EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K x B, with B a quasi-injective abelian group of odd order and either K = Q(8) (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A(5) is of injective type but that the binary icosahedral group SL(2, 5) is not.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

Prediction with measurement errors in finite populations

We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors. (C) 2011 Elsevier By. All rights reserved.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U -> infinity and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U -> 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Ankle-Brachial Index: A Simple Way to Predict Mortality among Patients on Hemodialysis - A Prospective Study

Background: Ankle-brachial index (ABI) can access peripheral artery disease and predict mortality in prevalent patients on hemodialysis. However, ABI has not yet been tested in incident patients, who present significant mortality. Typically, ABI is measured by Doppler, which is not always available, limiting its use in most patients. We therefore hypothesized that ABI, evaluated by a simplified method, can predict mortality in an incident hemodialysis population. Methodology/Principal Findings: We studied 119 patients with ESRD who had started hemodialysis three times weekly. ABI was calculated by using two oscillometric blood pressure devices simultaneously. Patients were followed until death or the end of the study. ABI was categorized in two groups normal (0.9-1.3) or abnormal (<0.9 and >1.3). There were 33 deaths during a median follow-up of 12 months (from 3 to 24 months). Age (1 year) (hazard of ratio, 1.026; p = 0.014) and ABI abnormal (hazard ratio, 3.664; p = 0.001) were independently related to mortality in a multiple regression analysis. Conclusions: An easy and inexpensive technique to measure ABI was tested and showed to be significant in predicting mortality. Both low and high ABI were associated to mortality in incident patients on hemodialysis. This technique allows nephrologists to identify high-risk patients and gives the opportunity of early intervention that could alter the natural progression of this population.

Spin accumulation encoded in electronic noise for mesoscopic billiards with finite tunneling rates

We study the effects of spin accumulation (inside reservoirs) on electronic transport with tunneling and reflections at the gates of a quantum dot. Within the stub model, the calculations focus on the current-current correlation function for the flux of electrons injected into the quantum dot. The linear response theory used allows us to obtain the noise power in the regime of thermal crossover as a function of parameters that reveal the spin polarization at the reservoirs. The calculation is performed employing diagrammatic integration within the universal groups (ensembles of Dyson) for a nonideal, nonequilibrium chaotic quantum dot. We show that changes in the spin distribution determine significant alterations in noise behavior at values of the tunneling rates close to zero, in the regime of strong reflection at the gates.

IMPROVEMENT TO THE MARGINAL COPING FIT OF COMMERCIALLY PURE TITANIUM CAST IN PHOSPHATE-BONDED INVESTMENT BY USING A SIMPLE PATTERN COATING TECHNIQUE

Statement of problem. Coatings of zirconite, Y2O3 or ZrO2 on wax patterns before investing in phosphate-bonded investments have been recommended to reduce the reaction layer in titanium castings, but they are not easily obtainable. Spinel-based investments are relatively stable with molten titanium and could be used as coatings to improve the quality of castings made with those investments. Purpose. The purpose of this study was to evaluate the effect of pattern coating with a commercial spinel-based investment before investing in 1 of 3 phosphate-bonded investments on the marginal coping fit and surface roughness of commercially pure titanium castings. Material and methods. Ten square acrylic resin patterns (12 x 12 x 2 mm) per group were invested in the phosphate-bonded investments Rematitan Plus (RP), Rema Exakt (RE), and Castorit Super C (CA) with or without a coating of the spinel-based investment, Rematitan Ultra (RU). After casting, the specimens were cleaned and the surface roughness was measured with a profilometer. Copings for dental implants with conical abutment were invested, eliminated, and cast as previously described. The copings were cleaned and misfit was measured with a profile projector (n=10). For both tests, the difference between the mean value of RU only and each value of the phosphate-bonded investment was calculated, and the data were analyzed by 2-way ANOVA and Tukey's HSD test (alpha=.05). In addition, the investment roughness was measured in bar specimens (30 x 10 x 10 mm), and the data (n=10) were analyzed by 1-way ANOVA and Tukey's HSD post hoc test (alpha=.05). Results. Two-way ANOVA for casting surface roughness was significant because of the investment, the coating technique, and the interaction between variables. One-way ANOVA was performed to prove the interaction term, and Tukey's post hoc test showed that RP with coating had the lowest mean, while RP had the highest. CA with coating was not different from RP with coating or CA without coating. RE with coating was similar to CA, while RE was different from all groups. For coping marginal fit, the 2-way ANOVA was significant for the investment, the coating technique, and the interaction between variables. The interaction was analyzed by1-way ANOVA and Tukey's HSD test that showed no significant difference among the coated groups, which had better marginal fit than the groups without coating. Among the groups without coating, CA had significant lower marginal misfit than RP, while RE was not different from CA and RP. For the investment surface roughness, the 1-way ANOVA was significant. CA and RU were smoother than RE and RP (P<.001). Conclusions. The coating technique improved the quality of castings fabricated with phosphate-bonded investments. (J Prosthet Dent 2012;108:51-57)

Multiple Radial Midpupil Lid Distances: A Simple Method for Lid Contour Analysis

Purpose: To describe a new computerized method for the analysis of lid contour based on the measurement of multiple radial midpupil lid distances. Design: Evaluation of diagnostic technology. Participants and Controls: Monocular palpebral fissure images of 35 patients with Graves' upper eyelid retraction and of 30 normal subjects. Methods: Custom software was used to measure the conventional midpupil upper lid distance (MPLD) and 12 oblique MPLDs on each 15 degrees across the temporal (105 degrees, 120 degrees, 135 degrees, 150 degrees, 165 degrees, and 180 degrees) and nasal (75 degrees, 60 degrees, 45 degrees, 30 degrees, 15 degrees, and 0 degrees) sectors of the lid fissure. Main Outcome Measures: Mean, standard deviation, 5th and 95th percentiles of the oblique MPLDs obtained for patients and controls. Temporal/nasal MPLD ratios of the same angles with respect to the midline. Results: The MPLDs increased from the vertical midline in both nasal and temporal sectors of the fissure. In the control group the differences between the mean central MPLD (90 degrees) and those up to 30 degrees in the nasal (75 degrees and 60 degrees) and temporal sectors (105 degrees and 120 degrees) were not significant. For greater eccentricities, all temporal and nasal mean MPLDs increased significantly. When the MPLDs of the same angles were compared between groups, the mean values of the Graves' patients differed from control at all angles (F = 4192; P<0.0001). The greatest temporal/nasal asymmetry occurred 60 degrees from the vertical midline. Conclusions: The measurement of radial MPLD is a simple and effective way to characterize lid contour abnormalities. In patients with Graves' upper eyelid retraction, the method demonstrated that the maximum amplitude of the lateral lid flare sign occurred at 60 degrees from the vertical midline. Financial Disclosure(s): The authors have no proprietary or commercial interest in any of the materials discussed in this article. Ophthalmology 2012; 119: 625-628 (C) 2012 by the American Academy of Ophthalmology.

Morse taper implants at different bone levels: a finite element analysis of stress distribution

AIM: To explore the biomechanical effects of the different implantation bone levels of Morse taper implants, employing a finite element analysis (FEA). METHODS: Dental implants (TitamaxCM) with 4x13 mm and 4x11 mm, and their respective abutments with 3.5 mm height, simulating a screwed premolar metal-ceramic crown, had their design performed using the software AnsysWorkbench 10.0. They were positioned in bone blocks, covered by 2.5 mm thickness of mucosa. The cortical bone was designed with 1.5 mm thickness and the trabecular bone completed the bone block. Four groups were formed: group 11CBL (11 mm implant length on cortical bone level), group 11TBL (11 mm implant length on trabecular bone level), group 13CBL (13mm implant length on cortical bone level) and group 13TBL (13 mm implant length on trabecular bone level). Oblique 200 N loads were applied. Von Mises equivalent stresses in cortical and trabecular bones were evaluated with the same design program. RESULTS: The results were shown qualitatively and quantitatively by standard scales for each type of bone. By the results obtained, it can be suggested that positioning the implant completely in trabecular bone brings harm with respect to the generated stresses. Its implantation in the cortical bone has advantages with respect to better anchoring and locking, reflecting a better dissipation of the stresses along the implant/bone interfaces. In addition, the search for anchoring the implant in its apical region in cortical bone is of great value to improve stabilization and consequently better stress distribution. CONCLUSIONS: The implant position slightly below the bone in relation to the bone crest brings advantages as the best long-term predictability with respect to the expected neck bone loss.