A new coherent states approach to semiclassics which gives Scott's correction

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules.Comment: A misprint in the definition of new coherent states correcte

Crystal structure of the high-pressure phase of the oxonitridosilicate chloride Ce4[Si4O3 + xN7 − x]Cl1 − xOx, x≃0.2

The structural compression mechanism of Ce4[Si4O3 + xN7 − x]Cl1 − xOx, x≃ 0.2, was investigated by in situ single-crystal synchrotron X-ray diffraction at pressures of 3.0, 8.5 and 8.6 GPa using the diamond–anvil cell technique. On increasing pressure the low-pressure cubic structure first undergoes only minor structural changes. Between 8.5 and 8.6 GPa a first-order phase transition occurs, accompanied by a change of the single-crystal colour from light orange to dark red. The main structural mechanisms, leading to a volume reduction of about 5% at the phase transition, are an increase in and a rearrangement of the Ce coordination, the loss of the Ce2, Ce3 split position, and a bending of some of the inter-polyhedral Si—N—Si angles in the arrangement of the corner-sharing Si tetrahedra. The latter is responsible for the short c axis of the orthorhombic high-pressure structure compared with the cell parameter of the cubic low-pressure structure

Scientific Contributions of Population-Based Studies to Cardiovascular Epidemiology in the GWAS Era

Longitudinal, well phenotyped, population-based cohort studies offer unique research opportunities in the context of genome-wide association studies (GWAS), including GWAS for new-onset (incident) cardiovascular disease (CVD) events, the assessment of gene x lifestyle interactions, and evaluating the incremental predictive utility of genetic information in apparently healthy individuals. Furthermore, comprehensively phenotyped community-dwelling samples have contributed to GWAS of numerous traits that reflect normal organ function (e.g., cardiac structure and systolic and diastolic function) and for many traits along the CVD continuum (e.g., risk factors, circulating biomarkers, and subclinical disease traits). These GWAS have heretofore identified many genetic loci implicated in normal organ function and different stages of the CVD continuum. Finally, population-based cohort studies have made important contributions to Mendelian Randomization analyses, a statistical approach that uses genetic information to assess observed associations between cardiovascular traits and clinical CVD outcomes for potential causality

High-Pressure Phase Transition of the Oxonitridosilicate Chloride Ce4[Si4O3+xN7-x]Cl1-xOx with x = 0.12 and 0.18

The high-pressure behaviour of the oxonitridosilicate chlorides Ce4[Si4O3þxN7-x]Cl1-xOx, x = 0.12 and 0.18, is investigated by in situ powder synchrotron X-ray diffraction. Pressures up to 28 GPa are generated using the diamond-anvil cell technique. A reversible phase transition of first order occurs at pressures between 8 and 10 GPa. Within this pressure range the high- and the low-pressure phases are observed concomitantly. At the phase transition the unit cell volume is reduced by about 5%, and the cubic symmetry (space group P213) is reduced to orthorhombic (space group P212121) following a translationengleiche group-subgroup relationship of index 3. A fit of a third-order Birch-Murnaghan equation of state to the p-V data results in a bulk modulus B0 = 124(5) GPa with its pressure derivative B0 = 5(1) at V0 = 1134.3(4) Å3 for the low-pressure phase and in B0 = 153(10) GPa with B0 = 3.0(6) at V0 = 1071(3) Å3 for the high-pressure phase. The orthorhombic phase shows an anisotropic axial compression with the a axis (which is the shortest axis) being more compressible (k(a) = 0.0143(4) 1/GPa) than the b and c axes (k(b) = 0.0045(2), k(c) = 0.0058(2) 1/GPa). The experimental results confirm an earlier prediction of the pressureinduced instability of isotypic Ce4[Si4O4N6]O, and also show that the bulk modulus was predicted reasonably well

Compressibility of the nitridosilicate SrYb[Si4N7] and the oxonitridoaluminosilicates MYb[Si4−xAlxOxN7−x] (x = 2; M = Sr, Ba)

The compressibilities of the nitridosilicate SrYb[Si4N7] and the oxonitridoaluminosilicates MYb[Si4−xAlxOxN7−x] (x = 2; M = Sr, Ba) were investigated by in situ high-pressure X-ray powder diffraction. Pressures up to 42 GPa were generated using the diamond–anvil cell technique. The title compounds are structurally stable to the highest pressure obtained. A fit of a third-order Birch–Murnaghan equation-of-state to the p–V data results in V0 = 302.91 (6) Å3, B0 = 176 (2) GPa and B′ = 4.4 (2) for SrYb[Si4N7]; V0 = 310.4 (1) Å3, B0 = 161 (2) GPa and B′ = 4.6 (2) for SrYb[Si4−xAlxOxN7−x]; and V0 = 317.3 (5) Å3, B0 = 168 (2) GPa and B′ = 4.7 (2) for BaYb[Si4−xAlxOxN7−x]. While the linear compressibilities of the a and c axes of BaYb[Si4−xAlxOxN7−x] are very similar up to 30 GPa, distinct differences were observed for SrYb[Si4N7] and SrYb[Si4−xAlxOxN7−x], with the c axis being the most compressible axis. In all of the investigated compounds the bulk compressibility is dominated by the compression behaviour of the tetrahedral network, while the size of the substituted cation plays a minor role

Coupled Al/Si and O/N order/disorder in BaYb[Si4–xAlxOxN7–x]sialon

The fractions of aluminium, [Al]/[Al + Si], and oxygen, [O]/[O + N], in crystallographically distinct sites of BaYb[Si4–xAlxOxN7–x] oxonitridoaluminosilicate (space group P63mc, No. 186) were refined based on the results of neutron powder diffraction for a synthetic sample with the composition of x = 2.2(2) and simulated as functions of temperature for the compositions x = 2 and x = 2.3 using a combination of static lattice energy calculations (SLEC) and Monte Carlo simulations. The SLEC calcu lations have been performed on a set of 800 structures differing in the distribution of Al/Si and O/N within the 2 × 2 × 2 supercell containing 36 formula units of BaYb[Si4–xAlxOxN7–x]. The SLEC were based on a transferable set of empirical interatomic potentials developed within the present study. The static lattice energies of these structures have been expanded in the basis set of pair-wise ordering energies and on-site chemical potentials. The ordering energies and the chemical potentials have been used to calculate the configuration energies of the oxonitridoaluminosilicates (so-called sialons) using a Monte Carlo algorithm. The simulations suggest that Al and O are distributed unevenly over two non-equivalent T(Si/Al) and three L(N/O) sites, respectively, and the distribution shows strong dependence both on the temperature and the composition. Both simulated samples exhibit order/disorder transitions in the temperature range 500–1000 K to phases with partial long-range order below these temperatures. Above the transition temperatures the Si/Al and N/O distributions are affected by short-range ordering. The predicted site occupancies are in a qualitative agreement with the neutron diffraction results

Klein-Gordon lower bound to the semirelativistic ground-state energy

For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the corresponding Klein--Gordon problem (p^2 + m^2)\phi = (V(r) -e)^2\phi. Detailed results are presented for the exponential and Woods--Saxon potentials.Comment: 7 pages, 4 figure

Gravitating semirelativistic N-boson systems

Analytic energy bounds for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For gravity v=c/N, these bounds are substantially tighter than earlier bounds and they are shown to coincide with known results in the nonrelativistic limit.Comment: 7 pages, 2 figures It is now proved that the reduced Hamiltonian is bounded below by the simple N/2 Hamiltonia

Plasma Leptin Levels and Incidence of Heart Failure, Cardiovascular Disease, and Total Mortality in Elderly Individuals

OBJECTIVE: Obesity predisposes individuals to congestive heart failure (CHF) and cardiovascular disease (CVD). Leptin regulates energy homeostasis, is elevated in obesity, and influences ventricular and vascular remodeling. We tested the hypothesis that leptin levels are associated with greater risk of CHF, CVD, and mortality in elderly individuals. RESEARCH DESIGN AND METHODS: We evaluated 818 elderly (mean age 79 years, 62% women) Framingham Study participants attending a routine examination at which plasma leptin was assayed. RESULTS: Leptin levels were higher in women and strongly correlated with BMI (P < 0.0001). On follow-up (mean 8.0 years), 129 (of 775 free of CHF) participants developed CHF, 187 (of 532 free of CVD) experienced a first CVD event, and 391 individuals died. In multivariable Cox regression models adjusting for established risk factors, log-leptin was positively associated with incidence of CHF and CVD (hazard ratio [HR] per SD increment 1.26 [95% CI 1.03–1.55] and 1.28 [1.09–1.50], respectively). Additional adjustment for BMI nullified the association with CHF (0.97 [0.75–1.24]) but only modestly attenuated the relation to CVD incidence (1.23 [1.00–1.51], P = 0.052). We observed a nonlinear, U-shaped relation between log-leptin and mortality (P = 0.005 for quadratic term) with greater risk of death evident at both low and high leptin levels. CONCLUSIONS: In our moderate-sized community-based elderly sample, higher circulating leptin levels were associated with a greater risk of CHF and CVD, but leptin did not provide incremental prognostic information beyond BMI. Additional investigations are warranted to elucidate the U-shaped relation of leptin to mortality.National Institutes of Health's National Heart, Lung, and Blood Institute (N01-HC25195, N01-HV28178, K24-HL04334, R01-DK080739