Eigenvalue ratios of vibrating strings

Summary New results for the eigenvalue ratios of vibrating strings are presented partially in connection with previous results concerning Schr?dinger operators.     

Sequencing games without initial order

In this note we study uncertainty sequencing situations, i.e., one-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (Eur J Oper Res 40:344–351, 1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times.     

Group-valued measures on coarse-grained quantum logics

In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.     

Spectral Properties of Four-Dimensional Compact Flat Manifolds

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral. Mathematics Subject Classifications (2000): 58J53, 58C22, 20H15.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

The LPCTrap experiment: measurement of the β–ν angular correlation in 6He using a transparent Paul trap

We report on the status of the LPCTrap experiment, devoted to measure the β–ν angular correlation in the pure Gamow–Teller decay of ⁶He. This measurement is motivated by the search for the presence of tensor type contributions to the weak interaction. The ⁶He ions are confined in a novel transparent Paul trap. The β particles and the recoil ions are detected in coincidence to deduce the angular correlation parameter. The commissioning run performed in 2005 has given the proof of principle of this experiment. Up to 10⁵ coincidences were recorded during a second run in 2006.     

A polar macroporous sorbent for gas chromatography

Summary The gas chromatographic behaviour of crosslinked macroporous 2-hydroxyethyl methacrylate grafted with 2-methyloxazoline was investigated and the range of applicability of the copolymer was assessed. Retention index values were measured on this copolymer and compared with those obtained on the terpolymer 2-hydroxyethyl methacrylate-ethylene dimethacrylate-acrylonitrile. Rohrschneider constants and efficiency data for selected sorbates are given. The use of this type of polymer in the separation of various types of compounds is documented by various examples.