The Global Dimension of Schur Algebras for GL2 and GL3

AbstractWe first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL2 and SL3. We use these to show that the global dimension of a Schur algebra for GL2 and GL3 is twice the good filtration dimension. To do this for SL3, we give an explicit filtration of the modules ∇(λ) by modules of the form ∇(μ)F⊗L(ν) where μ is a dominant weight and ν is p-restricted

On the global and \nabla-filtration dimensions of quasi-hereditary algebras

In this paper we consider how the \nabla-, \Delta- and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if \mu < \lambda then \nabla fd(L(\mu)) < \nabla fd(L(\lambda)) where \mu, \lambda are in the poset and L(\mu), L(\lambda) are the corresponding simples. We show that in this case the global dimension of the algebra is twice its \nabla-filtration dimension. We then consider more general quasi-hereditary algebras and look at how these dimensions are affected by the Ringel dual and by two forms of truncation. We restrict again to quasi-hereditary algebras with simple preserving duality and consider various orders on the poset compatible with quasi-hereditary structure and the \nabla-, \Delta- and injective dimensions of the simple and the costandard modules.Comment: 18 pages, uses xypi

Tube-side mass transfer for hollow fibre membrane contactors operated in the low Graetz range

Transformation of the tube-side mass transfer coefficient derived in hollow fibre membrane contactors (HFMC) of different characteristic length scales (equivalent diameter and fibre length) has been studied when operated in the low Graetz range (Gz < 10). Within the low Gz range, mass transfer is generally described by the Graetz problem (Sh=3.67) which assumes that the concentration profile comprises a constant shape over the fibre radius. In this study, it is experimentally evidenced that this assumption over predicts mass transfer within the low Graetz range. Furthermore, within the low Gz range (below 2), a proportional relationship between the experimentally determined mass transfer coefficient (Kov) and the Graetz number has been identified. For Gz numbers below 2, the experimental Sh number approached unity, which suggests that mass transfer is strongly dependent upon diffusion. However, within this diffusion controlled region of mass transfer, tube-side fluid velocity remained important. For Gz numbers above 2, Sh could be satisfactorily described by extension to the Lévêque solution, which can be ascribed to the constrained growth of the concentration boundary layer adjacent to the fibre wall. Importantly this study demonstrates that whilst mass transfer in the low Graetz range does not explicitly conform to either the Graetz problem or classical Lévêque solution, it is possible to transform the experimentally derived overall mass transfer coefficient (Kov) between characteristic length scales (dh and L). This was corroborated by comparison of the empirical relationship determined in this study (Sh=0.36Gz) with previously published studies operated in the low Gz range. This analysis provides important insight for process design when slow tube-side flows, or low Schmidt numbers (coincident with gases) constrain operation of hollow fibre membrane contactors to the low Gz range

Penta­fluoro­phenyl (3R,4R,5S)-5-{[(3R,4R,5S)-5-azido­methyl-3,4-dimeth­oxy-2,3,4,5-tetra­hydro­furan-3-carboxamido]­meth­yl}-3,4-dimeth­oxy-2,3,4,5-tetra­hydro­furan-3-carboxyl­ate

The title compound, C22H25F5N4O9, is a stable penta­fluoro­phenyl ester inter­mediate in the synthesis of novel homo-oligomeric structures containing branched carbon chains. The structure is epimeric to the previously characterized dimeric penta­fluoro­phenyl ester with stereochemistry (3R,4R,5R), which was synthesized using d-ribose as starting material. The crystal structure of the title mol­ecule removes any ambiguities arising from the relative stereochemistries of the six chiral centres. Two hydrogen bonds, bifurcating from the NH group, stabilize the crystal: one intra­molecular and one inter­molecular, both involving O atoms of the meth­oxy groups. The asymmetric unit contains two independent mol­ecules not related by any pseudo-symmetry operators. The major conformational differences are localized, leading to one mol­ecule being extended compared to the other. The collected crystal was twinned (twin ratio is 0.939:0.061), and the azide group is positionally disordered over two positions in one mol­ecule [occupancy ratio 0.511 (18):0.489 (18)]

The effectiveness of simple psychological and exercise interventions for high prevalence mental health problems in young people: a factorial randomised controlled trial

<p>Abstract</p> <p>Background</p> <p>The prevalence of mental illness in young people is the highest of any age group, with the onset of depression, anxiety and substance use peaking between 18 and 24 years. Effective treatments that target sub-threshold or mild to moderate levels of disorder in young people are required to reduce the risk of persistence and recurrence. The aims of this study are to evaluate whether treatments that are less intensive than cognitive-behaviour therapy, such as problem solving therapy and exercise treatments, are acceptable and effective in managing depression and anxiety symptoms in young people and to identify possible attributes in those who are likely to respond to these treatments.</p> <p>Methods/design</p> <p>This is a factorial randomised controlled trial conducted at a large, metropolitan youth mental health service. Participants are young help-seekers aged 15-25 years with sub-threshold or mild to moderate levels of depression and anxiety (with or without comorbid substance use). The interventions comprise 4 treatment combinations delivered by psychologists over 6 sessions on a weekly basis: a psychological intervention (problem solving therapy versus supportive counselling) and an exercise intervention (behavioural exercise versus psychoeducation). Structured assessments occur at baseline, mid-point, end-point (6 weeks) and at a 6- and 12-month follow-up. The primary outcomes are depression and anxiety symptoms as measured by the Beck Depression and Anxiety Inventories. Secondary outcomes include remission (defined as no longer meeting the diagnostic criteria for a disorder if threshold level was reached at baseline, or no longer scoring in the clinical range on scale scores if sub-threshold at baseline), substance use, and functioning.</p> <p>Discussion</p> <p>The effectiveness of less complex psychological and exercise interventions in young help-seekers with sub-threshold or mild to moderate presentations of high prevalence disorders is yet to be explored. This study has been designed to examine the effectiveness of these interventions delivered alone, or in combination, in a youth-specific service. If effective, the interventions have the potential to prevent the progression of early symptoms and distress to later and potentially more serious stages of mental disorder and reduce the likelihood of ongoing problems associated with the risk of persistence and recurrence.</p> <p>Trial registration</p> <p>Australian New Zealand Clinical Trials Registry <a href="http://www.anzctr.org.au/ACTRN12608000550303.aspx">ACTRN12608000550303</a></p

Homomorphisms and Higher Extensions for Schur algebras and symmetric groups

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined