Related papers: From analytical mechanical problems to rewriting t…
Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to…
We draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic dynamics. In particular we prove in any…
Anick introduced a resolution, that now bears his name, of a field using an augmented algebra over that field. We present here what one could call a dictionary between Anick's original paper and the other resources on the matter, most of…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
We extend the Eruguin result exposed in the paper "Construction of the whole set of ordinary differential equations with a given integral curve" published in 1952 and construct a differential system in $\Bbb{R}^N$ which admits a given set…
This thesis consists of two parts. In the first part we investigate the worldvolume supersymmetry algebra of multiple membrane theories. We begin with a description of M-theory branes and their intersections from the perspective of…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…
Integral geometry deals with those integral transforms which associate to ``functions'' on a manifold their integrals along submanifolds parameterized by another manifold. Basic problems in this context are range characterization--where…
We propose and extension of the tableau-based first-order automated theorem prover Zenon Modulo to polarized rewriting. We introduce the framework and explain the potential benefits. The first target is an industrial benchmark composed of B…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur-Weyl duality. Variations on this principle yield analogous connections between the symmetric group and other…
Moduli theory has captured the imagination of algebraic geometers for at least two centuries. Up until the end of the 20th century, moduli spaces were constructed and studied by rigidifying the moduli problem using extrinsic data and…
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations. Strikingly, although both theories are…
The primary contribution of this thesis is to introduce and examine the planar modular partition monoid for parameters $m, k \in \mathbb{Z}_{>0}$, which has simultaneously and independently generated interest from other researchers as…