Zur regioselektiven nucleophilen Addition an 2,3-Dihydrobilatriene-abc

Donors are added regioselectively to position 10 of 2,3-dihydrobilatrienes-abc in a reversible reaction, which is complicated in case of strongly basic donors due to the easy deprotonation of the partially saturated ring. Compared to the bilatrienes-abc the addition equilibrium is retarded by about two orders of magnitude.

     

Analysis of protamine peptides in insulin pharmaceutical formulations by capillary electrophoresis

Protamines are a group of highly basic peptides that are sometimes added to insulin formulations to prolong the pharmacological action. In this study, different methods were investigated to identify protamine in insulin formulations. Capillary electrophoresis in aqueous and non‐aqueous media was tested to separate these peptides with very close amino acid sequences. Different buffers (phosphate or formate, both acidified) and various additives (principally negatively charged and neutral surfactants) were investigated to optimize peptide separation. Finally, a micellar electrokinetic capillary chromatography method using a capillary of 120 cm effective length and an aqueous background electrolyte made up of 100 mM phosphate buffer (pH 2) and 50 mM Thesit® gave the best results, providing the separation of the four major protamine peptides within 25 min.     

Photocatalytic deoxygenation of N–O bonds with rhenium complexes: from the reduction of nitrous oxide to pyridine N-oxides

The accumulation of nitrogen oxides in the environment calls for new pathways to interconvert the various oxidation states of nitrogen, and especially their reduction. However, the large spectrum of reduction potentials covered by nitrogen oxides makes it difficult to find general systems capable of efficiently reducing various N-oxides. Here, photocatalysis unlocks high energy species able both to circumvent the inherent low reactivity of the greenhouse gas and oxidant N₂O (E⁰(N₂O/N₂) = +1.77 V vs. SHE), and to reduce pyridine N-oxides (E_1/2(pyridine N-oxide/pyridine) = −1.04 V vs. SHE). The rhenium complex [Re(4,4′-tBu-bpy)(CO)₃Cl] proved to be efficient in performing both reactions under ambient conditions, enabling the deoxygenation of N₂O as well as synthetically relevant and functionalized pyridine N-oxides.

A rhenium-based photocatalyst enables the deoxygenation of several compounds containing N–O bonds, such as N₂O and pyridine N-oxides.     

Organic transformations via metal silane reagents: syntheses of vinyl ethers from dimethyl ketals and (CO)5MnSi(CH3)3

The reaction of dimethyl ketals with (CO)₅MnSi(CH₃)₃ ($\text{1}$ at 50 °C in CH₃CN affords methyl enol ethers, generally in 75–95% yields.     

Chain and Ring Phosphorus Compounds—Analogies between Phosphorus and Carbon Chemistry

Up to about 15 years ago compounds with a skeleton of phosphorus chains or rings were regarded as “exotic” in the field of nonmetal chemistry. Aside from a number of examples of molecules with two P atoms directly bonded to each other and a few sporadically discovered monocyclic ring compounds, only solids of undefined composition and structure were known. Since then the state of our knowledge in this sector has made considerable progress: between PH₃ and its derivatives on the one hand, and the high-molecular modifications of elementary phosphorus on the other, an unexpected variety of well defined compounds have been discovered, showing many similarities to the analogous compounds of carbon. However, surprises can still occur even with “small” phosphorus-containing molecules, as shown by the likewise recently discovered field of phosphorus three-membered ring compounds.     

Some consequences of Rado’s selection lemma

We prove in set theory without the Axiom of Choice, that Rado’s selection lemma ( ${\mathbf{RL}}$ ) implies the Hahn-Banach axiom. We also prove that ${\mathbf{RL}}$ is equivalent to several consequences of the Tychonov theorem for compact Hausdorff spaces: in particular, ${\mathbf{RL}}$ implies that every filter on a well orderable set is included in a ultrafilter. In set theory with atoms, the “Multiple Choice” axiom implies ${\mathbf{RL}}$ .     

Zusammenhang der Fixpunktmenge bei kompakten Volterra-Operatoren

We show that the set of fixed points of a compact and uniformly finite approachable Volterra-OperatorT∶X→X, X aF-normed function-space, is not empty, compact and connected inX and apply this result to several differential and integral equations.      

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.