Endomorphisms of the measure algebra commutative hypergroups are investigated. We focus on derivations and higher order which closely related to moment function sequences rank. describe exact connection between those endomorphisms if it is considered as a module over ring continuous functions.

and Applied Analysis 3 for x, y, z ∈ A. A Banach non-Archimedean ternary algebra is a normed non-Archimedean ternary algebra such that the normed non-Archimedean vector space with norm ‖ · ‖ is complete. The ternary algebras have been studied in nineteenth century. Their structures appeared more or less naturally in various domains of mathematical physics and data processing. The discovery of t...

Human sleep depth was traditionally assessed by scoring electro-encephalographic slow-wave amplitudes at the globally standardized C4-M1 electrode derivation. Since 2007, the American Association of Sleep Medicine (AASM) has accepted three additional derivations for the same purpose. These might well differ in slow wave amplitudes which would bias the scorings. Some derivations might also intro...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea Full list of author information is available at the end of the article Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of q...

This paper provides a mathematical analysis of the relationship between vernacular and for-malised derivations of programs; in particular, when the vernacular derivations deploy general recursion. We introduce a calculus VPD to represent vernacular derivations and a constructive theory of operations and types, EOT , to represent formal derivations. We provide an intensional semantics for VPD wi...

In 1] Buchholz presented a method to build notation systems for innnite sequent-style derivations, analogous to well-known systems of notation for ordinals. The essential feature is that from a notation one can read oo by a primitive (not "0-) recursive function its n-th predecessor and e.g. the last rule applied. Here we extend the method to the more general setting of innnite (typed) terms, i...

Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K⌊x1, . . . , xn⌋ be the Grassmann algebra over a commutative ring K with 12 ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ of an even and odd skew derivation. Explicit formulae are given for δ and δ via the ele...