A problem about Feynman integrals on Riemannian manifolds
A problem concerning locally- functions in a commutative Banach algebra
A proof of the Baues-Lemaire conjecture in rational homotopy theory
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...
A quaternionic treatment of Navier-Stokes equations
A remark on natural quantum Lagrangians and natural generalized Schrödinger operators in Galilei quantum mechanics
A remark on the -splitting conjecture
A remark on the topology of higher order frames
A representation of the coalgebra of derivations for smooth spaces
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.
A short philosophical note on the origin of smoothed aggregations
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...
A strengthening of the Poincaré recurrence theorem on MV-algebras
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 sufficient condition for non-oscillatory behavior of some input/output models
A simple condition sufficient for non-oscillatory behavior of input/output systems is formulated and discussed.
A survey of boundary value problems for bundles over complex spaces
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...
A survey of dimension theory
A survey of minimal topological spaces
A survey on tent spaces and their application to weighted inequalities
A tribute to Bernard Bolzano
A unified construction of the Alexander- and the Jones-invariant
A vector lattice variant of the ergodic theorem
Abgeschwächte Trennungsaxiome
About duality and Killing tensors
Summary: In this paper the isometries of the dual space were investigated. The dual structural equations of a Killing tensor of order two were found. The general results are applied to the case of the flat space.