Related papers: Isotropic vectors over global fields

We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

We propose a randomized polynomial time algorithm for computing nontrivial zeros of quadratic forms in 4 or more variables over $\mathbb{F}_q(t)$, where $\mathbb{F}_q$ is a finite field of odd characteristic. The algorithm is based on a…

We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic…

The forms of the generalized quantities that we have recently introduced are dependent on the phase of the probability amplitudes for spin-projection measurements. In this paper, we show explicitly that changing the phase gives different…

A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…

We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…

We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive definite binary generalized form of this type representing every…

Let $K$ be a field with characteristic different from 2 and let $S$ be a symbol algebra over $K$. We compute the symmetric powers of hyperbolic quadratic forms over $K$. Also, we compute the symmetric powers of the quadratic trace form of…

In this article we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods. This work is continuation of a stochastic quantization program reported earlier.

Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…

The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…

Generalized symmetry integrability test for discrete equations on the square lattice is studied. Integrability conditions are discussed. A method for searching higher symmetries (including non-autonomous ones) for quad graph equations is…

Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms. This is obtained from a more…

We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.

Let $K$ be a global field or $\overline{\mathbb Q}$, $F$ a nonzero quadratic form on $K^N$, $N \geq 2$, and $V$ a subspace of $K^N$. We prove the existence of an infinite collection of finite families of small-height maximal totally…

To various kinds of quadratic functors, homotopy types of two stage spaces are assigned. It is investigated what kind of homotopy types are obtainable in this way.

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a…

We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…

We show how to compute globally optimal solutions to inverse kinematics (IK) by formulating the problem as an indefinite quadratically constrained quadratic program. Our approach makes it feasible to solve IK instances of generic redundant…