Die Kinetik der Spaltung dinuklearer Tri-μ-hydroxo-kobalt(III)-Komplexe N3Co(Oh)3CoN33+ (triole) mit Säure

The kinetics of formation of dinuclear di-μ-hydroxo-diaquo-bis-cobalt(III) complexes from the corresponding tri-μ-hydroxo complexes: has been investigated with three different compounds to start with: Ammonia-Triol [N₃ = (NH₃)₃], Dien-Triol [N₃ = H₂N—CH₂—CH₂—NH—CH₂—CH₂—NH₂] and Tach-Triol [N₃ = C₆H₉(NH₂)₃ = cis-cis-1,3,5-triaminocyclohexane]. With respect to the otherwise very inert cobalt(III)-complexes, reaction (1) is unusually rapid and takes place in two steps, the first being about 100 times faster than the second. The process begins with an exceptionally slow proton transfer to one of the bridging OH with half life of 0,2, 0,03 and 0,025 sec. respectively (perchlorate medium μ 1 M , 20°, pH = 0). The rate of the back reaction could also be determined, yielding ratios of the two rate constants corresponding to pK-values between 0 and 1,5. Whereas Tach-Triol is protonated to the di-μ-hydroxo-μ-aquo complex at about pH 1, it is deprotonated to the di-μ-hydroxo-μ-oxo complex at about pH 14 (Siroky [16]). The second step of (1), the aquation of the di-μ-hydroxo-μ-aquo species to the di-μ-hydroxo-diaquo complex (Diol) takes place with half lives between 4 and 9 sec. The final cleavage to the mononuclear triaquo complex needs many hours to go half way and is again initiated by protonation of one of the remaining two OH-bridges. Neither the μ-aquo complex produced thereby, nor the Mono-ol [mono-μ-hydroxo-tetraaquo complex] formed as an intermediate cause any observable changes of the spectrum. The Mono-ol aquates at a rate which is inverse in [H⁺] because of the labilisation brought about by deprotonation of its aquo ligands.     

On Distributional Properties of Perpetuities

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of p-moments, p>0, as well as exponential moments. In particular, a formula for the abscissa of convergence of the moment generating function is provided. The results are illustrated with a number of examples at the end of the article.      

Limit Theorems for Stopped Functionals of Markov Renewal Processes

Some results for stopped random walks are extended to the Markov renewal setup where the random walk is driven by a Harris recurrent Markov chain. Some interesting applications are given; for example, a generalization of the alternating renewal process.     

On the weak‐field approximation of nonlinear vacuum electrodynamics of the Plebański class

Plebański's class of nonlinear vacuum electrodynamics is considered, which is for several reasons of interest at the present time. In particular, the question is answered under which circumstances Maxwell's original field equations are recovered approximately and which ‘post‐Maxwellian’ effects could arise. To this end, a weak field approximation method is developed, allowing to calculate ‘post‐Maxwellian’ corrections up to Nth order. In some respect, this is analogue of determining ‘post‐Newtonian’ corrections from relativistic mechanics by a low velocity approximation. As a result, we got a series of linear field equations that can be solved order by order. In this context, the solutions of the lower orders occur as source terms inside the higher order field equations and represent a ‘post‐Maxwellian’ self‐interaction of the electromagnetic field, which increases order by order. It becomes apparent that one has to distinguish between problems with and without external source terms because without sources also high frequency solutions can be approximately described by Maxwell's original equations. The higher order approximations, which describe ‘post‐Maxwellian’ effects, can give rise to experimental tests of Plebańksi's class. Finally, two boundary value problems are discussed to have examples at hand.     

Octahedral cation partitioning in Mg,Fe2+-olivine. Mössbauer spectroscopic study of synthetic (Mg0.5 Fe2+ 0.5)2SiO4 (Fa50)

The high-temperature partitioning of Fe²⁺ and Mg between the two non-equivalent octahedral M1 and M2 sites in synthetic olivine (Fa₅₀) was studied by Mössbauer spectroscopy. Powder samples have been equilibrated in annealing experiments performed under reducing oxygen fugacity at temperatures between 500 and 800°C followed by rapid quenching in order to prevent redistribution of cations. M-site ordering with Fe²⁺ preferring M1, Mg preferring M2 sites increases continuously with rising equilibrium temperature. K _D values increase from 1.21 at 500°C to 1.48 at 750°C. The results are consistent with both room temperature as well as in situ high temperature single crystal X-ray diffraction experiments of Heinemann et al. [8, 9].     

Regio- and Stereoselective Syntheses with Organocopper Reagents

Of all of the organometallic reagents currently used to form carbon–carbon bonds, organocopper reagents rank amongst the most important. Interest in these reagents centers not only on their regioselectivity, but also increasingly on their application in stereoselective transformations (principally Michael additions and S_N2′ reactions); the use of suitable substrates or chirally modified cuprates can lead to highly diastereo- and enantioselective reactions. Simultaneously, extensions of methods for the preparation and application of these reagents (for example functionalized organocopper species and Lewis acid catalysis, respectively) have opened up new horizons for organocopper reagents. Mechanistically, the reactions are well-documented and understood, but this aspect of the subject has not kept pace with the many rapid developments in preparative chemistry. Organocopper ragents have proved to be indispensable in the synthesis of complex natural products and pharmaceuticals, chiral auxiliaries, and molecules with interesting structural features. In this review we will discuss some of the more recent important developments in this area; the organization will follow the type of selectivity (regio-, diastereo-, and enantioselectivity).     

Zur Theorie der dynamischen Messung kalorischer Grö\en nach dem Prinzip der Differential-Thermoanalyse

Zusammenfassung Es wurden Untersuchungen zur Theorie des Me\verfahrens des Zwillings-Differenz-Kalorimeters durchgeführt. Die erhaltenen Beziehungen gestatten die Ermittlung des Temperaturverlaufes der spezifischen WÄrme und von Enthalpiedifferenzen aus den Thermogrammen dieses dynamischen Me\verfahrens.Dem Ministerium für Wasser- und Atomwirtschaft, jetzt Bundesministerium für wissenschaftliche Forschung sind wir für die finanzielle Förderung dieser Untersuchungen sehr zu Dank verpflichtet.