A problem about Feynman integrals on Riemannian manifolds
This paper contains an announcement of a result, which settles the connection between various algebraic models for rational homotopy theory: the models of Quillen, Sullivan and Adams-Hilton-Anick. It is shown how this result, combined with a recent result of Anick, implies a conjecture of H. J. Baues and J. M. Lemaire [Math. Ann. 225, 219-245 (1977; Zbl 0322.55019)].We describe in some detail the construction of these models (Section 1). We present a variant of the Adams-Hilton model, which is defined...
L’interprétation dans la langue naturelle d’un résultat mathématique peut être délicate. La théorie des bifurcations fournit un exemple récent ou des problème d’interprétation ont motive des développements mathématiques nouveaux de la théorie. L’article plaide pour une plus grande prise en considération de ces questions dans les revues mathématiques.
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.
We derive the smoothed aggregation two-level method from the variational objective to minimize the final error after finishing the entire iteration. This contrasts to a standard variational two-level method, where the coarse-grid correction vector is chosen to minimize the error after coarse-grid correction procedure, which represents merely an intermediate stage of computing. Thus, we enforce the global minimization of the error. The method with smoothed prolongator is thus interpreted as a qualitatively...
The strong version of the Poincaré recurrence theorem states that for any probability space , any -measure preserving transformation and any almost every point of returns to infinitely many times. In [8] (see also [4]) the theorem has been proved for MV-algebras of some type. The present paper contains a remarkable strengthening of the result stated in [8].
A simple condition sufficient for non-oscillatory behavior of input/output systems is formulated and discussed.
Let be a reduced -dimensional complex space, for which the set of singularities consists of finitely many points. If denotes the set of smooth points, the author considers a holomorphic vector bundle , equipped with a Hermitian metric , where represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of across , or across the singular points of if . The approach taken here is via the metric...