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Displaying similar documents to “Two notes on eventually differentiable families of operators”

Remarks on the uniqueness of second order ODEs

Dalibor Pražák (2011)

Applications of Mathematics

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We are concerned with the uniqueness problem for solutions to the second order ODE of the form x ' ' + f ( x , t ) = 0 , subject to appropriate initial conditions, under the sole assumption that f is non-decreasing with respect to x , for each t fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable. The interest in this problem comes, among other, from the study of oscillations of lumped parameter systems...

Natural operators lifting vector fields to bundles of Weil contact elements

Miroslav Kureš, Włodzimierz M. Mikulski (2004)

Czechoslovak Mathematical Journal

Similarity:

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m -manifolds to the bundle functor K A of Weil contact elements and the subalgebra of fixed elements S A of the Weil algebra A is determined and the bijection between all natural affinors on K A and S A is deduced. Furthermore, the rigidity of the functor K A is proved. Requisite results about the structure of S A are obtained by a purely algebraic approach, namely the existence of nontrivial S A is discussed. ...