Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1.

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.

Peat as a natural solid-phase for copper preconcentration and determination in a multicommuted flow system coupled to flame atomic absorption spectrometry

The physical and chemical characteristics of peat were assessed through measurement of pH, percentage of organic matter, cationic exchange capacity (CEC), elemental analysis, infrared spectroscopy and quantitative analysis of metals by ICP OES. Despite the material showed to be very acid in view of the percentage of organic matter, its CEC was significant, showing potential for retention of metal ions. This characteristic was exploited by coupling a peat mini-column to a flow system based on the multicommutation approach for the in-line copper concentration prior to flame atomic absorption spectrometric determination. Cu(II) ions were adsorbed at pH 4.5 and eluted with 0.50 mol L(-1) HNO(3). The influence of chemical and hydrodynamic parameters, such as sample pH, buffer concentration, eluent type and concentration, sample flow-rate and preconcentration time were investigated. Under the optimized conditions, a linear response was observed between 16 and 100 mu g L(-1), with a detection limit estimated as 3 mu g L(-1) at the 99.7% confidence level and an enrichment factor of 16. The relative standard deviation was estimated as 3.3% (n = 20). The mini-column was used for at least 100 sampling cycles without significant variation in the analytical response. Recoveries from copper spiked to lake water or groundwater as well as concentrates used in hemodialysis were in the 97.3-111 % range. The results obtained for copper determination in these samples agreed with those achieved by graphite furnace atomic absorption spectrometry (GFAAS) at the 95% confidence level. (C) 2009 Elsevier B.V. All rights reserved.

Creating Prestige and Global Networks through Conference Rituals

An international conference is a secular ritual which serves to create, recreate and shape global-wide translocal cultural sharings. Social anthropological theories and methods are used to show that, besides being an information flow junction, the international conference is a network crossroad and a way of socialising new members into aninternational research community. It is also capable of creating prestige and honour for the individual researcher,for the arranging research team, university and city. Rituals do not merely reflect the social relations or cosmology of a society, but are events that in themselves do important things through ritual forms and symbolic statements.

The Place of Writing in the Poetry of W. B. Yeats and Patrick Kavanagh

Abstract This article addresses the theme of place in the poetry of W. B. Yeats and Patrick Kavanagh, focusing on the concept of place as a physical and psychological entity. The article explores place as a creative force in the work of these two poets, in relation to the act of writing. Seamus Heaney, in his essay “The Sense of Place,” talks about the “history of our sensibilities” that looks to the stable element of the land for continuity: “We are dwellers, we are namers, we are lovers, we make homes and search for our histories” (Heaney 1980: 148-9). Thus, in a physical sense, place is understood as a site in which identity is located and defined, but in a metaphysical sense, place is also an imaginative space that maps the landscapes of the mind. This article compares the different ways in which Yeats and Kavanagh relate to their place of writing, physically and artistically, where place is understood as a physical lived space, and as a liberating site for an exploration of poetic voice, where the poet creates his own country of the mind.

The place of writing in the poetry of W.B Yeats and Patrick Kavanagh

This article addresses the theme of place in the poetry of W. B. Yeats and Patrick Kavanagh, focusing on the concept of place as a physical and psychological entity. The article explores place as a creative force in the work of these two poets, in relation to the act of writing. Seamus Heaney, in his essay “The Sense of Place,” talks about the “history of our sensibilities” that looks to the stable element of the land for continuity: “We are dwellers, we are namers, we are lovers, we make homes and search for our histories” (Heaney 1980: 148-9). Thus, in a physical sense, place is understood as a site in which identity is located and defined, but in a metaphysical sense, place is also an imaginative space that maps the landscapes of the mind. This article compares the different ways in which Yeats and Kavanagh relate to their place of writing, physically and artistically, where place is understood as a physical lived space, and as a liberating site for an exploration of poetic voice, where the poet creates his own country of the mind.