Related papers: Changements de variable pour un th`eme.
This article is the continuation of [B. 13-b] where we show how the isomorphism class of a $[\lambda]-$primitive theme with a given Bernstein polynomial may be characterized by a (small) finite number of complex parameters. We construct…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
In this paper we consider holomorphic families of frescos (i.e. filtered differential equations with a regular singularity) and we construct a locally versal holomorphic family for every fixed Bernstein polynomial. We construct also several…
We study continuity of the roots of nonmonic polynomials as a function of their coefficients using only the most elementary results from an introductory course in real analysis and the theory of single variable polynomials. Our approach…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
We study the r-th elementary symmetric polynomial in $n$ variables with 2<r<n. There are two kinds of linear transformations on the parameter space that leave this polynomial invariant: Namely, any permutation of the variables and…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
When we consider a proper holomorphic map \ $\tilde{f}: X \to C$ \ of a complex manifold \ $X$ \ on a smooth complex curve \ $C$ \ with a critical value at a point \ $0$ \ in \ $C$, the choice of a local coordinate near this point allows to…
In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invariant is the discriminant, which characterizes the singularity…
In this article we study holomorphic deformations of the filtered Gauss-Manin systems associated to a vanishing period integral. For that purpose we introduce a new sub-class of the class of monogenic (a,b)-modules (Brieskorn modules) which…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
In this paper, we investigate parameter families of iterated function systems and continuity. Specifically, if we have a set of iterated function systems that depend continuously on a parameter, which properties of the invariant sets will…
This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics…
We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…
In this paper we prove that given a non-isotrivial family of hyperbolic curves in positive characteristic, the isomorphism type of the geometric fundamental group is not constant on the fibres of the family.
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…