar, A. H.
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Representation by Quadratic Forms
Canadian Journal of Mathematics, 1949 1. Introduction. The elementary portions of the theory of integral representation of numbers or forms by quadratic forms will be somewhat simplified and generalized in this article. This indicates certain directions in which new applications can be made.
Gordon Pall
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Canadian Journal of Mathematics, 1952 Hermite [4] in the course of his investigations on the transformation theory of abelian functions, introduced the notion of abelian quadratic forms. They are quadratic forms whose matrices of orders 2n, satisfywhere k ≠ 0 is a real number, and is the unit matrix of order n.
K. G. Ramanathan
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On quadratic differential forms
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1998The authors develop a theory for linear time-invariant differential systems and quadratic functionals. It is shown that for systems described by one-variable polynomial matrices, the appropriate tool to express quadratic functionals of the system variables are two-variable polynomial matrices. The authors present a description of the interaction of one-
Willems, Jan C., Trentelman, Harry L.
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Canadian Journal of Mathematics, 1969
We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence
Kaplansky, Irving, Shaker, Richard J.
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We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence
Kaplansky, Irving, Shaker, Richard J.
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DISTRIBUTIONS OF QUADRATIC FORMS
Australian Journal of Statistics, 1988summaryExact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where χ2m and χ2nχ2n are independent chi‐square random variables with m and n degrees of freedom respectively. (The positive ci are distinct).
Bock, Mary Ellen, Solomon, Herbert
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Journal of the London Mathematical Society, 1983
Let \(k\) be a fixed algebraically closed field. The author associates to each basic \(k\)-algebra \(A\), whose ordinary quiver \(Q\) has no oriented cycles, a quadratic form, called its Tits form, as follows: Denote by \(Q_ 0\) and \(Q_ 1\) the sets of vertices and arrows of \(Q\) respectively and by \(S_ i\) the simple \(A\)-module corresponding to ...
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Let \(k\) be a fixed algebraically closed field. The author associates to each basic \(k\)-algebra \(A\), whose ordinary quiver \(Q\) has no oriented cycles, a quadratic form, called its Tits form, as follows: Denote by \(Q_ 0\) and \(Q_ 1\) the sets of vertices and arrows of \(Q\) respectively and by \(S_ i\) the simple \(A\)-module corresponding to ...
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Inventiones mathematicae, 2005
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Proceedings of the London Mathematical Society, 1987
Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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The Annals of Mathematics, 1952
?1. Let (E be the matrix of a quadratic form with rational integral coefficients and F (e) the group of integral solutions U of 25 [U] = U'2U = S. The group F (e) is called the unit group of (E and its elements the units of S. Eisenstein defined the measure of F (5), when (E is definite, as the reciprocal of the order of F (S).
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?1. Let (E be the matrix of a quadratic form with rational integral coefficients and F (e) the group of integral solutions U of 25 [U] = U'2U = S. The group F (e) is called the unit group of (E and its elements the units of S. Eisenstein defined the measure of F (5), when (E is definite, as the reciprocal of the order of F (S).
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