Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Nuclear Weapons as Symbols. The Role of Norms in Nuclear Policy Making

Throughout history, nuclear weapons have been considered to be the ultimate weapons. This understanding largely detached them from the portfolio of conventional military means and assigned them a symbolic meaning that influenced the identity and norms creation of nations. In most countries today, the development of nuclear weapons is considered morally prohibitive, incompatible with a country’s identity and international outlook. In some states, however, these negative norms are overridden by a positive set of norms, causing nuclear weapons to become either symbols of invulnerability to perceived threats or the regalia of major power status. Main purpose of this paper is to explore on the conditions that cause most states to develop a moral aversion to nuclear weapons, yet effectively lead to their glorification in others. Many studies on the normative understanding of nuclear weapons consider the existence of a negative normative predisposition, often referred to as ‘nuclear taboo’, as a major factor in preventing their acquisition and use. Other studies acknowledge the existence of a nuclear taboo inhibiting the use of nuclear weapons, but point to the existence of the opposing effect of norms, frequently referred to as the ‘nuclear myth’, when it comes to the acquisition of nuclear weapons. This myth emerges when certain symbolic meanings are attached to nuclear weapons, such as a state’s identity, self-image, and its desired position in the international system. With 180 odd countries in the world abstaining from the acquisition of nuclear weapons and 8 countries in possession of them (with two further countries assumed to have pursued their acquisition), one might consider the dominance of the nuclear taboo over the nuclear myth to be the rule. The core question is thus why and how this relationship reversed in the case of defectors.

State Symbols of Iowa, 2003

Includes color illustrations and descriptions of Iowa's state flag, flower, bird, tree, and rock.

Between pluralism and majoritarianism: the European Court of Human Rights on religious symbols and education

How is it possible to square the development of a consistent Europeanapproach to religious diversity with the recognition of the sometimes-conflictiveplurality of state-religion models? The Court´s support of the liberalprinciples of separation and neutrality have either been deplored by Christianconservatives as the result of European Christophobia, or celebratedby secularists as contributing to the formation of a Europe free of religion.In contrast, the present chapter argues for a differentiated approach toEuropean jurisprudence, outlining how the Court has been oscillating betweenan appealing liberal-pluralist perspective or framework, and a questionablemajoritarian one. Both perspectives are illustrated by focusing onrepresentative decisions in the area of religious education and symbols.

Restarting automata with restricted utilization of auxiliary symbols

The restarting automaton is a restricted model of computation that was introduced by Jancar et al. to model the so-called analysis by reduction, which is a technique used in linguistics to analyze sentences of natural languages. The most general models of restarting automata make use of auxiliary symbols in their rewrite operations, although this ability does not directly correspond to any aspect of the analysis by reduction. Here we put restrictions on the way in which restarting automata use auxiliary symbols, and we investigate the influence of these restrictions on their expressive power. In fact, we consider two types of restrictions. First, we consider the number of auxiliary symbols in the tape alphabet of a restarting automaton as a measure of its descriptional complexity. Secondly, we consider the number of occurrences of auxiliary symbols on the tape as a dynamic complexity measure. We establish some lower and upper bounds with respect to these complexity measures concerning the ability of restarting automata to recognize the (deterministic) context-free languages and some of their subclasses.

Quantities, units and symbols in physical chemistry, 3rd edition

The first IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (the Green Book) of which this is the direct successor, was published in 1969, with the object of 'securing clarity and precision, and wider agreement in the use of symbols, by chemists in different countries, among physicists, chemists and engineers, and by editors of scientific journals'. Subsequent revisions have taken account of many developments in the field, culminating in the major extension and revision represented by the 1988 edition under the simplified title Quantities, Units and Symbols in Physical Chemistry. This 2007, third edition, is a further revision of the material which reflects the experience of the contributors with the previous editions. The book has been systematically brought up to date and new sections have been added. It strives to improve the exchange of scientific information among the readers in different disciplines and across different nations. In a rapidly expanding volume of scientific literature where each discipline has a tendency to retreat into its own jargon this book attempts to provide a readable compilation of widely used terms and symbols from many sources together with brief understandable definitions. This is the definitive guide for scientists and organizations working across a multitude of disciplines requiring internationally approved nomenclature.

The choice of names and symbols for quantities in chemistry

The importance of maintaining a clear distinction between the names and symbols for quantities and the names and symbols for units.