Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

Sociology, Gender and Educational Aspirations: Girls and their Ambitions

This study helps develop an overall understanding as to why some students achieve where others don't. Debate on the effects of class on educational attainment is well documented and typically centres on the reproductive nature of class whilst studies of the effect of class on educational aspirations also predict outcomes that see education reinforcing and reproducing a student's class background.Despite a number of government initiatives to help raise higher education participation to 50 per cent by 2010, for the working class numbers have altered little. Using data from an ethnographic case study of a low-achieving girls school, the author explores aspirations and argues that whilst class is very powerful in explaining educational attainment, understanding educational aspirations is somewhat more complex. The purpose of this book, therefore, is to question and challenge popular assumptions surrounding class-based theory in making sense of girls' aspirations and to question the usefulness of the continued over reliance of such broad categorisations by both academics and policy makers

On a Class of Vertex Folkman Numbers

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).

Construction timbers in Queensland. Book 1 and Book 2: Properties and specifications for satisfactory performance of construction timbers in Queensland. Class 1 and Class 10 buildings (houses, carports, garages, greenhouses and sheds). 2013 edition.

This publication lists the more important wood properties of commercial timbers used for construction in Queensland. It also provides requirements and conditions of use for these timbers to provide appropriate design service life in various construction applications. The correct specification of timber considers a range of timber properties including, but not limited to, stress grade; durability class; moisture content and insect resistance. For the specification of timber sizes and spans, relevant Australian Standards and design manuals should be consulted—e.g. Australian Standard AS 1684 series Residential timber—framed construction parts 2 and 3 (Standards Australia 2006a;b.) Book 1 explains the terms used; with reference to nomenclature; origin and timber properties presented under specific column headings in the schedules (Book 2). It also explains target design life; applications and decay hazard zones; presented in the Book 2 Schedules. Book 2 consists of reference tables; presented as schedules A; B and C: • Schedule A contains commercial mixtures of unidentified timbers and of some Australian and imported softwoods. Index numbers 1–10 • Schedule B contains Australian-grown timber species; including both natural forests and plantations. Index numbers 11–493 • Schedule C contains timbers imported into Australia from overseas. Index numbers 494–606 Each schedule has two parts presenting data in tables. • Part 1: Nomenclature, origin and properties of imported timber species • Part 2: Approved uses for commercial mixtures of imported timber species The recommendations made in this publication assume that good building practice will be carried out.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Badly approximable numbers and vectors in Cantor-like sets

We show that a large class of Cantor-like sets of R-d, d >= 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d >= 2. An analogous result is also proved for subsets of R-d arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable numbers in R. Furthermore, we describe a condition on sets, which is fulfilled by a large class, ensuring a large intersection with these Cantor-like sets.

Index numbers and productivity measurement in multispecies fisheries: an application to the Pacific Coast Trawl Fleet

This study is concerned with the measurement of total factor prodnctivity in the marine fishing industries in general and in the Pacific coast trawl fishery in particular. The study is divided into two parts. Part I contains suitable empirical and introductory theoretical material for the examination of productivity in the Pacific coast trawl Deet. It is self-contained, and contains the basic formulae, empirical results, and discussion. Because the economic theory of index numbers and productivity is constantly evolving and is widely scattered throughout the economics literature, Part D draws together the theoretical literature into one place to allow ready access for readers interested in more details. The major methodological focus of the study is upon the type of economic index number that is most appropriate for use by economists with the National Marine Fisheries Service. This study recommends that the following types of economic index numbers be used: chain rather than fIxed base; bilateral rather than multilateral; one of the class of superlative indices, such as the Tornqvist or Fisher Ideal. (PDF file contains 40 pages.)

Computationally Guided Monomerization of Red Fluorescent Proteins of the Class Anthozoa

Red fluorescent proteins (RFPs) have attracted significant engineering focus because of the promise of near infrared fluorescent proteins, whose light penetrates biological tissue, and which would allow imaging inside of vertebrate animals. The RFP landscape, which numbers ~200 members, is mostly populated by engineered variants of four native RFPs, leaving the vast majority of native RFP biodiversity untouched. This is largely due to the fact that native RFPs are obligate tetramers, limiting their usefulness as fusion proteins. Monomerization has imposed critical costs on these evolved tetramers, however, as it has invariably led to loss of brightness, and often to many other adverse effects on the fluorescent properties of the derived monomeric variants. Here we have attempted to understand why monomerization has taken such a large toll on Anthozoa class RFPs, and to outline a clear strategy for their monomerization. We begin with a structural study of the far-red fluorescence of AQ143, one of the furthest red emitting RFPs. We then try to separate the problem of stable and bright fluorescence from the design of a soluble monomeric β-barrel surface by engineering a hybrid protein (DsRmCh) with an oligomeric parent that had been previously monomerized, DsRed, and a pre-stabilized monomeric core from mCherry. This allows us to use computational design to successfully design a stable, soluble, fluorescent monomer. Next we took HcRed, which is a previously unmonomerized RFP that has far-red fluorescence (λemission = 633 nm) and attempted to monomerize it making use of lessons learned from DsRmCh. We engineered two monomeric proteins by pre-stabilizing HcRed’s core, then monomerizing in stages, making use of computational design and directed evolution techniques such as error-prone mutagenesis and DNA shuffling. We call these proteins mGinger0.1 (λem = 637 nm / Φ = 0.02) and mGinger0.2 (λem = 631 nm Φ = 0.04). They are the furthest red first generation monomeric RFPs ever developed, are significantly thermostabilized, and add diversity to a small field of far-red monomeric FPs. We anticipate that the techniques we describe will be facilitate future RFP monomerization, and that further core optimization of the mGingers may allow significant improvements in brightness.

TCR V alpha- and V beta-gene segment use in T-cell subcultures derived from a type-III bare lymphocyte syndrome patient deficient in MHC class-II expression.

Previously, we and others have shown that MHC class-II deficient humans have greatly reduced numbers of CD4+CD8- peripheral T cells. These type-III Bare Lymphocyte Syndrome patients lack MHC class-II and have an impaired MHC class-I antigen expression. In this study, we analyzed the impact of the MHC class-II deficient environment on the TCR V-gene segment usage in this reduced CD4+CD8- T-cell subset. For these studies, we employed TcR V-region-specific monoclonal antibodies (mAbs) and a semiquantitative PCR technique with V alpha and V beta amplimers, specific for each of the most known V alpha- and V beta-gene region families. The results of our studies demonstrate that some of the V alpha-gene segments are used less frequent in the CD4+CD8- T-cell subset of the patient, whereas the majority of the TCR V alpha- and V beta-gene segments investigated were used with similar frequencies in both subsets in the type-III Bare Lymphocyte Syndrome patient compared to healthy control family members. Interestingly, the frequency of TcR V alpha 12 transcripts was greatly diminished in the patient, both in the CD4+CD8- as well as in the CD4-CD8+ compartment, whereas this gene segment could easily be detected in the healthy family controls. On the basis of the results obtained in this study, it is concluded that within the reduced CD4+CD8- T-cell subset of this patient, most of the TCR V-gene segments tested for are employed. However, a skewing in the usage frequency of some of the V alpha-gene segments toward the CD4-CD8+ T-cell subset was noticeable in the MHC class-II deficient patient that differed from those observed in the healthy family controls.

Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Rapid acidification and alkylation: Redox analysis of the MHC class I pathway

The technique of rapid acidification and alkylation can be used to characterise the redox status of oxidoreductases, and to determine numbers of free cysteine residues within substrate proteins. We have previously used this method to analyse interacting components of the MHC class I pathway, namely ERp57 and tapasin. Here, we have applied rapid acidification alkylation as a novel approach to analysing the redox status of MHC class I molecules. This analysis of the redox status of the MHC class I molecules HLA-A2 and HLA-B27, which is strongly associated with a group of inflammatory arthritic disorders referred to as Spondyloarthropathies, revealed structural and conformational information. We propose that this assay provides a useful tool in the study of in vivo MHC class I structure. (c) 2008 Elsevier B.V. All rights reserved.

Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.