SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.Comment: 47 pages, minor changes, to appear in Reviews in Mathematical Physic

Assessing Financial Reporting Quality of Early Stage Private Companies

There are a variety of widely accepted methods that are used in order to evaluate the financial positioning of companies that are traded on stock exchanges. However, these methods that are common in the public markets do not suffice for assessing companies that are privately held. Attempting to devise an intrinsic value using anticipated cash flows is ineffective given that most companies are pre-revenue. Deriving a value based off of assets held is also inaccurate given that a young company will be in the process of capitalizing itself and more of its assets cannot be represented on a balance sheet, compared to public companies. Furthermore, the sheer lack of raw data provided by the companies in some cases can also contribute to pitfalls in valuation attempts. In addition, the lack of reliability of private companies’ financial information makes the valuation of these companies difficult. This study aims to develop a framework to assess the financial reporting quality of these early stage private companies

Shallow-water residency and limited dispersal of Atlantic halibut in the Gulf of Maine

• Atlantic halibut (Hippoglossus hippoglossus), once abundant in the Gulf of Maine (GOM) on the northeast coast, were overfished until the stock collapsed in the 1940s. • In 2007, a three-year tagging study using electronic tags was done by the Maine Dept. of Marine Resources. • The objective of the study was to determine if GOM halibut migrate to spawning grounds on the Scotian Shelf and mix with Canadian halibut stock

An analysis of Matthew Fox’s mystical immanence

The key objective of this research is to explore Matthew Fox’s mystical immanence, as developed in his panentheistic Creation-centred theology. Focussing on the key theme in his thought, the relationship between prayer and social justice, this thesis provides what is essentially an auteur critique. That is to say, his theology is excavated by means of biographical analysis, exploring his principal formative influences. In Chapter One the thesis seeks to identify and chronicle his spiritual odyssey, from his home environment via his seminary training within the Dominican Order to his acceptance into the Episcopal priesthood in 1994. Chapter Two focuses on the main influences on Fox’s thought, particularly: Marie-Dominique Chenu, who transformed Catholic thought in the twentieth century; Jewish spirituality, as developed by Martin Buber, Abraham Heschel, and Otto Rank; and Robert Bly, the American poet, author, activist and leader of the Mythopoetic Men’s Movement. Turning specifically to the principal developments in his theology, the third chapter, analyses Fox’s mysticism. His consistent use of the term ‘Creation’ is an indication of the cosmic orientation of this thinking, while his ‘creation spirituality’ is undergirded by his embrace of Thomas Aquinas, the Rhineland mystics and his rejection of Augustine. This chapter also evaluates the diverse scholarly critiques which have attempted to classify his work as New Age, pantheist, and monist. The fourth chapter turns to his complex understanding of the historical Jesus and his quest for the ‘Cosmic Christ’ in the Hebrew Bible, the New Testament and the Church Fathers. The thesis concludes with an examination of, firstly, Fox’s understanding of ‘Wisdom’, focussing on the ‘sophiological problem’ within the Russian religious consciousness and, secondly, his interpretation of liberation theology and social justice, as developed in his theology of work, Gaia, and eco-feminism

Ignition means for monopropellant Patent

Catalyst bed ignition system for hydrazine propellant

Computation of group table alphanumeric display

Computer program, using only group elements as input data, provides machine computation of group tables used for proving theorems and algorithms of finite groups. Program is written for second generation computers

Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

Trace-scaling automorphisms of certain stable AF algebras

Trace scaling automorphisms of stable AF algebras with dimension group totally ordered are outer conjugate if the scaling factors are the same (not equal to one). This is an adaptation of a similar result for the AFD type II_infty factor by Connes and extends the previous result for stable UHF algebras.Comment: 12 pages, late

Modular invariants from subfactors

In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling matrix comparing two kinds of braided sector induction ("alpha-induction"). It has non-negative integer entries, is normalized and commutes with the S- and T-matrices arising from the braiding. Thus it is a physical modular invariant in the usual sense of rational conformal field theory. The algebraic treatment of conformal field theory models, e.g. $SU(n)_k$ models, produces subfactors which realize their known modular invariants. Several properties of modular invariants have so far been noticed empirically and considered mysterious such as their intimate relationship to graphs, as for example the A-D-E classification for $SU(2)_k$. In the subfactor context these properties can be rigorously derived in a very general setting. Moreover the fusion rule isomorphism for maximally extended chiral algebras due to Moore-Seiberg, Dijkgraaf-Verlinde finds a clear and very general proof and interpretation through intermediate subfactors, not even referring to modularity of $S$ and $T$. Finally we give an overview on the current state of affairs concerning the relations between the classifications of braided subfactors and two-dimensional conformal field theories. We demonstrate in particular how to realize twisted (type II) descendant modular invariants of conformal inclusions from subfactors and illustrate the method by new examples.Comment: Typos corrected and a few minor changes, 37 pages, AMS LaTeX, epic, eepic, doc-class conm-p-l.cl

Modular invariants and subfactors

In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction ("$\alpha$-induction") arising from the treatment of conformal field theory in the Doplicher-Haag-Roberts framework. Many properties of modular invariants which have so far been noticed empirically and considered mysterious can be rigorously derived in a very general setting in the subfactor context. For example, the connection between modular invariants and graphs (cf. the A-D-E classification for $SU(2)_k$) finds a natural explanation and interpretation. We try to give an overview on the current state of affairs concerning the expected equivalence between the classifications of braided subfactors and modular invariant two-dimensional conformal field theories.Comment: 25 pages, AMS LaTeX, epic, eepic, doc-class fic-1.cl