A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.

Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

REALIZING PROFINITE REDUCED SPECIAL GROUPS

Special groups are an axiomatization of the algebraic theory of quadratic forms over fields. It is known that any finite reduced special group is the special group of some field. We show that any special group that is the projective limit of a projective system of finite reduced special groups is also the special group of some field.

Construction of extrusion limit diagram for AZ31 magnesium alloy by FE simulation

The maximum speed at which magnesium can be extruded is considerably slower than that of many common aluminium extrusion alloys. This affects both the economies of production and the final mechanical behaviour. The present work quantifies the limiting extrusion speeds and ratios of magnesium alloy AZ31 as a function of billet temperature. This is done by combining hot compression test results, FE simulations and extrusion trials. Hot working stress–strain curves displayed a distinct dynamic recrystallisation peak. These data were used as a “look-up” table for the FE simulations in which the cracking limit was assumed to occur when the surface temperature reaches the incipient melting point. The maximum extrusion ratio predicted using FE analysis dropped from 90 to 40 when the extrusion ram speed was raised from 5 to 50 mm/s. The predicted limits agree well with the occurrence of cracking in both a laboratory and a commercial extrusion trial.

When does physiology limit the foraging behaviour of freely diving mammals?

Diving animals offer a unique opportunity to study the importance of physiological constraint and the limitation it can impose on animal's behaviour in nature. This paper examines the interaction between physiology and behaviour and its impact on the diving capability of five eared seal species (Family Otariidae; three sea lions and two fur seals). An important physiological component of diving marine mammals is the aerobic dive limit (ADL). The ADL of these five seal species was estimated from measurements of their total body oxygen stores, coupled with estimates of their metabolic rate while diving. The tendency of each species to exceed its calculated ADL was compared relative to its diving behaviour. Overall, our analyses reveal that seals which forage benthically (i.e. on the sea floor) have a greater tendency to approach or exceed their ADL compared to seals that forage epipelagically (i.e. near the sea surface). Furthermore, the marked differences in foraging behaviour and physiology appear to be coupled with a species demography. For example, benthic foraging species have smaller populations and lower growth rates compared to seal species that forage epipelagically. These patterns are relevant to the conservation and management of diving vertebrates.

No limits : exploring the psychology of unsolicited credit card limit increase offers

The issue of credit card debt has become an increasing concern in recent years. In Australia, for example, there is currently $42.5 billion worth of outstanding debt on credit cards, with $30 billion (over 70 per cent) bearing interest. Further, in 2001, Visa reported that 32 per cent of consumers had not paid their card off in the previous 12 months, which suggests that interest-bearing debt in Australia is held by approximately only 113 of credit card borrowers. An important element of credit card marketing is the use of psychological manipulations to encourage consumers to take-up credit. In this article, we examine the use of language and imagery in unsolicited credit card limit increase offers, and how these might influence consumers' decisions to increase their credit card limit. The analysis found that the use of terms that focused on the benefits of credit card use, such as "choice", "freedom", and "peace of mind" were used consistently to convince consumers to increase their credit card limit, whereas the use the of terms that could be considered more pragmatic and with direct reference to the nature of the product, such as "debt", "repayment" and "loan", were rarely used. Similarly, the use of colour, text changes, and images, were used which may have an influence over a consumer's ability to rationally consider whether the increase is appropriate for them. The paper concludes by recommending that government and representative bodies need to take into account the psychological manipulations used by credit card providers when developing consumer policy and codes of ethics.

Congratulations, you're pre-approved! : an analysis of credit limit upselling letters

Consumer Action commissioned Dr Paul Harrison, Deakin Business School, Deakin University and Marta Massi, School of Marketing and Communication, Lumsa University (Rome), to study the psychological aspects of one form of credit marketing – unsolicited credit card limit-increase offers (UCCLIOs). The researchers studied 21 UCCLIO letters – 17 provided by consumers and four provided by banks – and applied theories developed from previous research in the fields of marketing, consumer behavior, behavioural economics and cognitive psychology, to describe likely ways in which UCCLIO’s influenced consumer behavior and decision making. The researchers make some recommendations from a behavioural perspective based on their findings, and Consumer Action proposes how these findings might be applied to consumer policy.

Sounding alien, touching the future : beyond the sonorous limit in science fiction film

In this paper I examine two particular aspects of sounding science fiction film: first, the ulterior, Othering sounds of the alien, whether it is creature, object, technology or environment; and second, the soundscape that accompanies or underscores the type of space travel that crosses temporal and spatial thresholds. In both instances of sounding science fiction film I suggest that human limits are reached and breached, leading to a deterritorialization of the self and a hearing that touches the future which is a moment of pure becoming. I focus on the womanly sonority of the alien to suggest that patriarchal and heterosexist sound devices can be ultimately corrupted. In the analysis of sounding space travel I suggest that science film can create a series of moments in which one experiences the double sublime. This spectacular rendering of a liquid chaos enables the viewer to experience the logic of sensation beyond bodily integrity. In this paper my over-arching position is one that hears in science fiction film the profound potential of a radical alterity that exists beyond the sonorous limit.

Three dimensional stability charts for slopes based on limit analysis methods

This paper uses finite element upper and lower bound limit analysis to produce chart solutions for three-dimensional (3D) natural slopes for both short- and long-term stability. The presented chart solutions are convenient tools that can be used for preliminary design purposes. The rigorous limit analysis results in this paper were found to bracket the true factor of safety within ±10% or better, which can be used as a benchmark for the solutions from other methods. The depth of the slip surfaces is observed to be generally shallow for most analyzed cases, particularly for the long-term slope stability problem. In addition, it was found that using a two-dimensional (2D) analysis may lead to significant differences in estimating safety factors, which can differ by 2%–60% depending on the slope geometry and soil properties. Therefore, great care and judgement are required when applying 2D analyses to 3D slope problems.