Infinite dimensional quadratic forms admitting composition

Composition algebras with a unit element constitute a well-known class of algebras. In this paper, those composition algebras with a one-sided unit element are characterized and examples are given of arbitrary infinite dimension.

     

The particular role of radiopharmacy within bioorganometallic chemistry

This article will emphasize the particular role of organometallic radiopharmaceutical chemistry, namely the need for syntheses from water and the emerging implications for other (bio)organometallic fields. After some basic insights into the different directions of bioorganometallic chemistry, some facets of the [M(CO)₃]⁺ (M = Tc, Re) moiety are reviewed and discussed in the respective context. The mechanism for the synthesis of [M(OH₂)₃(CO)₃]⁺ which is still little understood, will be touched. The formation of additional M-C bonds is exemplified with cyclopentadienyl chemistry, the potential impact on targeted molecular imaging with the labelling of amino acids and the reactivity towards essential biomolecules such as guanine is shown. Future perspectives and implications for organometallic radiopharmaceutical chemistry will close this article.     

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.     

Thermal isomerization of trifluoromethyl trifluorovinyl ether to pentafluoropropionyl fluoride

The thermal rearrangement of trifluoromethyl trifluorovinyl ether (MVE) to pentafluoropropionyl fluoride (PPF) under pressure with and without radical initiators has been studied. The reaction typically gives a mixture of different acyl fluorides. The influence of the reaction parameters (pressure, temperature, concentration, type of initiator and contact time) on the conversion and the selectivity of the process has been carefully examined. In addition, a mechanism which accounts for the formation of all the products has been proposed.     

Quantum Conservative Gates for Finite-Valued Logics

We introduce some conservative gates for finite-valued logics which are able to realize all the main connectives of the many-valued logics of ?ukasiewicz, the MV-algebras of Chang and Brower–Zadeh algebras. After a brief exposition of the motivations for this work, the gates are defined and their properties are explored. Finally, a possible quantum realization of them is proposed, using three techniques: a “brute force” method--an extension of the Conditional Quantum Control argument, and a new technique which we call the Constants Method. For all these techniques, the unitary operator which describes the gate is a sum of local operators.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Cohomology and extension problems for semi <Emphasis Type="Italic">q</Emphasis>-coronae

We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly using cohomological techniques.     

Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.