Related papers: Inversion of the Indefinite Double Covering Map

In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

Let E be a rank two vector bundle on a scheme X. The following three structures are shown to be equivalent : a) A primitive quadratic map q: E --> L, with values in an invertible module L. b) A double covering f: Y --> X endowed with an…

Building upon the foundational work of Thomas and Williams on the modular sweep map, Garsia and Xin have developed a straightforward algorithm for the inversion of the sweep map on rational $(m,n)$-Dyck paths, where $(m,n)$ represents…

This paper develops an infinitesimal order of magnitude coupled with overflow technique that allows nonnumerical proofs of nondegenerate and degenerate inverse mapping theorems for mappings minimally regular at a point. This approach is…

By the Fourier transformations, any group-invariant functions over finite Abelian groups are transformed into group-invariant functions over the character groups. In this paper, we calculate matrix elements of this transformations under…

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…

Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…

Motivated by the recent work of Xiao and Zhong [AIMS Math. 9 (2024), 35125--35150: MR4840882], we propose a generalized inverse for a hyper-dual matrix called hyper-dual group generalized inverse (HDGGI). Under certain necessary and…

In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…

In 1953, Carlitz~\cite{Car53} showed that all permutation polynomials over $\F_q$, where $q>2$ is a power of a prime, are generated by the special permutation polynomials $x^{q-2}$ (the inversion) and $ ax+b$ (affine functions, where $0\neq…

This paper introduces a systematic approach towards the inverse problem for arboreal Galois representations of finite index attached to quadratic polynomials. Let $F$ be a field of characteristic $\neq 2$, $f\in F[x]$ be monic and quadratic…

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.