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.

Search for scalar leptoquarks and T-odd quarks in the acoplanar jet topology using 2.5 fb(-1) of p(p)over-bar collision data at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

4f-4f intensities of the Tm3+ ions in fluoroindate glasses: the influence of third-order effects through odd intensity parameters

In this work an analysis of the phenomenological Omega(lambda) intensity parameters for the Tm3+ ion in fluoroindate glass is made using the standard Judd-Ofelt theory, and a modified oscillator strength taking into account odd-order contributions is utilized. Different sets of phenomenological intensity parameters Omega(lambda) (lambda=1,2,3,4,5,6) are discussed. The set of better quality is used to analyze the influence of third-order effects through odd intensity parameters in the new approximation. Fluoroindate glasses of compositions (40-x)InF3-20ZnF(2)-20SrF(2)-16BaF(2)-2GdF(3)-2NaF-xTmF(3) with x=1, 2 and 3 mol% were prepared, and the absorption spectra at room temperature in the spectral range from 300 to 2500 nm were obtained. The experimental oscillator strengths determined from the area under the absorption band are compared to the calculated ones. (C) 1998 Elsevier B.V. S.A.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Judd-Ofelt analysis of Pr3+ ions in fluoroindate glasses: Influence of odd third order intensity parameters

In this work an analysis of the Judd-Ofelt phenomenological Ωλ intensity parameters for the Pr3+ ion in fluoroindate glass is made. Different Pr3+ concentrations, namely 1, 2, 3 and 4 mol% are used. The experimental oscillator strengths have been determined from the absorption spectra. A consistent set of parameters is obtained only with the inclusion of odd rank third order intensity parameters and if the band at 21 470 cm-1 is assigned to the 3H4 → 3P1 transition and the 1I6 component is incorporated in the 3H4 → 3P2 transition at 22 700 cm-1.

Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)