Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Free actions of abelian p-groups on the n-torus

In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus T-n. Set congruent to Z(pk1)(h1) x Z(pk2)(h2) x...x Z(pkr)(hr), r >= 1, k(1) >= k(2) >=...>= k(r) >= 1, p prime. Suppose that the group H acts freely on T-n and the induced representation on pi(1)(T-n) congruent to Z(n) is faithful and has first Betti number b. We show that the numbers n, p, b, k(i) and h(i) (i = 1,..,r) satisfy some relation. In particular, when H congruent to Z(p)(h), the minimum value of n is phi(p) + b when b >= 1. Also when H congruent to Z(pk1) x Z(p) the minimum value of n is phi(p(k1)) + p - 1 + b for b >= 1. Here phi denotes the Euler function.

Patterns of kinship in groups of free-living sperm whales (Physeter macrocephalus) revealed by multiple molecular genetic analyses.

Mature female sperm whales (Physeter macrocephalus) live in socially cohesive groups of 10-30, which include immature animals of both sexes, and within which there is communal care of the young. We examined kinship in such groups using analyses of microsatellite DNA, mitochondrial DNA sequence, and sex-linked markers on samples of sloughed skin collected noninvasively from animals in three groups off the coast of Ecuador. Social groups were defined through photographic identification of individuals. Each group contained about 26 members, mostly female (79%). Relatedness was greater within groups, as compared to between groups. Particular mitochondrial haplotypes were characteristic of groups, but all groups contained more than one haplotype. The data are generally consistent with each group being comprised of several matrillines from which males disperse at about the age of 6 years. There are indications of paternal relatedness among grouped individuals with different mitochondrial haplotypes, suggesting long-term associations between different matrilines.

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Seven-membered Rings Through Metal-free Rearrangement Mediated By Hypervalent Iodine.

A versatile and metal-free approach for the synthesis of carbocycles and of heterocycles bearing seven- and eight-membered rings is described. The strategy is based on ring expansion of 1-vinylcycloalkanols (or the corresponding silyl or methyl ether) mediated by the hypervalent iodine reagent HTIB (PhI(OH)OTs). Reaction conditions can be easily adjusted to give ring expansion products bearing different functional groups. A route to medium-ring lactones was also developed.

A simplified minimal residual disease polymerase chain reaction method at early treatment points can stratify children with acute lymphoblastic leukemia into good and poor outcome groups

Background Minimal residual disease is an important independent prognostic factor in childhood acute lymphoblastic leukemia. The classical detection methods such as multiparameter flow cytometry and real-time quantitative polymerase chain reaction analysis are expensive, time-consuming and complex, and require considerable technical expertise. Design and Methods We analyzed 229 consecutive children with acute lymphoblastic leukemia treated according to the GBTLI-99 protocol at three different Brazilian centers. Minimal residual disease was analyzed in bone marrow samples at diagnosis and on days 14 and 28 by conventional homo/heteroduplex polymerase chain reaction using a simplified approach with consensus primers for IG and TCR gene rearrangements. Results At least one marker was detected by polymerase chain reaction in 96.4%, of the patients. By combining the minimal residual disease results obtained on days 14 and 28, three different prognostic groups were identified: minimal residual disease negative on days 14 and 28, positive on day 14/negative on day 28, and positive on both. Five-year event-free survival rates were 85%, 75.6%,, and 27.8%, respectively (p<0.0001). The same pattern of stratification held true for the group of intensively treated children. When analyzed in other subgroups of patients such as those at standard and high risk at diagnosis, those with positive B-derived CD10, patients positive for the TEL/AML1 transcript, and patients in morphological remission on a day 28 marrow, the event-free survival rate was found to be significantly lower in patients with positive minimal residual disease on day 28. Multivariate analysis demonstrated that the detection of minimal residual disease on day 28 is the most significant prognostic factor. Conclusions This simplified strategy for detection of minimal residual disease was feasible, reproducible, cheaper and simpler when compared with other methods, and allowed powerful discrimination between children with acute lymphoblastic leukemia with a good and poor outcome.

Theory of small-signal ac response of a dielectric liquid containing two groups of ions

The analysis of Macdonald for electrolytes is generalized to the case in which two groups of ions are present. We assume that the electrolyte can be considered as a dispersion of ions in a dielectric liquid, and that the ionic recombination can be neglected. We present the differential equations governing the ionic redistribution when the liquid is subjected to an external electric field, describing the simultaneous diffusion of the two groups of ions in the presence of their own space charge fields. We investigate the influence of the ions on the impedance spectroscopy of an electrolytic cell. In the analysis, we assume that each group of ions have equal mobility, the electrodes perfectly block and that the adsorption phenomena can be neglected. In this framework, it is shown that the real part of the electrical impedance of the cell has a frequency dependence presenting two plateaux, related to a type of ambipolar and free diffusion coefficients. The importance of the considered problem on the ionic characterization performed by means of the impedance spectroscopy technique was discussed. (c) 2008 American Institute of Physics.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Body weight as an indicator of fat-free mass in active elderly women

Objective: Fat-free mass (FFM) reduction and the tendency for a reduction in surrounding fatty issue and increase in the middle are a natural consequence of growing old and should be studied in order to gain a better understanding of the aging process. This study set out to find the FFM differences between active elderly women in two age groups (60-69 and 70-80 years) and to determine which of the anthropometric measurements, body weight (BW), abdominal circumference (AC), or body mass index (BMI) are the best predictors of FFM variation within the group. Methods: Eighty-one (n = 81) active elderly women of the Third Age willingly signed up to participate in the research during the activities at the University of the Third Age (UTA) in Brazil. The research was approved by the Research Ethics Committee of the Faculty of Medical Sciences of the State University of Campinas (UNICAMP). Body weight (BW), height (H) and the BMI were measured according to the international standards. The AC was measured in centimetres at the H of the navel and body composition was ascertained using bioimpedance analysis. The SAS program was used to perform the statistical analysis of independent samples and parametric data. Results: The results showed FFM values with significant differences between the two groups, with the lowest values occurring among the women who were over 70 years of age. In the analysis, the Pearson`s Correlation Coefficient for each measured independent variable was ascertained, with the BW measurement showing the highest ratio (0.900). Conclusions: The BW measurement was regarded as reliable, low-cost and easy to use for monitoring FFM in elderly women who engage in physical activities. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Effects of margarines and butter consumption on lipid profiles, inflammation markers and lipid transfer to HDL particles in free-living subjects with the metabolic syndrome

Objective: Our purpose was to examine the effects of daily servings of butter, no-trans-fat margarine and plant sterol margarine, within recommended amounts, on plasma lipids, apolipoproteins (Apos), biomarkers of inflammation and endothelial dysfunction, and on the transfer of lipids to HDL particles in free-living subjects with the metabolic syndrome. Methods: This was a randomized, single-blind study where 53 metabolic syndrome subjects (62% women, mean age 54 years) received isocaloric servings of butter, no-trans-fat margarine or plant sterol margarine in addition to their usual diets for 5 weeks. The main outcome measures were plasma lipids, Apo, inflammatory and endothelial dysfunction markers (CRP, IL-6, CD40L or E-selectin), small dense LDL cholesterol concentrations and in vitro radioactive lipid transfer from cholesterol-rich emulsions to HDL. Difference among groups was evaluated by analysis of variance. Results: There was a significant reduction in Apo-B (-10.4 %, P = 0.043) and in the Apo-B/Apo-A-1 ratio (-11.1%, P = 0.034) with plant sterol margarine. No changes in plasma lipids were noticed with butter and no-trans-fat margarine. Transfer rates of lipids to HDL were reduced in the no-trans-fat margarine group: triglycerides -42.0%, (P<0.001 vs butter and sterol margarine) and free cholesterol -16.2% (P = 0.006 vs sterol margarine). No significant effects were noted on the concentrations of inflammatory and endothelial dysfunction markers among the groups. Conclusions: In free-living subjects with the metabolic syndrome consumption of plant sterol and no-trans-fat margarines within recommended amounts reduced, respectively, Apo-B concentrations and the ability of HDL to accept lipids. European Journal of Clinical Nutrition (2010) 64, 1141-1149; doi:10.1038/ejcn.2010.122; published online 21 July 2010

Structures of free and complexed forms of Escherichia coli xanthine-guanine phosphoribosyltransferase

Structures of free, substrate-bound and product-bound forms of Escherichia coli xanthine-guanine phosphoribosyltransferase (XGPRT) have been determined by X-ray crystallography. These are compared with the previously determined structure of magnesium and sulphate-bound XPRT. The structure of free XGPRT at 2.25 Angstrom resolution confirms the flexibility of residues in and around a mobile loop identified in other PRTases and shows that the cis-peptide conformation of Arg37 at the active site is maintained in the absence of bound ligands. The structures of XGPRT complexed with the purine base substrates guanine or xanthine in combination with cPRib-PP, an analog of the second substrate PRib-PP, have been solved to 2.0 Angstrom resolution. In these two structures the disordered phosphate-binding loop of uncomplexed XGPRT becomes ordered through interactions with the 5'-phosphate group of cPRib-PP. The cyclopentane ring of cPRib-PP has the C3 exo pucker conformation, stabilised by the cPRib-PP-bound Mg2+. The purine base specificity of XGPRT appears to be due to water-mediated interactions between the 2-exocyclic groups of guanine or xanthine and side-chains of Glu136 and Asp140, as well as the main-chain oxygen atom of Ile135. Asp92, together with Lys115, could help stabilise the N7-protonated tautomer of the incoming base and could act as a general base to remove the proton from N7 .when the nucleotide product is formed. The 2.6 Angstrom resolution structure of XGPRT complexed with product GMP is similar to the substrate-bound complexes. However, the ribose ring of GMP is rotated by similar to 24 degrees compared with the equivalent ring in cPRib-PP. This rotation results in the loss of all interactions between the ribosyl group and the enzyme in the product complex. (C) 1998 Academic Press.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.

Inactive free : total prostate specific antigen ratios in ejaculate from men with suspected and known prostate cancer, compared with young control men

Objective To measure free:total prostate specific antigen (PSA) ratios in ejaculate from men with suspected and known prostate cancer, and in young control men, to determine if this ratio might be useful in discriminating benign from malignant prostatic conditions. Patients, subjects and methods Forty-seven men with prostate cancer (positive biopsies), 52 men with suspected prostate cancer but who had negative biopsies and 28 young men (< 30 years old) and with no family history of cancer, provided either a single ejaculate specimen (total 59) or multiple specimens (total 193) on subsequent occasions. Free and total PSA were measured using appropriate assays. All specimens were diluted in a PSA-negative female serum pool. Results The median free:total PSA ratios were 0.76-0.81 among the patient groups and control men, and there was no statistical difference between the groups. These data presumably only reflect the inactive component of free PSA, given that any alpha(2)-macroglobulin or alpha(1)-antichymotrypsin in the assay serum diluent was likely to have bound the active free PSA component in these samples. Similar results were obtained from those providing single and multiple samples, suggesting that a single specimen is sufficient to reflect the seminal plasma free:total PSA ratio over that period. There was no relationship between seminal plasma free:total PSA ratio and age for the controls or the positive biopsy group, although there was a negative relationship (i.e. a decline with age) that almost reached significance in those with negative biopsies (P = 0.058, R-2 = 0.07). Conclusions This is the first report of free:total PSA ratios in the ejaculate of men with suspected and known prostate cancer compared with young control men. Although no significant changes were detected in the free:total PSA ratios in ejaculate, these results may be confounded by differences in ratios with age, as is the case for serum PSA or different molecular forms of PSA. Indeed, these data suggest that a large proportion of free PSA in seminal plasma may be inactive. Further studies are needed to determine the potential utility of measuring free:total PSA, or other candidate markers, in ejaculate to better discriminate benign from malignant prostate disease.