On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.     

Cosmological Consequences of Scale-Related Comoving Masses for Cosmic Pressure, Mass, and Vacuum Energy Density

According to ideas of Mach, Whitrow, Dirac, or Hoyle, inertial masses of particles should not be a genuine, predetermined quantity; rather they should represent a relational quantity which by its value somehow reflects the deposition and constellation of all other objects in their cosmic environment. In this paper we want to pick up suggestions given by Thirring and by Hoyle of how, due to requirements of the equivalence of rotations and of general relativistic conformal scale invariance, the particle masses of cosmic objects should vary with the cosmic length scale. We study cosmological consequences of comoving cosmic masses which co-evolve by mass with the expansion of the universe. The vanishing of the covariant divergence of the cosmic energy-momentum tensor under the new prerequisite that matter density only falls off with the reciproke of the squared cosmic scale S(t) then leads to the astonishing result that cosmic pressuredoes not fall off adiabatically but rather falls off in a quasi-isothermal behaviour, varying with S(t) as matter density does. Hence, as a new cosmological fact, it arises that, even in the late phases of cosmic expansion, pressure cannot be neglected what concerns its gravitational action on the cosmic dynamics. We then show that under these conditions the cosmological equations can, however, only be solved if, in addition to matter, also pressure and energy density of the cosmic vacuum are included in the calculation. An unaccelerated expansion with a Hubble parameter falling off with S(t)⁻¹ is obtained for a vacuum energy density decay according to S(t)⁻² with a well-tuned proportion of matter and vacuum pressures. As it appears from these results, a universe with particle masses increasing with the cosmic sale S(t) is in fact physically conceivable in an energetically consistent manner, if vacuum energy at the expansion of the universe is converted into mass density of real matter with no net energy loss occuring. This universe in addition also happens to be an economical one which has and keeps a vanishing total energy.     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

The use of an atomizer for chemical pleurodesis

Summary An atomizer had been designed that could create an aerosol of a liquid with high viscosity. The amount of additional driving gas that had to be used was very low. In a cooperation with the University Hospital in Zurich the atomizer was miniaturized and used for treating six patients.     

Wrinkle-free solutions in the theory of annular elastic membranes

Rotationally symmetric deformations of a flat annular elastic membrane under a gravitational force are studied, with prescribed radial stresses or horizontal displacements at the edges. The small-finitedeflection theory of Föppl-Hencky as well as a simplified version of Reissner's static first approximation theory of thin shells of revolution are applied which lead to consider a single, second-order, ordinary differential equation for the derivation of the principal stresses in the membrane. Using analytical methods, the range of those boundary data is determined for which the solutions of the differential equation are wrinkle free in the sense that both the radial and the circumferential stress components are nonnegative everywhere.     

Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations

A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations nearT _c over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scaling functions. Since the amount of information extracted from a simulation in this way is drastically increased as compared to conventional methods, the investigation of mixtures with long chains or built-in asymmetries is now possible. As an example, the critical points, exponents, and amplitudes of dense, symmetric polymer mixtures with chain lengths ranging fromN=16 up toN=256 are determined within the framework of the 3D bond fluctuation model using grand canonical simulation techniques. As an example for an asymmetry, the generalization of the method to asymmetric monomer potentials is briefly discussed.