Results 271 to 280 of about 111,125 (310)
Some of the next articles are maybe not open access.
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
openaire +2 more sources
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 ...
openaire +1 more source
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 ...
openaire +1 more source
Inventiones mathematicae, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noga Alon +3 more
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noga Alon +3 more
openaire +2 more sources
Representation by Quadratic Forms
Canadian Journal of Mathematics, 19491. 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.
openaire +3 more sources
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.
openaire +1 more source
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.
openaire +1 more source
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).
openaire +1 more source
?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).
openaire +1 more source
Mathematical Programming, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Chen, Ya-Xiang Yuan
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Chen, Ya-Xiang Yuan
openaire +2 more sources
On the Theory of Quadratic Forms
The Annals of Mathematics, 1949In this note we give an extention of the analytic theory of quadratic forms of C. L. Siegel'. We use the well-known matrix notation, if the contrary is not expressly mentioned we suppose the elements of all matrices to be rational integers. Let A(S, T; P, v) denote the number of solutions X of the Diophantic matrix equation X'SX = T, which satisfy the ...
openaire +1 more source
Canadian Journal of Mathematics, 1983
0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both ...
openaire +2 more sources
0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both ...
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources