On solving integral equations using Markov chain Monte Carlo methods

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.     

Low-energy electron beam source

Experimental results of research into a ferroelectric-plasma-source-assisted hollow anode (HA) discharge as a source of low-energy electron beams are presented. To generate electron beams, the HA auto-bias negative voltage was achieved by the discharge current flowing through the resistor connecting the HA and the grounded electrode. It is shown that this method allows reliable and reproducible generation of low-energy electron beams with electron energy of several hundreds of eV, electron current density up to several A/cm² and pulse duration of several tens of microseconds.     

Recoil leader formation and development

The existing interpretation in the lightning literature, based on field measurements, defines recoil leaders as negative leaders. However recoil leaders are floating conductors, and, based on this physical assumption, they should be defined as bipolar and bidirectional leaders. This physics-based assumption has never previously been verified experimentally. Such verification, reported in this paper, has been obtained from observations of branched upward positive leaders from a tall tower using a high-speed video system synchronized with electric and magnetic field change and luminosity measurements on the ground. The analysis of these observations clearly reveals the nature of recoil and dart leaders as bidirectional and bipolar electrodeless discharges that develop from a small region along a path of the decayed channels of a previous positive leader, or a positively charged return stroke of negative CG flashes.     

3-Nitro-2H-chromenes in [3+2] cycloaddition reaction with azomethine ylides derived from N-unsubstituted α-amino acids and isatins: regio- and stereoselective synthesis of spirochromeno[3,4-c]pyrrolidines

Chemistry of Heterocyclic Compounds - A regio- and stereoselective method was developed for the synthesis of tetrahydro-4H-spiro[chromeno[3,4-c]pyrrole-1,3'-indolin]-2'-ones in 72−96%...     

Cu2+ Effects on Beta-Amyloid Oligomerisation Monitored by the Fluorescence of Intrinsic Tyrosine

A non-invasive intrinsic fluorescence sensing of the early stages of Alzheimer's beta amyloid peptide aggregation in the presence of copper ions is reported. By using time-resolved fluorescence techniques the formation of beta amyloid-copper complexes and the accelerated peptide aggregation are demonstrated. The shifts in the emission spectral peaks indicate that the peptides exhibit different aggregation pathways than in the absence of copper.     

The Bergman kernel for the Vekua equation

The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial \overline{{}_z}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding Bergman projection operator.     

Tackling N-Alkyl Imines with 3d Metal Catalysis: Highly Enantioselective Iron-Catalyzed Synthesis of α-Chiral Amines

A readily activated iron alkyl precatalyst effectively catalyzes the highly enantioselective hydroboration of N-alkyl imines. Employing a chiral bis(oxazolinylmethylidene)isoindoline pincer ligand, the asymmetric reduction of various acyclic N-alkyl imines provided the corresponding α-chiral amines in excellent yields and with up to >99 % ee. The applicability of this base metal catalytic system was further demonstrated with the synthesis of the pharmaceuticals Fendiline and Tecalcet.     

Characterization of deposits produced by TEA CO2 pulsed laser ablation of silicon mono- and dioxide

Silicon based deposits were prepared by TEA CO₂ pulsed laser ablation (PLA) of SiO and SiO₂ targets in the atmosphere of selected gases (N₂, He, Ne, Ar, Kr). These deposits possess high specific area of several hundreds m² per gram. Owing to the high specific area, some chemical groups and hydrogen related radical were detected by means of FTIR and EPR analyses and theoretical calculations: silyl (E′ center) Si, silylen Si:, silanon SiO, POL (peroxy linkage) SiOOSi and/or NBOHC (non-bridging oxygen hole center) SiO, POR (peroxy radical) SiOO and dioxysilirane Si(O)₂. In SiO₂ deposits the concentration of silyl Si resp. POR SiOO was determined to be 5.8 × 10¹⁸/g resp. 6.2 × 10¹⁹/g. In SiO deposits the ratio [Si:]:[Si] = (3.1-5.7) × 10¹⁹/g: (5.3-9.8) × 10¹⁹/g was measured. Estimated concentration of [Si] in deposits was increased nearly five times in comparison with SiO target. After exposure of the SiO deposits to H₂ EPR doublet with hyperfine splitting of 7.7 mT was observed. The best agreement between calculated theoretical and experimental values was found for the model [(HO)₃SiO]₂HSi. FTIR measurements and calculations of the silanol theoretical model clusters enabled us to discuss the chemical surroundings of the silanol and to determine the defects in the deposits.     

Enantioselective metal-free reduction of ketones by a user-friendly silane with a reusable chiral additive

1-Hydrosilatrane, a safe and easy-to-handle reducing reagent that can be inexpensively accessed, has been shown to reduce prochiral ketones asymmetrically in the presence of chiral 1,2-aminoalcohols with ees ranging from 8% to 86%. The best result was achieved using ephedrine as the source of chirality, which is readily commercially available. The additive can be recovered through extraction and reused without any erosion of enantioselectivity.