Results 261 to 270 of about 306,107 (293)

SIMULTANEOUS ZEROS OF A SYSTEM OF TWO QUADRATIC FORMS

2020
In this dissertation we investigate the existence of a nontrivial solution to a system of two quadratic forms over local fields and global fields. We specifically study a system of two quadratic forms over an arbitrary number field. The questions that are of particular interest are: How many variables are necessary to guarantee a nontrivial zero to a ...
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Investigation of Exponential Dichotomy of Itô Stochastic Systems by Using Quadratic Forms

Ukrainian Mathematical Journal, 2001
The author studies the stochastic Itô system \[ dx=A(t)x dt+\sum_{i=1}^{m}B_i(t)x dW_i(t).\tag{1} \] Here, \(A(t),B_1(t),\ldots,B_m(t)\) are deterministic matrices defined on the semi-axis \(t\geq 0\) and \(W_1(t),\ldots W_m(t)\) are totally independent scalar Wiener processes determined on a complete probability space \((\Omega,F,\text{P})\).
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Quadratic normal forms of nonlinear control systems with uncontrollable linearization

Proceedings of 1995 34th IEEE Conference on Decision and Control, 2002
The controller normal form of linear systems has been a useful tool for the study of many linear control problems. In Wei Kang and Krener (1992), Wei Kang (1991,1994), and Krener and Wei Kang (1991), normal forms of nonlinear control systems are found for linearly controllable systems. In this paper, the author addresses the problem of quadratic normal
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Deformations of Diophantine Systems for Quadratic Forms of the Root Lattices A n

Journal of Mathematical Sciences, 2006
The matrix equation \(Q[X] = {^tT}QT = A\) is studied, where \(Q\) and \(A\) are positive definite symmetric integral matrices of order \(n\) and \(m\), respectively, and \(T\) ranges over the set of \(n\times m\) integer matrices. When \(A = A' \oplus A''\), where the summands have squarefree and coprime determinants, a formula is found for the ...
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Representation of integers by a system of additive, positive quadratic forms

Journal of Soviet Mathematics, 1979
By the circle method, an asymptotic formula is obtained for the number of solutions of the system of equations $$\sum\limits_{j = 1}^s {q_{jk} x_j^2 = n_k } \left( {k = 1, \ldots ,2} \right)$$ , where qjk are given positive integers and nk are increasing ...
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A quantitative Oppenheim theorem for generic ternary quadratic forms

Journal of Modern Dynamics, 2018
Anish Ghosh
exaly  

Brauer–Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms

Compositio Mathematica, 2009
Jean-Louis Colliot-Thelene
exaly  

Random weighted projections, random quadratic forms and random eigenvectors

Random Structures and Algorithms, 2015
Van Vu, Ke Wang
exaly  

Asymptotic Distribution of Quadratic Forms

Annals of Probability, 1999
Friedrich Götze
exaly  

Isotropy of quadratic forms over the function field of a quadric in characteristic 2

Journal of Algebra, 2006
Detlev W Hoffmann
exaly