Encyclopaedia of quotations: a treasury of wisdom, wit and humor, odd comparisons and proverbs

UANL

A Note on Dividing Integers by Two

This note describes a simple method of dividing all integers, positive and negative, by two when represented in two's complement arithmetic.

Odd deposits and average practice. A critical history of the concept of structured deposition.

This paper presents a critical history of the concept of ‘structured deposition’. It examines the long-term development of this idea in archaeology, from its origins in the early 1980s through to the present day, looking at how it has been moulded and transformed. On the basis of this historical account, a number of problems are identified with the way that ‘structured deposition’ has generally been conceptualized and applied. It is suggested that the range of deposits described under a single banner as being ‘structured’ is unhelpfully broad, and that archaeologists have been too willing to view material culture patterning as intentionally produced – the result of symbolic or ritual action. It is also argued that the material signatures of ‘everyday’ practice have been undertheorized and all too often ignored. Ultimately, it is suggested that if we are ever to understand fully the archaeological signatures of past practice, it is vital to consider the ‘everyday’ as well as the ‘ritual’ processes which lie behind the patterns we uncover in the ground.

How Pragmatically Odd! Interface Delays and Pronominal Subject Distribution in the L2 Spanish of English Natives

Sorace (2000, 2005) has claimed that while L2 learners can easily acquire properties of L2 narrow syntax they have significant difficulty with regard to interpretation and the discourse distribution of related properties, resulting in so-called residual optionality. However, there is no consensus as to what this difficulty indicates. Is it related to an insurmountable grammatical representational deficit (in the sense of representation deficit approaches; e.g. Beck 1998, Franceschina 2001, Hawkins 2005), is it due to cross-linguistic interference, or is it just a delay due to a greater complexity involved in the acquisition of interface-conditioned properties? In this article, I explore the L2 distribution of null and overt subject pronouns of English speaking learners of L2 Spanish. While intermediate learners clearly have knowledge of the syntax of Spanish null subjects, they do not have target-like pragmatic knowledge of their distribution with overt subjects. The present data demonstrate, however, that this difficulty is overcome at highly advanced stages of L2 development, thus suggesting that properties at the syntax-pragmatics interface are not destined for inevitable fossilization.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

The odd bod, the icon and the modest woman : the differences and similarities amongst three Australian women music teachers, performers and composers

Throughout Australia's history there have been many women who have been active in music education, performance and composition, despite the traditional family commitments which women have negotiated, overcoming prevailing negative attitudes to success outside the home. The period 1900 to 1950 in Australia saw significant changes in the social structure such as universal suffrage, Federation and World War 1. These changes broadened opportunities for some women to negotiate a life-time career in music. The researcher has identified three significant women who were able to forge careers in music during this time in music teaching, composition and performance. The women were Mona McBurney, Ruby Davy and Ruth Flockart. The selected women were all unique; McBurney was an outstanding composer for her time, being the first woman in Australia to compose an opera. Also, she was the first woman in Australia to gain her Bachelor of Music. Despite these successes, she had a reputation for her overwhelming modesty and shyness. Davy was significant because of her diversified ability as a teacher, performer, composer and elocutionist, and because she was the first woman in Australia to gain her Doctorate of Music. Davy has been described by several people as unusual, strange, and an 'odd bod'. Flockart was a music teacher at Methodist Ladies' College Melbourne for almost fifty years, half of those as the Director of Music. She was a significant figure in contemporary music education, particularly as a choral conductor, where she has been described as an 'icon'. This research looks at the differences and similarities amongst these three women in terms of family life, social position, education and support systems, and their ability to negotiate a career in music teaching, performance and composition.

Who, and what, is odd here? De-naturalizing students' experiences of 'the other'

This paper reviews a teaching process that aimed to prepare final year social work students for critical practice with diverse and marginalized populations. Alongside lecture input, in small group discussions and in the two sequenced written assignments students were encouraged to personalize questions of bias and stigma by recalling both their experiences of being ‘other-ed’ as well as their participation in practices that ‘other-ed’, such as racist and homophobic imaging and acting. Feedback to the unit's first iteration in 2004 was generally positive yet a significant minority of students were clearly dissatisfied. Whilst retaining the same formal content in 2005, greater attention was devoted to generating a supportive group process and a positive environment for ‘negative’ self-disclosure. This milieu acted to contain and normalize the students' struggle with internalized stereotypes, a stage associated with their greater preparedness to identify and challenge their own personal, cultural and ideological locations. Within the context of the unit remaining explicit about its value stance, by adopting an approach to the teaching/learning process that neither collided nor colluded we believe the 2005 revision better achieved the units aims. First, the unit received broader positive appraisal from students and, second, it appeared that the unit more firmly promoted the prospects for students carrying forward a capacity for critical self review post graduation.