The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Two classes of metric spaces

The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.

The Lie That Tells the Truth: Creating Truth in Fiction and the Novel Delivering Hope

What makes fiction believable is the truth behind the words. This Capstone Project explores the ways in which authors put the truth on the page while simultaneously fabricating stories. The Reflective Paper examines writing techniques used to make the reader trust the story and the storyteller. The Creative Capstone is the result of applying these craft skills to Delivering Hope, a novel in progress about a critically ill baby bringing a dysfunctional family back together. The author relies on her personal experience of high- risk pregnancy and preterm birth to help create truth in her fiction.

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

An introduction to alysidal algebra (IV)

Purpose – Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues. Design/methodology/approach – Mathematical and logical development of human society ethical and normative structure. Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects. Originality/value – This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems.

An introduction to alysidal algebra (V): phenomenological components

Purpose – This paper aims to refer to a subjective approach to a type of complex system: human ecosystems, referred to as deontical impure systems (DIS) to capture a set of properties fundamental to the distinction between human and natural ecosystems. There are four main phenomenological components: directionality, intensity, connection energy and volume. The paper establishes thermodynamics of deontical systems based on the Law of Zipf and the temperature of information. Design/methodology/approach – Mathematical and logical development of human society structure. Findings – A fundamental question in this approach to DIS is the intensity or forces of a relation. Concepts are introduced as the system volume and propose a system thermodynamic theory. It hints at the possibility of adapting the fractal theory by introducing the fractal dimension of the system. Originality/value – This paper is a continuation of other previous papers and developing the theory of DIS.

Archives de l'Institut botanique de l'Université de Liège.

1, 1897

Archives de l'Institut botanique de l'Université de Liège.

2, 1900

Archives de l'Institut botanique de l'Université de Liège.

4, 1907

Un receuil: containing painting, penmanship, algebra and pieces selected from various authors in prose and verse, with a few pieces in French with their translation / by Phebe Folger of Nantucket : manuscript, 1797-1806

Written mostly in a copperplate hand in black ink, and illustrated with watercolor drawings.

Archives de l'Institut botanique de l'Université de Liège.

5, 1914

Archives de l'Institut botanique de l'Université de Liège.

3, 1901

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

Does the key to a WMD-free Middle East lie in a nuclear Iran? CEPS Commentary, 10 June 2013

After the presidential elections on June 14th, the Iranian regime will continue its catch-me-if-you-can game with the international community until it has reached the nuclear threshold. Paradoxically, the key to a solution on the nuclear issue might just lie in discussions on a WMD-free Middle East, but only after Iran has obtained nuclear military capability. At that point, and in the context of a new arms race, both regional and international players may be persuaded that the Middle East has more to gain from negotiations on non-proliferation than from prolonged isolation and the prospect of intractable war.