In this article, David Buckingham addresses the challenges media educators face in dealing with postmodern media culture. Buckingham begins by outlining the nature of contemporary developments in children’s media environments and how these relate to broader changes in their social status. He argues that these developments represent a fundamental challenge to the modernist project of media educa...

The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study v...

In this paper, the possibility of verifying π-calculus processes via Promela translation is investigated. A general translation method from π-calculus processes to Promela models is presented and its usefulness is shown by performing verification tasks with translated π-calculus examples and SPIN. Model checking translated π-calculus processes in SPIN is shown to overcome shortcomings of the Mo...

Generalizing an example from (Fine 1975) and inspired by a theorem in (Jónsson 1994), we prove that any modal formula of the form π(p ∨ q) ↔ π(p) ∨ π(q) (with π(p) a positive formula) is canonical. We also prove that any such formula is strongly sound and complete with respect to an elementary class of frames, definable by a first order formula which can be read off from π.

1.1. Main theorem. In usual, the irreducible decomposition of a representation of an operator algebra does not make sense because there is no uniqueness of such decomposition in general. This fact disturbs an intention to study an ordinary representation theory of operator algebras like that of semisimple Lie algebras and quantum groups. In spite of this, permutative representations of the Cunt...

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecula...

Let K be a nonarchimedean local field. As explained in the previous lecture, to complete our proof the existence theorem of local class field theory (Theorem 27.8), which states that every finite index open subgroup of K× is a norm group, we need to construct a system of totally ramified abelian extensions Kπ,n/K and a homomorphism θπ : K × → Gal(Kab π /K) satisfying the hypotheses of Theorem 3...

Proof of Theorem 1. In our following proof, we will only consider the case when φ is not an integer multiple of π, because we will not need the case when φ is a multiple of π in our later applications of Theorem 1. Besides, our following proof can be easily modified to work for the case of φ being a multiple of π as well (this modification is left to the reader). We will establish Theorem 1 by ...

counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . However, they will have an abstract counterpart in . There is also a natural embedding of A into ∗∗ ∗∗ ∗∗ ⊆ A A A such that . The most common way to construct a von Neumann algebra is to start with a C*-algebra and an abstract state A ω , construct a representation ( , ω ) π ω π H ( via the GNS theorem...

We consider sufficient conditions for a degree sequence π to be forcibly k-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially k-factor graphical. We first give a theorem for π to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most β ≥ 0. These theorems ...