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Showing 1 to 20 of 36 for “"quadratic forms"”.
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Aspects of multivariate complex quadratic forms
… properties of certain multivariate complex quadratic forms and their characteristic roots are investigated. Multivariate complex distribution theory was originally introduced by Wooding (1956), Turin (1960) and Goodman (1963a) when they derived and studied the multivariate complex normal …
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Curves of genus 2 and quadratic forms
… focuses on a special associated integral quadratic form qC, which is intrinsically attached to a curve C of genus 2. This form, known as the refined Humbert invariant, was introduced by Kani (1994). Our first main result is the classification of those imprimitive ternary quadratic forms …
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Diophantine Avoidance, Number Fields, and Quadratic Forms
… we study small-size integer zeros of integral quadratic forms with avoidance conditions. We apply our results to the problem of effective distribution of angles between vectors in Z n .</p>
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Quadratic forms : harmonic transformations and gradient curves
Thesis: M.S., Massachusetts Institute of Technology, Sloan School of Management, 1980
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Quadratic forms over fields of characteristic 2
This thesis is concerned with the study of quadratic forms over fields of characteristic 2. First, we consider the extension of quadratic forms to fields of characteristic ≠ 2. Then we make the adjustments necessary to make the characteristic 2 case non-trivial, and investigate the structure of …
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Quadratic Forms Representing All Integers Coprime to 3
… expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 …
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STRICT REGULARITY OF POSITIVE DEFINITE TERNARY QUADRATIC FORMS
An integral quadratic form is said to be strictly regular if it primitively represents all integers that are primitively represented by its genus. The goal of this dissertation is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices …
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Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms
<p>Let $F$ be a non-degenerate quadratic form on an $n$-dimensional vector space $V$ over the rational numbers, and let $J$ be the symmetric matrix associated to $F$. One is interested in counting the number of zeros of the quadratic form whose coordinates are restricted in a smoothed box of size …
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On the integral extensions of isometries of quadratic forms over local fields
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1964.
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Representation by Quaternary Quadratic Forms whose Coefficients are 1, 2, 7 and 14
… of a positive integer n by the quaternary quadratic forms a_1x_1^2+a_2x_2^2+a_3x_3^2+a_4x_4^2, where a_1, a_2, a_3, a_4 in {1,2,7,14}. We use a modular form approach.
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On the Distribution of Quadratic Expressions in Various Types of Random Vectors
… approximations to the distribution of indefinite quadratic expressions in possibly singular Gaussian random vectors and ratios thereof are obtained in this dissertation. It is established that such quadratic expressions can be represented in their most general form as the difference of two …
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Explicit Composition Identities for Higher Composition Laws in the Quadratic Case
… theory of Gauss composition of integer binary quadratic forms provides a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. …
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Relative oriented class groups of quadratic extensions
… relative oriented class groups associated to quadratic extensions of number fields L/K, extending work of Bhargava concerning composition laws for binary quadratic forms over number fields of higher degree. This work generalized the classical correspondence between ideal classes of quadratic …
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Invariance Properties of Statistical Tests for Dependent Observations
… for which the distributional properties of the quadratic forms in ANOVA problems remain invariant. These results are contained in Chapter 3.</p> <p>In Chapters 4 and 5, we generalize our results to the multivariate test statistics, first considering a special covariance structure that occurs in …
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A robustness type optimality criterion for experimental design
… is carried out concerning the distribution of quadratic forms in non-normal variables. A general formula is proved for the characteristic function of a quadratic form which is not positive (or negative) semi-definite, and in which the random vector is not normally distributed. This formula is …
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Topics in the algebraic theory of higher degree forms
… F. In degree d=2 there is an extensive theory of quadratic forms. We consider forms of degree d>2. The following are among the new results we have proved: 1. A nonsingular form over a field of characteristic zero has nonzero Hessian. This was proved by Harrison in degree d=3. We use some basic …
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Advances in Copula Estimation and Distribution Theory
… As well, approximations to the distributions of quadratic forms in gamma, inverse Gaussian, binomial and Poisson random variables, which hinge on the determination of their moments via a symbolic approach, are proposed and several applications are pointed out. Additionally, an accurate density …
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