Proper maps which are Lipschitz α up to the boundary

In this paper we shall construct proper holomorphic mappings from strictly pseudoconvex domains in Cⁿ into the unit ball in C^N which satisfy some regularity conditions up to the boundary. If we only require continuity of the map, but not more, then there is a large class of such maps (see [2], [3], and [5]). On the other hand, if F is C^k on the closure, k > N ? n + 1, then there is a very small class of such maps. In fact such F must be holomorphic across the boundary (see [1] and [4]). We are interested in maps F that are less than C^N ? n + 1, but more than continuous on the closure. Namely, we want to find out if this is a very small or a large class. Our main result is as follows. Theorem, (a) Let ga < 1/6; then there exists an N = N(α, n) such that we can find a map F: Bⁿ → B^N that is proper, holomorphic, and Lipschitz α up to the boundary, but F is not holomorphic across the boundary. (b) If D is a general strictly pseudoconvex domain with C^∞ -boundary in Cⁿ, then we can find a map F: D → B^N, N = N(α, n), that is proper, holomorphic, and Lipschitz α up to the boundary of D. To do part (a) of the theorem we only need to show that we can find a proper holomorphic map F = (f₁, …, F_N): Bⁿ → B^N that is Lipschitz α and f_N(z) = c(1 - Z₁)^1/6 for some constant c > 0. With this we can in fact ensure that the map in (a) is at most Lipschitz 1/6 on the closure of Bⁿ.     

Modeling a central ligand in the nitrogenase FeMo cofactor

In very recent work by Einsle et al. (Science 2002, 297, 1696), a new X-ray crystallographic structure of the FeMo cofactor of nitrogenase with a central ligand was presented. The central ligand is a light atom (N, O, or C), and Einsle et al. suggest that it is nitrogen. We present density functional calculations on the FeMo cofactor, and we investigate N, O, and C as central ligands. We show that both N and O lead to energetically stable FeMo cofactor structures, whereas C is energetically unfavorable. By comparison of bond geometries with the crystallographically determined values, we show that the central ligand is most likely nitrogen.     

Nutraceutical Approaches of Autophagy and Neuroinflammation in Alzheimer’s Disease: A Systematic Review

Aging and the emergence of age-associated illnesses are one of the major challenges of our present society. Alzheimer’s disease (AD) is closely associated with aging and is defined by increasing memory loss and severe dementia. Currently, there are no therapy options available that halt AD progression. This work investigates three hallmarks of the disease (autophagy, neuroinflammation, and senescence) and systematically analyzes if there is a beneficial effect from three substances derived from food sources, the so called “nutraceuticals” epigallocatechin gallate, fisetin, and spermidine, on these hallmarks. The results imply a positive outlook for the reviewed substances to qualify as a novel treatment option for AD. A combination of nutraceutical substances and other preventive measures could have significant clinical impact in a multi-layered therapy approach to counter AD.     

Commemorating two centuries of iodine research: an interdisciplinary overview of current research

Iodine was discovered as a novel element in 1811 during the Napoleonic Wars. To celebrate the bicentennial anniversary of this event we reflect on the history and highlight the many facets of iodine research that have evolved since its discovery. Iodine has an impact on many aspects of life on Earth as well as on human civilization. It is accumulated in high concentrations by marine algae, which are the origin of strong iodine fluxes into the coastal atmosphere which influence climatic processes, and dissolved iodine is considered a biophilic element in marine sediments. Iodine is central to thyroid function in vertebrates, with paramount implications for human health. Iodine can exist in a wide range of oxidation states and it features a diverse supramolecular chemistry. Iodine is amenable to several analytical techniques, and iodine compounds have found widespread use in organic synthesis. Elemental iodine is produced on an industrial scale and has found a wide range of applications in innovative materials, including semiconductors--in particular, in solar cells.     

Decomposition of an M/D/r·k queue with FIFO into k Ek/D/r queues with FIFO

It is observed that the queuing system M/D/r·k with FIFO has the same waiting time distribution as the queuing system E_k/D/r with FIFO. Using this simple equivalence we can apply numerical methods and tables for M/Dn to solve E_k/D/r.