On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

An indecomposable Banach space of continuous functions which has small density

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

MSC 2010: 26A33

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how scoliosis affects bone density distribution within the vertebrae. In this study, existing CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. Five key bone density profile measures were identified from each normalised bone density distribution, and multiple regression analysis was performed to explore the relationship between bone density distribution and patient demographics (age, height, weight, body mass index (BMI), skeletal maturity, time since Menarche, vertebral level, and scoliosis curve severity). Results showed a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. At the apical vertebra, mean bone density at the left side (concave) cortical shell was 23.5% higher than for the right (convex) cortical shell, and cancellous bone density along the central 60% of the lateral path from convex to concave increased by 13.8%. The centre of mass of the bone density profile at the thoracic curve apex was located 53.8% of the distance along the lateral path, indicating a shift of nearly 4% toward the concavity of the deformity. These lateral bone density gradients tapered off when moving away from the apical vertebra. Multi-linear regressions showed that the right cortical shell peak bone density is significantly correlated with skeletal maturity, with each Risser increment corresponding to an increase in mineral equivalent bone density of 4-5%. There were also statistically significant relationships between patient height, weight and BMI, and the gradient of cancellous bone density along the central 60% of the lateral path. Bone density gradient is positively correlated with weight, and negatively correlated with height and BMI, such that at the apical vertebra, a unit decrease in BMI corresponds to an almost 100% increase in bone density gradient.

The role of land use and psycho-social factors in high density residents' work travel mode choices : implications for sustainable transport policy

Imperatives to improve the sustainability of cities often hinge upon plans to increase urban residential density to facilitate greater reliance on sustainable forms of transport and minimise car use. However there is ongoing debate about whether high residential density land use in isolation results in sustainable transport outcomes. Findings from surveys with residents of inner-urban high density dwellings in Brisbane, Australia, suggest that solo car travel accounts for the greatest modal share of typical work journeys and attitudes toward dwelling and neighbourhood transport-related features, residential sorting factors and socio-demographics, alongside land use such as public transport availability, are significantly associated with work travel mode choice. We discuss the implications of our findings for transport policy and management including encouraging relatively sustainable intermodal forms of transport for work journeys.

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computerbased simulation technique for modeling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be redicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness of the proximal femur were more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and threedimensional FEA demonstrating a non-linear increase and decrease in sensitivity, respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three dimensional FEA demonstrated a parabolic-type relationship, with maximum stiffness achieved at an angle of approximately 15o. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and twodimensional FEA had statistically equal sensitivities (0.41±0.20 and 0.42±0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24±0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent upon anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.