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.     

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.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

5-Spirocyclopropane Isoxazolidines as Versatile Intermediates in Organic Synthesis

The review outlines the various different azaheterocycles available from 5-spirocyclopropane isoxazolidines. These compounds can be regarded as versatile direct precursors of tetrahydro-, dihydropyridone and azetidinone derivatives. The current scope and limitations, and the selectivity aspects of the different processes are discussed therein.     

On the multidimensional distribution of the subset sum generator of pseudorandom numbers

We show that for a random choice of the parameters, the subset sum pseudorandom number generator produces a sequence of uniformly and independently distributed pseudorandom numbers. The result can be useful for both cryptographic and quasi-Monte Carlo applications and relies on bounds of exponential sums.

     

Charge manipulation and imaging of the Mn acceptor state in GaAs by cross-sectional scanning tunneling microscopy

An individual Mn acceptor in GaAs is mapped by cross-sectional scanning tunneling microscopy (X-STM) at room temperature and a strongly anisotropic shape of the acceptor state is observed. An acceptor state manifests itself as a cross-like feature which we attribute to a valence hole weakly bound to the Mn ion forming the (Mn²⁺3d⁵+hole) complex. We propose that the observed anisotropy of the Mn acceptor wavefunction is due to the d-wave present in the acceptor ground state.     

Application of directed metallation in synthesis. Part 3: Studies in the synthesis of (±)-semivioxanthin and its analogues

The synthesis of several analogues of (±)-semivioxanthin including five thiophene analogues, using directed metalation are reported. The strategy consisted of the synthesis of functionalized naphthalene or benzo[b]thiophene as building blocks followed by annelation of the pyrone.     

Anisotropic alpha-emission in the223Ra decay chain

Anisotropic α-emission from nuclei in the decay chain from²²³Ra to²⁰⁷Tl has been observed using low temperature nuclear orientation in combination with high resolution α-detection at 4.2 K. Information on partial wave amplitudes as well as hyperfine interactions has been extracted.