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A new infinite order formulation of variational sequences

Raffaele Vitolo (1998)

Archivum Mathematicum

The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition...

A new Taylor type formula and C ∞ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have C ∞ extensions from any subpolysector; the Gevrey case is included.

A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi, Alberto Tognoli (2004)

Bollettino dell'Unione Matematica Italiana

It is shown that every connected global Nash subvariety of R n is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.

A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation

Ursula Ludwig (2011)

Annales de l’institut Fourier

The Witten deformation is an analytic method proposed by Witten which, given a Morse function f : M → R on a smooth compact manifold M , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...

A special type of triangulations in numerical nonlinear analysis.

J. M. Soriano (1990)

Collectanea Mathematica

To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.

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