Embedded eigenvalues of Sturm Liouville operators

In this work we study the behavior of embedded eigenvalues of Sturm-Liouville problems in the half axis under local perturbations. When the derivative of the spectral function is strictly positive, we prove that the embedded eigenvalues either disappear or remain fixed. In this case we show that local perturbations cannot add eigenvalues in the continuous spectrum. If the condition on the spectral function is removed then a local perturbation can add infinitely many eigenvalues.     

Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

Angular distribution of muon pairs produced by negative pions on deuterium and tungsten in terms of coherent states

Recently published data on thep _T dependence of the angular distributions of muon pairs produced in collisions of negative pions with deuterium and tungsten nuclei reveal an unexpected tendency. We show that the quantum statistical approach involving expansions in terms of coherent states leads in this case to an exact, non-perturbative result which in the lowest order approximation describes the observed trends with sufficient accuracy. In this procedure, the non-vanishing correlations between the coordinates and momenta of dimuons play a decisive role.     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Physics, mind, society: Back and forth

The life course of the physicist and biologist George Feher may be seen as an epitome of science of the second half of the 20th century and the beginning of the 21st century. Feher, a native of Slovakia, barely escaped Nazism and communism and became a scientist in the USA. The Nazi concentration camps and the communist gulags have become a symbol of the 20th century. This symbol stands here to pose a question: How the two totalitarian systems, fraught with irrationality, may have arisen and thrived in parallel with an unprecedented expansion of science, the paragon of rationalism? The question has become even more urgent in the 21st century. The Ground Zero, an empty spot left after the collapse of the twin towers of the World Trade Center on 11 September 2001, has become the symbol of the entrance of humankind into the new millennium. We can do much, but we understand too little about who we are and what we are doing — this is a message that the two symbols convey about the precarious stage of our evolution. The second message concerns the role of artifacts, specifically scientific instruments, in the advancement of science. Human cultural evolution has been steadily progressing, in a form of a ratchet, only because artifacts have been continually evolving. Contrary to the common Popperian wisdom, the demarcation in science may not consist in the amenability to theoretical falsification, but rather in the amenability to instrumental grasping. Scientific instruments have empowered humans for impressive feats of manipulation with Nature and themselves. Knowledge arising in the course of autonomous evolution of artifacts may surpass the horizon of human understanding and grasping. New knowledge may still be power, but no longer the power of humans. We may need a revision of some fundamental ideas of European thought. Our understanding of the human mind may entirely reshape our comprehension of the nature of physical knowledge, and vice versa.     

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.     

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.