Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

Abnormal bone geometry at the metacarpal bone shaft of rheumatoid arthritis patients with maintained muscle-bone relationship

OBJECTIVES:: Metacarpal juxta-articular bone is altered in Rheumatoid Arthritis (RA). However, a detailed analysis of disease related geometrical adaptations of the metacarpal shaft is missing. The aim of the present study was to assess the role of RA disease, forearm muscle cross-sectional area (CSA), age and sex on bone geometry at the metacarpal shaft. METHODS:: In 64 RA patients and 128 control subjects geometric properties of the third metacarpal bone mid-shaft and forearm muscle CSA were measured by peripheral quantitative computed tomography (pQCT). Linear models were performed for cortical CSA, total bone CSA, polar stress-strain Index (polar SSI, a surrogate for bone's resistance to bending and torsion), cortical thickness and Metacarpal Index (MI=cortical CSA/total CSA) with explanatory variables muscle CSA, age, RA status and sex. RESULTS:: Forearm muscle CSA was associated with cortical and total metacarpal CSA, and polar SSI. RA group status was associated with all bone parameters except cortical CSA. There was a significant interaction between RA status and age, indicating that the RA group had a greater age-related decrease in cortical CSA, cortical thickness and MI. CONCLUSIONS:: Bone geometry of the metacarpal shaft is altered in RA patients compared to healthy controls. While bone mass of the metacarpal shaft is adapted to forearm muscle mass, cortical thickness and MI are reduced but outer bone shaft circumference and polar SSI increased in RA patients. These adaptations correspond to an enhanced aging pattern in RA patients.

Operator variability using different polishing methods and surface geometry of a nanohybrid composite

This study evaluated the operator variability of different finishing and polishing techniques. After placing 120 composite restorations (Tetric EvoCeram) in plexiglassmolds, the surface of the specimens was roughened in a standardized manner. Twelve operators with different experience levels polished the specimens using the following finishing/polishing procedures: method 1 (40 ?m diamond [40D], 15 ?m diamond [15D], 42 ?m silicon carbide polisher [42S], 6 ?m silicon carbide polisher [6S] and Occlubrush [O]); method 2 (40D, 42S, 6S and O); method 3 (40D, 42S, 6S and PoGo); method 4 (40D, 42S and PoGo) and method 5 (40D, 42S and O). The mean surface roughness (Ra) was measured with a profilometer. Differences between the methods were analyzed with non-parametric ANOVA and pairwise Wilcoxon signed rank tests (?=0.05). All the restorations were qualitatively assessed using SEM. Methods 3 and 4 showed the best polishing results and method 5 demonstrated the poorest. Method 5 was also most dependent on the skills of the operator. Except for method 5, all of the tested procedures reached a clinically acceptable surface polish of Ra?0.2 ?m. Polishing procedures can be simplified without increasing variability between operators and without jeopardizing polishing results.

Long-term course of lung clearance index between infancy and school-age in cystic fibrosis subjects

Multiple breath washout (MBW) measurements have recently been shown to be sensitive for detection of early cystic fibrosis (CF) lung disease, with the lung clearance index (LCI) being the most common measure for ventilation inhomogeneity. The aim of this observational study was to describe the longitudinal course of LCI from time of clinical diagnosis during infancy to school-age in eleven children with CF. Elevated LCI during infancy was present in seven subjects, especially in those with later clinical diagnosis. Tracking of LCI at follow-up was evident only in the four most severe cases. We provide the first longitudinal data describing the long-term course of LCI in a small group of infants with CF. Our findings support the clinical usefulness of MBW measurements to detect and monitor early lung disease in children with CF already present shortly after clinical diagnosis.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Microstructural Parameters of Bone Evaluated Using HR-pQCT Correlate with the DXA-Derived Cortical Index and the Trabecular Bone Score in a Cohort of Randomly Selected Premenopausal Women.

BACKGROUND Areal bone mineral density is predictive for fracture risk. Microstructural bone parameters evaluated at the appendicular skeleton by high-resolution peripheral quantitative computed tomography (HR-pQCT) display differences between healthy patients and fracture patients. With the simple geometry of the cortex at the distal tibial diaphysis, a cortical index of the tibia combining material and mechanical properties correlated highly with bone strength ex vivo. The trabecular bone score derived from the scan of the lumbar spine by dual-energy X-ray absorptiometry (DXA) correlated ex vivo with the micro architectural parameters. It is unknown if these microstructural correlations could be made in healthy premenopausal women. METHODS Randomly selected women between 20-40 years of age were examined by DXA and HR-pQCT at the standard regions of interest and at customized sub regions to focus on cortical and trabecular parameters of strength separately. For cortical strength, at the distal tibia the volumetric cortical index was calculated directly from HR-pQCT and the areal cortical index was derived from the DXA scan using a Canny threshold-based tool. For trabecular strength, the trabecular bone score was calculated based on the DXA scan of the lumbar spine and was compared with the corresponding parameters derived from the HR-pQCT measurements at radius and tibia. RESULTS Seventy-two healthy women were included (average age 33.8 years, average BMI 23.2 kg/m(2)). The areal cortical index correlated highly with the volumetric cortical index at the distal tibia (R  =  0.798). The trabecular bone score correlated moderately with the microstructural parameters of the trabecular bone. CONCLUSION This study in randomly selected premenopausal women demonstrated that microstructural parameters of the bone evaluated by HR-pQCT correlated with the DXA derived parameters of skeletal regions containing predominantly cortical or cancellous bone. Whether these indexes are suitable for better predictions of the fracture risk deserves further investigation.

Nonperturbative results for two-index conformal windows

Via large and small N c relations we derive nonperturbative results about the conformal window of two-index theories. Using Schwinger-Dyson methods as well as four-loops results we estimate subleading corrections and show that naive large number of colors extrapolations are unreliable when N c is less than about six. Nevertheless useful nonper-turbative inequalities for the size of the conformal windows, for any number of colors, can be derived. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large N c two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small N c) expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(N c) with two and four symmetric Dirac flavors.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.