Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

Un model geometric al legaturilor directe dintre fenomenele economice

Abstract. In this paper we approach the issue of the evolution of economic phenomena that influence one another. First of all, we introduce a geometric model to establish whether there is a direct influence between two economic phenomena. After this, we find out the strength of this influence and, finally, we suggest a model for the form of this influence.Key words: economic phenomenon; evolution; development; increase; decrease

Seismic scattering and absorption mapping from intermediate-depth earthquakes reveals complex tectonic interactions acting in the Vrancea region and surroundings (Romania)

The present study was performed during a stay at the University of Münster financed by a grant awarded by the German Academic Exchange Service (DAAD) in 2014. Data used in the present study were provided by the National Institute for Earth Physics (Romania) and processed within the National Data Centre in Magurele. Seismic Analysis Code (SAC) (Goldstein and Snoke, 2005) and GMT (Wessel et al., 2013) codes were used. We thank the College of Physical Sciences (University of Aberdeen) and the Santander Mobility Award for providing travel grant to LDS to complete this manuscript. We are grateful as well to the anonymous reviewer for his useful remarks which helped us to improve the paper.Peer reviewedPostprin

A planar calculus for infinite index subfactors

We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.Comment: 56 pages, many figure

Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.Comment: 14 page

DEFENSIBLE SPACES: IDEOLOGIES OF PROFESSIONALISM AND TEACHERS' WORK IN THE ROMANIAN PRIVATE TUTORING SYSTEM

This study seeks to analyze the nature and extent of as well as the reasons for the private tutoringactivity practiced by fifty-one Romanian secondary education teachers. The findings of my research draw to the conclusion that, although undeniably present, material self-interest does not prevail in their work as private tutors. Instead, their chief goal has been consistently to gain more professional and social status - a goal challenged by successive regimes of contrasting political hues. While identifying the ways in which their work in schools has been "proletarianized" and in which the economic and the political have pervaded their teaching activities, they understand their private tutoring work as a critical solution in a critical period of transition in the Romanian society. This practice has grown into a very well organized, hierarchical system, which aims to recuperate an ideal type of relation teacher-student and to offer them authority, autonomy, prestige and economic rewards - exactly the elements that are at the heart of their ideals of "professionalism". Besides being a subtle answer to the education policy changes, private tutoring is a momentous attempt at re-legitimating their profession and restoring their professional and social images

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.Comment: 13 pages, 11 Figure