Regioselectivity in the ene-reaction of singlet oxygen with cyclic alkenes: photooxygenation of methyl-substituted 1,4-cyclohexadiene derivatives

The photooxygenation of the 1-methyl-, 2,3-dimethyl-, and 1,4-dimethylcyclohexa-1,4-dienes, which are readily available through Birch reduction, yielded the corresponding ene-products. The formed endocyclic dienes were trapped by the addition of singlet oxygen to give the corresponding bicyclic endoperoxy hydroperoxides. In the case of 1-methylcyclohexa-1,4-diene and 1,4-dimethylcyclohexa-1,4,-diene, the cis-effect determined the product distribution. Photooxygenation of 2,3-dimethylcyclohexa-1,4-dienes gave mainly exocyclic olefin, which was attributed to the lowered rotational barrier of the methyl group and increased reactivity of the methyl groups.     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

A finite cutting plane method for facial disjunctive programs

This paper shows that any linear disjunctive program with a finite number of constraints can be transformed into an equivalent facial program. Based upon linear programming technique, a new, finite cutting plane method is presented for the facial programs.

---

Zusammenfassung Die Arbeit zeigt, daß jedes lineare disjunktive Optimierungsproblem mit endlich vielen Restriktionen in ein äquivalentes Fazetten-Problem transformiert werden kann. Auf der Grundlage von linearer Optimierungstechnik wird für das Fazetten-Problem ein neues, endliches Schnittebenenverfahren vorgestellt.

     

Book reviews

Ohne Zusammenfassung

---

Book reviews

     

Pourquoi, pour qui enseigner les mathématiques? Une mise en perspective historique de l’évolution des programmes de mathématiques dans la société française au XXe siècle

Evolutions of mathematical curricula in French society have been marked by the successive answers intitutions have given to the following question since one century: Why and whom teaching mathematics? Here I present two of these, one given in 1908 and one in 1967. Each symbolises a breaking period of reforms in secondary mathematics teaching in France. We will see in the two first part of this paper that they belong to two different worlds, with social, institutional, ideological and mathematical specific features. In the third part, I’ll focus on geometry, showing the effects of the different answers concerning the public and the aims of mathematical teaching.     

Towards a characterization of generalized twisted field planes

In this work we study semifield planes of orderq ⁿ(q=p ^r ,p prime) with a collineation whose order is ap-primitive divisor ofq ⁿ–1.Research supported in part by NSF Grant No. DMS-9107372Research supported in part by NSF grants RII-9014056, component IV of the EPSCoR of Puerto Rico grant and ARO grant for Cornell MSI.     

An aqueous route to organically functionalized silica diatom skeletons

Diatomaceous earth was functionalized by grafting organotrialkoxysilane precursors onto the surface of the porous silica cell walls of this biomineral. Vinyl- and mercapto-containing structures were prepared in aqueous media without disruption of the diatomic architecture. Successful grafting of the organic moieties was confirmed using solid state ²⁹Si MAS NMR spectroscopy, and the presence of the intact diatom framework by scanning electron microscopy. The sorption properties of mercaptopropyl-functionalized diatoms towards heavy metals was studied by measuring the accessibility and diffusion rates of mercury(II) species to the binding sites (-SH) by the means of electrochemical methods.     

Dendrimers and combinatorial chemistry—tools for fluorescent enhancement in protease assays

FRET based systems are some of the best methods available to detect and monitor proteolytic activity. To enhance fluorescent signals and hence assay sensitivity, two different systems were developed using two different dendrimeric constructs. In the first case, a triple branched dendrimer bearing three dansyl groups was used to enhance assay sensitivity and showed a significant enhancement of fluorescence following enzymatic cleavage. In another example, a tris-fluorescein probe, that undergoes self-quenching, was utilized in a combinatorial library synthesis to map the substrate specificity of proteases.     

Construction of nonanuclear supramolecular structures from simple modular units

A porphyrazine based supramolecule with a nonanuclear structure has been prepared by the ready coordination of pyridine donor sites in octakis(4-pyridoxyethylthio)porphyrazinatomagnesium with vanadyl bis(acetylacetonate) and characterized by EPR spectroscopy.