Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Measuring math anxiety in Italian college and high school students: Validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS)

Given that the ability to manage numbers is essential in a modern society, mathematics anxiety – which has been demonstrated to have unfortunate consequences in terms of mastery of math – has become a subject of increasing interest, and the need to accurately measure it has arisen. One of the widely employed scales to measure math anxiety is the Abbreviated Math Anxiety Scale (AMAS) (Hopko, Mahadevan, Bare & Hunt, 2003). The first aim of the present paper was to confirm the factor structure of the AMAS when administered to Italian high school and college students, and to test the invariance of the scale across educational levels. Additionally, we assessed the reliability and validity of the Italian version of the scale. Finally, we tested the invariance of the AMAS across genders. The overall findings provide evidence for the validity and reliability of the AMAS when administered to Italian students.

A review of behaviour change theories and techniques used in group based self-management programmes for chronic low back pain and arthritis

Background: Medical Research Council (MRC) guidelines recommend applying theory within complex interventions to explain how behaviour change occurs. Guidelines endorse self-management of chronic low back pain (CLBP) and osteoarthritis (OA), but evidence for its effectiveness is weak. Objective: This literature review aimed to determine the use of behaviour change theory and techniques within randomised controlled trials of group-based self-management programmes for chronic musculoskeletal pain, specifically CLBP and OA. Methods: A two-phase search strategy of electronic databases was used to identify systematic reviews and studies relevant to this area. Articles were coded for their use of behaviour change theory, and the number of behaviour change techniques (BCTs) was identified using a 93-item taxonomy, Taxonomy (v1). Results: 25 articles of 22 studies met the inclusion criteria, of which only three reported having based their intervention on theory, and all used Social Cognitive Theory. A total of 33 BCTs were coded across all articles with the most commonly identified techniques being '. instruction on how to perform the behaviour', '. demonstration of the behaviour', '. behavioural practice', '. credible source', '. graded tasks' and '. body changes'. Conclusion: Results demonstrate that theoretically driven research within group based self-management programmes for chronic musculoskeletal pain is lacking, or is poorly reported. Future research that follows recommended guidelines regarding the use of theory in study design and reporting is warranted.

Can I Count on Getting Better? Association between Math Anxiety and Poorer Understanding of Medical Risk Reductions

BACKGROUND: Lower numerical ability is associated with poorer understanding of health statistics, such as risk reductions of medical treatment. For many people, despite good numeracy skills, math provokes anxiety that impedes an ability to evaluate numerical information. Math-anxious individuals also report less confidence in their ability to perform math tasks. We hypothesized that, independent of objective numeracy, math anxiety would be associated with poorer responding and lower confidence when calculating risk reductions of medical treatments.

METHODS: Objective numeracy was assessed using an 11-item objective numeracy scale. A 13-item self-report scale was used to assess math anxiety. In experiment 1, participants were asked to interpret the baseline risk of disease and risk reductions associated with treatment options. Participants in experiment 2 were additionally provided a graphical display designed to facilitate the processing of math information and alleviate effects of math anxiety. Confidence ratings were provided on a 7-point scale.

RESULTS: Individuals of higher objective numeracy were more likely to respond correctly to baseline risks and risk reductions associated with treatment options and were more confident in their interpretations. Individuals who scored high in math anxiety were instead less likely to correctly interpret the baseline risks and risk reductions and were less confident in their risk calculations as well as in their assessments of the effectiveness of treatment options. Math anxiety predicted confidence levels but not correct responding when controlling for objective numeracy. The graphical display was most effective in increasing confidence among math-anxious individuals.

CONCLUSIONS: The findings suggest that math anxiety is associated with poorer medical risk interpretation but is more strongly related to confidence in interpretations.

A descriptive study of the usage of spinal manipulative therapy techniques within a randomised clinical trial in acute low back pain

The majority of randomized clinical trials (RCTs) of spinal manipulative therapy have not adequately de?ned the terms ‘mobilization’ and ‘manipulation’, nor distinguished between these terms in reporting the trial interventions. The purpose of this study was to describe the spinal manipulative therapy techniques utilized within a RCT of manipulative therapy (MT; n=80), interferential therapy (IFT; n=80), and a combination of both (CT; n=80) for people with acute low back pain (LBP). Spinal manipulative therapy was de?ned as any ‘mobilization’ (low velocity manual force without a thrust) or ‘manipulation’ (high velocity
thrust) techniques of the spine described by Maitland and Cyriax.
The 16 physiotherapists, all members of the Society of Orthopaedic Medicine, utilized three spinal manipulative therapy patterns in the RCT: Maitland Mobilization (40.4%, n=59), Maitland Mobilization/Cyriax Manipulation (40.4%, n=59) and Cyriax Manipulation (19.1%, n=28). There was a signi?cant difference between the MT and CT groups in their usage of spinal manipulative therapy techniques (w2=9.178; df=2;P=0.01); subjects randomized to the CT group received three times more Cyriax Manipulation (29.2%, n=21/72) than those randomized to the MT group (9.5%, n=7/74; df=1; P=0.003).
The use of mobilization techniques within the trial was comparable with their usage by the general population of physiotherapists in Britain and Ireland for LBP management. However, the usage of manipulation techniques was considerably higher than reported in physiotherapy surveys and may re?ect the postgraduate training of trial therapists.

Effects of vasectomy on spermatogenesis and fertility outcomes after assisted conception

Abstract BACKGROUND: Each year 40,000 men have a vasectomy in the UK whilst another 2400 request a reversal to begin a second family. Sperm can now be obtained by testicular biopsy and subsequently used in assisted conception with intracytoplasmic sperm injection (ICSI). The study aims were to compare sperm yields of men post-vasectomy or with obstructive azoospermia (OA) of unknown aetiology with fertile men and to assess any alteration in the clinical pregnancy rates after ICSI. METHODS: Testicular tissue was obtained by Trucut needle from men who had undergone a vasectomy >5yrs previously, had OA from other causes and from fertile men during vasectomy. Seminiferous tubules were milked to measure sperm yields. Numbers of Sertoli cells, spermatids and thickness of the seminiferous tubule walls were assessed using quantitative computerized analysis. RESULTS and CONCLUSIONS: Sperm yields/g testis were significantly decreased in men post-vasectomy and in men with OA, relative to fertile men. Significant reductions were also observed in early (40%) and mature (29%) spermatid numbers and an increase of 31% was seen in the seminiferous tubule wall (basal membrane and collagen thickness) of vasectomised men compared to fertile men. Clinical pregnancy rates in couples who had had a vasectomy were also significantly reduced.

Modulating the selectivity for CO and butane oxidation over heterogeneous catalysis through amorphous catalyst coatings

The preparation of porous films directly deposited onto the surface of catalyst particles is attracting increasing attention. We report here for the first time a method that can be carried out at ambient pressure for the preparation of porous films deposited over 3 mm diameter catalyst particles of silica-supported Pt-Fe. Characterization of the sample prepared at ambient pressure (i.e., open air, OA) and its main structural differences as compared with a Na-A (LTA) coated catalyst made using an autoclave-based method are presented. The OA-coated material predominantly exhibited an amorphous film over the catalyst surface with between 4 and 13% of crystallinity as compared with fully crystallized LTA zeolite crystals. This coated sample was highly selective for CO oxidation in the presence of butane with no butane oxidation observed up to 350 degrees C. This indicates, for the first time, that the presence of a crystalline membrane is not necessary for the difference in light off temperature between CO and butane to be achieved and that amorphous films may also produce this effect. An examination of the space velocity dependence and adsorption of Na+ on the catalysts indicates that the variation in CO and butane oxidation activity is not caused by site blocking predominantly, although the Pt activity was lowered by contact with this alkali.

Response of surface horizons in an oak forest to prescribed burning

The reduction of forest floor ground cover and litter layers by prescribed fires may alter the morphology (field and micro) and physical properties of surface horizons. This study determined long-term (35 yr) changes in surface horizon bulk density, organic matter concentration and content, and morphology in response to periodic (5 yr) and annual (1 yr) prescribed fires. Soils were fine-silty, siliceous, thermic Glossic Fragiuldults, supporting mixed oak vegetation in middle Tennessee. Upper mineral soils (0- to 2-cm and 0- to 7.6-cm depths) were sampled and detailed field descriptions made. Periodic and control plots had a thin layer of Oi, Oe, and Oa horizons 5 yr after the 1993 burn, whereas on annual burn plots a 1- to 2-cm charred layer was present. Significant reductions in organic matter concentration and mean thickness of the A horizon were found from burning (A horizons thicknesses were 6.4, 4.6, and 2.9 cm in control, periodic, and annual plots, respectively). Periodic burns did not significantly alter the organic matter and bulk density of the upper 7.6 cm of mineral soil; however, annual burns did result in significantly higher bulk densities (1.01, 1.07, and 1.29 Mg m-3 in control, periodic, and annual plots, respectively) and lower organic matter concentrations and contents. Microscopic investigations confirmed that compaction was increased from annual burning. Thin sections also revealed that the granular structure of the A horizons in control and periodic plots resulted from bioterbation of macro and mesofauna, fungi, and roots. Long-term annual burning greatly affected surface soil properties, whereas periodic burning on a 5-yr cycle had only limited effects.