Linear groups, with an exposition of the Galois field theory,

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INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Synthesis of monocyclic and linear polystyrene using the reversible coupling/cleavage of thiol/disulfide groups

By carefully controlling the concentration of alpha,omega-thiol polystyrene in solution, we achieved formation of unique monocyclic polystyrene chains (i.e., polymer chains with only one disulfide linkage). The presence of cyclic polystyrene was confirmed by its lower than expected molecular weight due to a lower hydrodynamic volume and loss of thiol groups as detected by using Ellman's reagent. The alpha,omega-thiol polystyrene was synthesized by polymerizing styrene in the presence of a difunctional RAFT agent and subsequent conversion of the dithioester end groups to thiols via the addition of hexylamine. Oxidation gave either monocyclic polymer chains (i.e., with only one disulfide linkage) or linear multiblock polymers with many disulfide linkages depending on the concentration of polymer used with greater chance of cyclization in more dilute solutions. At high polymer concentrations, linear multiblock polymers were formed. To control the MWD of these linear multiblocks, monofunctional X-PSTY (X = PhCH2C(S)-S-) was added. It was found that the greatest ratio of X-PSTY to X-PSTY-X resulted in a low M-n and PDI. We have shown that we can control both the structure and MWD using this chemistry, but more importantly such disulfide linkages can be readily reduced back to the starting polystyrene with thiol end groups, which has potential use for a recyclable polymer material.

On the homotopy groups of the self-equivalences of linear spheres

Peer reviewed

On the homotopy groups of the self-equivalences of linear spheres

Peer reviewed

Influência da idade no comportamento da frequência cardíaca na transição repouso-exercício: uma análise por deltas e regressão linear

BACKGROUND: Changes in heart rate during rest-exercise transition can be characterized by the application of mathematical calculations, such as deltas 0-10 and 0-30 seconds to infer on the parasympathetic nervous system and linear regression and delta applied to data range from 60 to 240 seconds to infer on the sympathetic nervous system. The objective of this study was to test the hypothesis that young and middle-aged subjects have different heart rate responses in exercise of moderate and intense intensity, with different mathematical calculations. METHODS: Seven middle-aged men and ten young men apparently healthy were subject to constant load tests (intense and moderate) in cycle ergometer. The heart rate data were submitted to analysis of deltas (0-10, 0-30 and 60-240 seconds) and simple linear regression (60-240 seconds). The parameters obtained from simple linear regression analysis were: intercept and slope angle. We used the Shapiro-Wilk test to check the distribution of data and the t test for unpaired comparisons between groups. The level of statistical significance was 5%. RESULTS: The value of the intercept and delta 0-10 seconds was lower in middle age in two loads tested and the inclination angle was lower in moderate exercise in middle age. CONCLUSION: The young subjects present greater magnitude of vagal withdrawal in the initial stage of the HR response during constant load exercise and higher speed of adjustment of sympathetic response in moderate exercise.

Obesity due to Melanocortin 4 Receptor (MC4R) Deficiency Is Associated with Increased Linear Growth and Final Height, Fasting Hyperinsulinemia, and Incompletely Suppressed Growth Hormone Secretion

Context: Melanocortin receptor 4 (MC4R) deficiency is characterized by increased linear growth greater than expected for the degree of obesity. Objective: The objective of the investigation was to study the somatotroph axis in obese MC4R-deficient patients and equally obese controls. Patients and Methods: We obtained anthropometric measurements and insulin concentrations in 153 MC4R-deficient subjects and 1392 controls matched for age and severity of obesity. We measured fasting IGF-I, IGF-II, IGF binding protein (IGFBP)-1, IGFBP-3, and acid-labile subunit levels in a subset of 33 MC4R-deficient patients and 36 control subjects. We examined pulsatile GH secretion in six adult MC4R-deficient subjects and six obese controls. Results: Height so score was significantly greater in MC4R-deficient children under 5 yr of age compared with controls (mean +/- SEM: 2.3 +/- 0.06 vs. 1.8 +/- 0.04, P < 0.001), an effect that persisted throughout childhood. Final height (cm) was greater in MC4R-deficient men (mean +/- SEM 173 +/- 2.5 vs. 168 +/- 2.1, P < 0.001) and women (mean 165 +/- 2.1 vs. 158 +/- 1.9, P < 0.001). Fasting IGF-I, IGF-II, acid-labile subunit, and IGFBP-3 concentrations were similar in the two groups. GH levels were markedly suppressed in obese controls, but pulsatile GH secretion was retained in MC4R deficiency. The mean maximal GH secretion rate per burst (P < 0.05) and mass per burst (P < 0.05) were increased in MC4R deficiency, consistent with increased pulsatile and total GH secretion. Fasting insulin levels were markedly elevated in MC4R-deficient children. Conclusions: In MC4R deficiency, increased linear growth in childhood leads to increased adult final height, greater than predicted by obesity alone. GH pulsatility is maintained in MC4R deficiency, a finding consistent with animal studies, suggesting a role for MC4R in controlling hypothalamic somatostatinergic tone. Fasting insulin levels are significantly higher in children carrying MC4R mutations. Both of these factors may contribute to the accelerated growth phenotype characteristic of MC4R deficiency. (J Clin Endocrinol Metab 96: E181-E188, 2011)

Linear ketenimines. Variable structures of C,C-dicyanoketenimines and C,C-bis-sulfonylketenimines

C,C-Dicyanoketenimines 10a-c were generated by flash vacuum thermolysis of ketene NS-acetals 9a-c or by thermal or photochemical decomposition of alpha-azido-,beta-cyanocinnamonitrile 11. In the latter reaction, 3,3-dicyano-2-phenyl-1-azirine 12 is also formed. IR spectroscopy of the keteniminines isolated in Ar matrixes or as neat films, NMR spectroscopy of 10c, and theoretical calculations (B3LYP/6-31G*) demonstrate that these ketenimines have variable geometry, being essentially linear along the CCN-R framework in polar media (neat films and solution), but in the gas phase or Ar matrix they are bent, as is usual for ketenimines. Experiments and calculations agree that a single CN substituent as in 13 is not enough to enforce linearity, and sulfonyl groups are less effective that cyano groups in causing linearity. C,C-Bis(methylsulfonyl)ketenimines 4-5 and a C-cyano-C-(methylsulfonyl)ketenimine 15 are not linear. The compound p-O2NC6H4N=C= C(COOMe)2 previously reported in the literature is probably somewhat linearized along the CCNR moiety. A computational survey (B3LYP/6-31G*) of the inversion barrier at nitrogen indicates that electronegative C-substituents dramatically lower the barrier; this is also true of N-acyl substituents. Increasing polarity causes lower barriers. Although N-alkylbis(methylsulfonyl)ketenimines are not calculated to be linear, the barriers are so low that crystal lattice forces can induce planarity in N-methylbis(methylsulfonyl)ketenimine 3.

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades &-1 to &9) were separated, and each fraction was analysed for its chemical composition.The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø &8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar).To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend.Key words: sediment, geochemistry, grain size, regression, step function

Convergent Approaches for the Synthesis of the Anti-tumoral Peptide, Kahalalide F. Study of Orthogonal Protecting Groups

Kahalalide compounds are peptides that are isolated from a Hawaiian herbivorous marine species of mollusc, Elysia rufescens, and its diet, the green alga Bryopsis sp. Kahalalide F and its synthetic analogues are the most promising compounds of the Kahalalide family because they show anti-tumoral activity. Linear solid-phase syntheses of Kahalalide F have been reported. Here we describe several new improved synthetic routes based on convergent approaches with distinct orthogonal protection schemes for the preparation of Kahaladide analogues. These strategies allow a better control and characterization of the intermediates because more reactions are performed in solution. Five derivatives of Kahalalide F were synthesized using several convergent approaches.