Eine Theorie des revolutionären Verhaltens

How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”

“…in [110] or [59], [60], [61]) to assume that the power expended by internal or external (with respect to D) interactions is a linear and continuous functional when defined in the set of test functions (with respect to Fréchet topology). In other words we accept the following It is clear that, once the previous postulate is accepted, theorems and definitions of the theory of distributions, due to Schwartz (see [111]), become really relevant in continuum mechanics. In particular we know that (i) every distribution having compact support K can be represented as the sum of a finite number of derivatives of measures all having their support included in K, (ii) a distribution is said to have order smaller than or equal to k if one can represent it as the sum of derivatives with order smaller than or equal to k of measures, (iii) every distribution having support included in a regular embedded submanifold M can be uniquely decomposed as a finite sum of transversal derivatives of extensions of distributions defined on M .…”

Pseudorational Impulse Responses — Algebraic System Theory for Distributed Parameter Systems

“…M (−∞,0] denotes the subspace of E (R − ) consisting of measures, i.e., distributions of order 0. The order of a distribution ψ is denoted by ord ψ ( [12]). For a distribution f ∈ E (R − ), define real numbers ( f ) and r( f ) by…”

Analytic linearization of the Korteweg-de Vries equation

“…F n ) define uniquely (cf. [10]), by Fourier-Laplace transformation, distributions G n (resp. F n ) E S\W) with suppG" (resp.…”