Related papers: A Geometric Algebra Solution to Wahba's Problem
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
We consider GL$_m$-dimers of triangulations of regular convex $n$-gons, which give rise to a dimer model with boundary $Q$ and a dimer algebra $\Lambda_Q$. Let $e_b$ be the sum of the idempotents of all the boundary vertices, and…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
A simple method is proposed for deforming $A_\infty$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable…
The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie…
The algebraic geometry of a universal algebra $\mathbf{A}$ is defined as the collection of solution sets of term equations. Two algebras $\mathbf{A}_1$ and $\mathbf{A}_2$ are called algebraically equivalent if they have the same algebraic…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
Monogenic functions in the algebra of 5-dimensional spacetime have been used previously by the author as first principle in different areas of fundamental physics; the paper recovers that principle applying it to the hydrogen atom. The…
We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa--Holm equation. New proofs of asymptotic behavior of the solutions are given. In particular we recover well-known collision conditions. Additionally…
We establish tools to facilitate the computation and application of the Chekanov-Eliashberg differential graded algebra (DGA), a Legendrian-isotopy invariant of Legendrian knots in standard contact three-space. More specifically, we…
We generalize problems in Wasan geometry which involve no folded figures but are related to Haga's fold in origami. Using the tangent circles appeared in those problems we give a parametric representation of the generalized Haga's fold…
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…
Let C(X) be the algebra generated by the curvature 2-forms of the standard hermitian line bundles over the complex homogeneous manifold X=G/B. We calculate the Hilbert polynomial of C(X) and give its presentation as a quotient of a…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
The Askey-Wilson algebra $AW(3)$ with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra $sl_q(2)$. On the base of this hidden symmetry…
Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article illustrates how these two fields complement each other. Our…
A general half-plane contact problem in which the geometry is specified in a piecewise-quadratic sense over three segments is solved in closed form. This includes the effects of a moment applied sufficient to introduce separation of one…
The purpose of this note is to show that W3 algebras originate from an unusual interplay between the breakings of the reparametrization invariance under the diffemorphism action on the cotangent bundle of a Riemann surface. It is recalled…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…