Quasistationary distributions for one-dimensional diffusions with singular boundary points

In the present work we characterize the existence of quasistationary distributions for diffusions on $(0,\infty )$ allowing singular behavior at 0 and $\infty$. If absorption at 0 is certain, we show that there exists a quasistationary distribution as soon as the spectrum of the generator is strictly positive. This complements results of Cattiaux et al. (2009) and Kolb and Steinsaltz (2012) for 0 being a regular boundary point and extends results by Cattiaux et al. (2009) on singular diffusions.     

Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds

In this paper we extend the well-known Leinfelder–Simader theorem on the essential selfadjointness of singular Schrödinger operators to arbitrary complete Riemannian manifolds. This improves some earlier results of Shubin, Milatovic and others.     

Polydipropylsiloxane Single Crystals

Polydipropylsiloxane single crystals, grown from a dilute n-butylacetate solution, were characterized by electron microscopy and by selected-area electron-beam diffraction techniques. The electron diffraction study shows that the growth face was parallel to the (100) plane. Fracture of single crystals parallel to the fold plane takes place during the electron diffraction examination to give ribbon like lamellae about 300 A wide and 80 A thick. Fracture normal to the fold plane was also observed.     

Molecule-based kinetic modeling by Monte Carlo methods for heavy petroleum conversion

A methodology for kinetic modeling of conversion processes is presented.The proposed approach allows to overcome the lack of molecular detail of the petroleum fractions and to simulate the reactions of the process by means of a two-step procedure.In the first step,a synthetic mixture of molecules representing the feedstock is generated via a molecular reconstruction method,termed SR-REM molecular reconstruction.In the second step,a kinetic Monte Carlo method,termed stochastic simulation algorithm(SSA),is used to simulate the effect of the conversion reactions on the mixture of molecules.The resulting methodology is applied to the Athabasca vacuum residue hydrocracking.An adequate molecular representation of the vacuum residue is obtained using the SR-REM algorithm.The reaction simulations present a good agreement with the laboratory data for Athabasca vacuum residue conversion.In addition,the proposed methodology provides the molecular detail of the vacuum residue conversion throughout the reactions simulations.     

Improved Synthesis of Cyclic Tertiary Allylic Alcohols by Asymmetric 1,2‐Addition of AlMe3 to Enones

The development of an improved protocol for the enantioselective Rh^I/binap‐catalysed 1,2‐addition of AlMe₃ to cyclic enones is reported. ³¹P NMR analysis of the reaction revealed that the catalyst in its resting state is a chloride‐bridged dimer. This insight led to the use of AgBF₄ as an additive for in situ activation of the dimeric precatalyst. Thus, the catalyst loading can now be reduced to only 1 mol % with respect to rhodium. Various 5–7‐membered cyclic enones can be transformed into tertiary allylic alcohols with excellent levels of enantioselectivity and high yields. The obtained products are versatile synthetic building blocks, shown by a highly enantioselective formal total synthesis of the pheromone (?)‐frontalin as well as formation of a bicyclic lactone that has the core structure of the natural flavour component “wine lactone”.     

Uranium,thorium and potassium occurrences in the vicinity of hot springs in the northern neotectonic belt in the Eastern Cape Province,South Africa

Gamma ray measurements were carried out along two parallel lines close to each of the hot springs using a RS 125 spectrometer to find the concentration (ppm) of U, Th, and K at Polile Tshisa, Aliwal North, and Badfontein hot springs. The RS 125 spectrometer is auto-stabilized on the naturally occurring U, Th, and K, and provides concentrations (ppm) of the radioelements. The results show that the concentration of thorium is higher, and is below the world average hazardous threshold of 7.4 ppm. Thorium is related to the occurrence of monazite seen at the scanning electron microscope. Higher ratios of U/K are indicative of an increase of uranium relative to potassium. Binary diagrams (Th–U, K–U, and K–Th) do not show a clear best fit except at Polile Tshisa hot spring where thorium shows a quasi positive correlation to potassium. In general, it can be concluded that the concentrations of these three radioelements are quite low, acceptable for groundwater, and could be hazardous to the health of humans and animals if exposed to long time radiations.