Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The James constant, the Jordan-von Neumann constant, weak orthogonality, and fixed points for multivalued mappings

We give some sufficient conditions for the Domínguez-Lorenzo condition in terms of the James constant, the Jordan-von Neumann constant, and the coefficient of weak orthogonality. As a consequence, we obtain fixed point theorems for multivalued nonexpansive mappings.     

Dielectric properties of KDP-type ferroelectric crystals in the presence of external electric field

Considering external electric field as well as third- and fourth-order phonon anharmonic interaction terms in the pseudospin-lattice coupled mode (PLCM) model Hamiltonian for KDP-type ferroelectrics, expressions for field-dependent shift, width, renormalized soft mode frequency, Curie temperature, dielectric constant and dielectric loss are evaluated. For the calculation, method of statistical double-time temperature-dependent Green’s function has been used. By fitting model values of physical quantities, temperature and electric field dependences of soft mode frequency, dielectric constant and loss have been calculated which compare well with experimental results of Baumgartner [8] and Choi and Lockwood [9]. Both dielectric constant and loss decrease with electric field.     

Tests for Varying G

In this note we consider a variable G cosmology which is consistent with observation and which had successfully predicted an ever expanding accelerating universe with a small cosmological constant amongst other things. Three further tests are proposed in this note: First, the inexplicable anomalous accelerations of the Pioneer spacecrafts can be explained. It is then shown that the observed shortening of the orbital periods of binary pulsars is in good agreement with this model. Finally, more general changes in orbital parameters are deduced, which may be observed in the future.     

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.

     

Evaluation of PLE exhaustiveness for the extraction of PCBs from sediments and the influence of sediment characteristics

Pressurized liquid extractions were performed on eight sediments in order to investigate if a modified US EPA method (100 °C, 100 bar, n-heptane/acetone (1:1), 2 × 5 min) provided exhaustive extractions of polychlorinated biphenyls (PCBs) from sediment, and to study if the extractability of PCBs from the different sediments was affected by characteristics of the sediment. The recovery from the eight native sediments, contaminated in nature, was between 96.4% and 98.9%, as an average of the recoveries from 10 PCB congeners. Hundred percent recovery was defined as the sum of two consecutive extractions (2 × 5 min each) at the stated conditions. The recoveries of the individual congeners were above 94%, except for one congener in one sediment, which had a recovery of 92%. When the recoveries and different characteristics of the sediments were compared, no correlation appeared between recoveries and sediment PCB concentration, total organic carbon (TOC), soot carbon (SC) or amorphous carbon (AC). The fact that carbon did not influence the extractions was somewhat surprising, since previous experiments have indicated a connection. Instead, statistically significant (p < 0.05) correlations were observed for water content and carbon/nitrogen (C/N) ratio. The decrease in recoveries with decreased water content was attributed to less access of the solvent to the analytes due to less matrix swelling. The lowered recoveries with increased C/N ratio can indicate that a difference in structure of the organic matter exists, which influences the binding strength between the analytes and the matrix. The difference in structure can possibly be explained by different origin of the organic matter or by aging effects. Overall the method was found to be exhaustive and the excellent recoveries show that sediment characteristics do not influence the extractions markedly.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca