Related papers: On Algebraic-Geometry Approach to Ribaucour Transf…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper…
The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…
In this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under {appropriate} conditions the composition of two or more vectorial Ribaucour…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
In this work we generalize the surfaces studied in [8], we define the generalization of Ribaucour-type surfaces (in short, GRT-surfaces). We obtain present a representation for GRT-surfaces with prescribed Gauss map which depends on two…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis.…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how…
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
In this work, we present a multiscale approach for the reliable coarse-scale approximation of spatial network models represented by a linear system of equations with respect to the nodes of a graph. The method is based on the ideas of the…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We discuss the Ribaucour transformation of Legendre maps in Lie sphere geometry. In this context, we give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer--Tojeiro. We go on to…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as…