Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Holding it all together? The management of supply cover in the teaching profession

There have for some years been concerns in Scotland about the availability of supply cover, the quality of supply teachers and the adequacy of support and development provided for them. This is a report of a study which focuses on the management of supply cover in Scotland. It presents an analysis of qualitative and quantitative data collected from education authorities, schools and supply teachers

The management of supply cover in the teaching profession

There have for some years been concerns in Scotland about the availability of supplycover, the quality of supply teachers, and the adequacy of support and developmentprovided for them. This Insighthighlights key findings from a study of the managementof supply cover in Scotland. The research was commissioned by the Scottish ExecutiveEducation Department in October 2002 to inform the development of guidelines

Preservation of the Family Unit in Adolescent Novels

This thesis discusses the development of the family story from the late nineteenth century to the present, beginning with What Katy Did as an example of the earlier moral story from which this genre grows. It then focuses on Little Women as the beginning of the modern family story and uses Jo from Little Women as the starting point to discuss the development of the female adolescent protagonist in these stories. And lastly, comparing Little Women to modern family life stories which began to appear about 1940, the thesis discusses changes in didacticism which have occurred since the late nineteenth century. (In the years between 1890 and 1940, stories with adolescent female protagonists focused mainly on the female alone, often as an orphan, rather than as part of a family.) In the hundred years since What Katy Did appeared, codes of female behavior and family structure have changed extensively. However, the family story has not changed as much as might be expected. Modern families in these stories (like their real counterparts) deal with such crises as divorce, abandonment, and illegitimacy. No matter what the cause of the disruption, the message underlying these novels is that the family unit is worth preserving in some form. Jo in Little Women became the prototype for the modern adolescent female in the family story. Jo is allowed to be a tomboy, to make mistakes, to be a person. In stories like What Katy Did, however, tomboys who do not automatically conform to traditional female roles are forced to accept those roles or are punished until they do. The more modern characters, who follow in Jo\u27s footsteps, are not perfect daughters, nor do they automatically become perfect mothers. They have strengths and weaknesses; they do not always know the right answer. But there is no implication that God gets even with them for their shortcomings as there is in What Katy Did. As we move to the newer family stories, the family unit is still functional. In stories such as Vera and Bill Cleaver\u27s Where the Lilies Bloom (1969) and Cynthia Voigt\u27s Dicey\u27s Song (1982), the importance of the family is clear. The preaching in these stories, however, is even less obvious than it was in Little Women. The value of the family is inherent in the novel, but the codes of behavior are not as strict. Proper behavior in the Victorian sense does not apply as much as the individual family\u27s ability to determine what behavior best serves its needs. These families can no longer depend upon society to impose traditional codes of behavior. In their isolation they have to find answers for themselves. These books show the value of the family unit and endorse ways in which the families can remain functional in a world which provides little support for the family unit

The sensory acceptance of fibre-enriched cereal foods:a meta-analysis

Improved understanding of the sensory responses to fibre fortification may assist manufacturers and health promotion efforts. The effects of fibre fortification (or modified ingredients) on sensory acceptability of baked cereal foods (bread, cookies, muffins) were estimated by linear random-effects meta-analysis of twenty eligible studies (869 panellists, 34% male). As little as 2 g per 100 g fortification caused moderate–large reductions in overall acceptability, flavour acceptability, and appearance acceptability in most items, with cookies most negatively affected. Fortification of base nonfortified foods with low initial acceptability improved acceptability; however, at higher basic levels, fortification lowered acceptability. Fortification improved texture acceptability of muffins and bread with low base acceptability, but lowered texture acceptability when base acceptability was high. Flavour improvement of muffins with fortification decreased with increasing base food acceptability. Fibre fortification of baked cereal foods lowers acceptability, but food format and base food acceptability affect the magnitude and direction of responses. Refining fibre fortification approaches could improve consumer uptake

The evolution of Radio Loud Quasar host galaxies: AO observations at z = 3

We report on ESO--VLT adaptive optics imaging of one radio-loud quasar at z $\sim$ 3. In spite of the large distance of the object we are able to detect its surrounding extended nebulosity the properties of which are consistent with an underlying massive galaxy of M$_K$ $\sim$ --27 and effective radius R$_e$ = 7 kpc. As far as we know this is the clearest detection of a radio loud quasar host at high redshift. The host luminosity is indicative of the existence of massive spheroids even at this early cosmic epoch. The host luminosity is about 1 magnitude fainter than the expected value based on the average trend of the host galaxies of RLQ at lower redshift. The result, which however is based on a single object, suggests that at z $\sim$ 3 there is a deviation from a luminosity--redshift dependence regulated only by passive evolution.Comment: 6 pages, 3 figures, TeX uses elsart.cls, from workshop "QSO Host Galaxies: Evolution and Environment" (Univ. Leiden, Aug. 22-26, 2005

Proof of the Double Bubble Conjecture in R^n

The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble.Comment: 20 pages, 22 figure