Related papers: Classification rationnelle et confluence des syste…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…
The elementary theory of bivariate linear Diophantine equations over polynomial rings is used to construct causal lifting factorizations (elementary matrix decompositions) for causal two-channel FIR perfect reconstruction transfer matrices…
The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ for Gauss' hypergeometric functions. We define the tau-function of such a system as the…
Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group $\Gamma$ are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities…
Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric…
I relate some coefficients encountered when computing the functional determinants on spheres to the central differentials of nothing. In doing this I use some historic works, in particular transcribing the elegant symbolic formalism of…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
We develop a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions, based on connecting the Ehrhard-Regnier derivative from linear logic with the role of geometry in Watanabe's…
We construct covariant theories incorporating fluctuating boundaries and soft cutoffs by introducing dynamical reference frames (DRFs). This framework generalizes the covariant action from a hard-cutoff to a soft-cutoff formulation,…
Dropout is a simple yet effective algorithm for regularizing neural networks by randomly dropping out units through Bernoulli multiplicative noise, and for some restricted problem classes, such as linear or logistic regression, several…
In order to understand the deformations of determinants and Pfaffians resulting from deformations of matrices, we study the deformation theory of composites $f\circ F$, with isolated singularities, where $f:Y\to\C$ has Cohen-Macaulay…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
We consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters u=(u_1,...,u_n), which are eigenvalues of the leading matrix at the irregular singuilarity. At the same…
`Categorification' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category…
In the first part of the present work we consider periodically or quasiperiodically forced systems of the form $(d/dt)x = \epsilon f(x,t \omega )$, where $\epsilon\ll 1$, $\omega\in\mathbb{R}^d$ is a nonresonant vector of frequencies and…