Related papers: Isotropic vectors over global fields
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
The purpose of this paper is to propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field (genus>1) over a given ground field of characteristic >2 as well as over its algebraic extensions.
Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a…
We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite…
Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of…
The isotropic Grassmannian parametrizes isotropic subspaces of a vector space equipped with a quadratic form. In this paper, we show that any maximal isotropic Grassmannian in its Pl\"ucker embedding can be defined by pulling back the…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
For $\mathrm{O}(\mathrm{q},k)$, the orthogonal group over a field $k$ of characteristic 2 with respect to a quadratic form $\mathrm{q}$, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either…
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.
We classify degenerate singular points of $\C^2$-actions on complex surfaces.
The goal is to obtain an asymptotic formula for the number of quadratic extensions with bounded discriminant of a some quadratic number field with odd class number. This extends an already known result for Q.
We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, $\W_1$, as our basic tool we first examine geometrical properties…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
This paper extends and generalizes previous works on constructing combinatorial multivector fields from continuous systems (see [10]) and the construction of combinatorial vector fields from data (see [2]) by introducing an optimization…