Synthesis and Stereochemistry of Novel Dibrominated 1,5-Dioxaspiro[5.5]undecane Derivatives

 The synthesis and stereochemistry of new dibrominated spiro-1,3-dioxane derivatives are reported. Investigations by means of NMR methods and single crystal X-ray diffraction for two compounds revealed the high regio- and diastereoselectivity of the bromination reaction of some new spiro-1,3-dioxanes and the asymmetric induction of the chiral carbon atom located in the spiro skeleton.     

The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square

We investigate the relationship between the diagonal of the Fremlin projective tensor product of a Banach lattice E with itself and the 2-concavification of E.     

Mechanism of Intramolecular Photostabilization in Self‐Healing Cyanine Fluorophores

Organic fluorophores, which are popular labels for microscopy applications, intrinsically suffer from transient and irreversible excursions to dark‐states. An alternative to adding photostabilizers at high concentrations to the imaging buffer relies on the direct linkage to the fluorophore. However, the working principles of this approach are not yet fully understood. In this contribution, we investigate the mechanism of intramolecular photostabilization in self‐healing cyanines, in which photodamage is automatically repaired. Experimental evidence is provided to demonstrate that a single photostabilizer, that is, the vitamin E derivative Trolox, efficiently heals the cyanine fluorophore Cy5 in the absence of any photostabilizers in solution. A plausible mechanism is that Trolox interacts with the fluorophore through intramolecular quenching of triplet‐related dark‐states, which is a mechanism that appears to be common for both triplet‐state quenchers (cyclooctatetraene) and redox‐active compounds (Trolox, ascorbic acid, methylviologen). Additionally, the influence of solution‐additives, such as cysteamine and procatechuic acid, on the self‐healing process are studied. The results suggest the potential applicability of self‐healing fluorophores in stochastic optical reconstruction microscopy (STORM) with optical super‐resolution. The presented data contributes to an improved understanding of the mechanism involved in intramolecular photostabilization and has high relevance for the future development of self‐healing fluorophores, including their applications in various research fields.     

Analysis of thermal phases in calcareous Iron Age pottery using FT-IR and Raman spectroscopy

The work deals with the FT-IR and micro-Raman spectroscopy study of the pseudo-amorphous and crystalline thermal phases in the composition of calcareous Iron Age pottery from the Galilee. The application of second-derivative and curve-fitting techniques improves the identification of the thermal phases in the composition of the pottery and makes it possible to analyze the pseudo-amorphous phases which are formed during the firing of the clayey raw material to pottery. This technique makes it possible to distinguish between meta-smectite and meta-kaolinite and to estimate the firing temperature of the pottery. The Micro-Raman spectroscopy is sensitive to the structural degree of ordering of the thermal phases and enables point analysis of peculiar components in the composition of the pottery. Based on the spectroscopic study, it is concluded that the calcareous pottery contained large amounts of microcrystalline-recarbonated calcite mixed with the meta-clay. The large amount of recarbonated calcite in the pottery material and the relatively low firing temperature indicates that instead of sintering the clay, lime technology was used for the cementation of the calcareous vessels. This process took place after the firing by recarbonation of the decomposed calcite which leads to cementation of the vessels with microcrystalline calcite.     

Supremum self-decomposable random vectors

Summary An intrinsic definition of sup self-decomposable random vectors is given. It is proved that they are precisely the limits in distribution of certain normalized partial maxima of sequences of independent random vectors. The main further result is a representation of sup self-decomposable random vectors as functions of Poisson processes, which is the analogue of Wolfe's (1982) representation of additively self-decomposable random variables.The present paper grew out of a Master's Thesis under supervision of Wim Vervaat. Support was provided by the Netherlands Organization for the Advancement of Pure Research ZWO via the Mathematical Centre Foundation SMC (project 10-62-07)     

The M/M/c with critical jobs

We consider theM/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach.