For given triangular real Lie algebra $\mathfrak{g}$ we construct a certain completion $C^\infty(\mathfrak{g})$ of its universal enveloping algebra. It is Frechet-Arens-Michael algebra, which consists elements polynomial growth and satisfies to the following property: every homomorphism from Banach all whose are has an extension continuous $C^\infty(\mathfrak{g})$. Elements this can be called f...

abstract: in the present paper, we give a necessary and sufficient condition for contact cr-warped product to be contact cr-product in kenmotsu space forms.

assume that $a$‎, ‎$b$ are banach algebras and that $m:atimes brightarrow b$‎, ‎$m^prime:atimes arightarrow b$ are bounded bilinear mappings‎. ‎we study the relationships between arens regularity of $m$‎, ‎$m^prime$ and the banach algebras $a$‎, ‎$b$‎. ‎for a banach $a‎$‎-bimodule $b$‎, ‎we show that $b$ factors with respect to $a$ if and only if $b^{**}$ is unital as an $a^{**}‎$‎-module‎. ‎le...

mouse, and speech for input, and audio and screen-based feedback for output. Multimedia presentation. The system makes use of a number of dierent media for human-computer interaction; in particular text, graphics, animation, and prerecorded video (the latter acting as a \cheap", but nevertheless very eective, substitute for in-oce video cameras and/or active badges 3) Communications-oriented ca...

The paper by Daniel Arens and colleagues, published in this issue of The Veterinary Journal, is one of several that are further characterising the sheep as a model for osteoporosis – a severe debilitating metabolic disease that affects mainly women (Arens et al., 2007). Why do we need an animal model for osteoporosis when there is an abundance of human subjects, especially as baby boomers age? ...

In traditional natural language systems, the channel of communication between the user and the system was a narrow and constraining device. In many areas natural Ian guage-based information access requires the possibility for the user of exploring the domain and a system's comfortable habitability. The present work presents a rationale for building intelligent interfaces that combine natural la...

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.