Synthesis of Novel Tetrahydro-1<i>H</i>-pyrazolo[4,3-<i>c</i>]pyridines <i>via</i> Intramolecular Nitrilimine Cycloaddition

The preparation of novel tetrahydro-1H-pyrazolo[4,3-c]pyridines is reported. Pivotal to the synthesis of these compounds was the development of mild reaction conditions to generate a highly functionalized nitrilimine capable of undergoing an intramolecular cycloaddition with a tethered alkyne. The desired cycloadduct was formed as an equal mixture of diastereomers.     

Computational study of the mechanism and selectivity of palladium-catalyzed propargylic substitution with phosphorus nucleophiles

The mechanism and sources of selectivity in the palladium-catalyzed propargylic substitution reaction that involves phosphorus nucleophiles, and which yields predominantly allenylphosphonates and related compounds, have been studied computationally by means of density functional theory. Full free-energy profiles are computed for both H-phosphonate and H-phosphonothioate substrates. The calculations show that the special behavior of H-phosphonates among other heteroatom nucleophiles is indeed reflected in higher energy barriers for the attack on the central carbon atom of the allenyl/propargyl ligand relative to the ligand-exchange pathway, which leads to the experimentally observed products. It is argued that, to explain the preference of allenyl- versus propargyl-phosphonate/phosphonothioate formation in reactions that involve H-phosphonates and H-phosphonothioates, analysis of the complete free-energy surfaces is necessary, because the product ratio is determined by different transition states in the respective branches of the catalytic cycle. In addition, these transition states change in going from a H-phosphonate to a H-phosphonothioate nucleophile.     

Asynchronous Exponential Growth of a General Structured Population Model

We consider a class of structured cell population models described by a first order partial differential equation perturbed by a general birth operator which describes in a unified way a wide class of birth phenomena ranging from cell division to the McKendrick model. Using the theory of positive stochastic semigroups we establish new criteria for an asynchronous exponential growth of solutions to such equations.     

An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro–Macro decomposition

The concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 < ε ? 1, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields b and the simple extension to the case of a non-constant anisotropy intensity 1/ε. The mathematical approach and the numerical scheme are different from those presented in the previous work [P. Degond, F. Deluzet, A. Lozinski, J. Narski, C. Negulescu, Duality-based asymptotic-preserving method for highly anisotropic diffusion equations, Communications in Mathematical Sciences 10 (1) (2012) 1–31] and its considerable advantages are pointed out.     

Nuclear shape effect on the g factor of hydrogenlike ions

The nuclear shape correction to the g factor of a bound electron in the 1S state is calculated for a number of nuclei in the range of charge numbers from Z=6 up to Z=92. The leading relativistic deformation correction has been derived analytically, and also its influence on one-loop quantum electrodynamic terms has been evaluated. We show the leading corrections to become significant for mid-Z ions and for very heavy elements to even reach the 10(-6) level.     

Investigating the interaction of x-ray free electron laser radiation with grating structure

The interaction of free electron laser pulses with grating structure is investigated using 4.6±0.1 nm radiation at the FLASH facility in Hamburg. For fluences above 63.7±8.7 mJ/cm², the interaction triggers a damage process starting at the edge of the grating structure as evidenced by optical and atomic force microscopy. Simulations based on solution of the Helmholtz equation demonstrate an enhancement of the electric field intensity distribution at the edge of the grating structure. A procedure is finally deduced to evaluate damage threshold.     

Oil refinery dusts: morphological and size analysis by TEM

The objectives of this work were to develop a means of sampling atmospheric dusts on the premises of an oil refinery for electron microscopic study to carry out preliminary morphological analyses and to compare these dusts with those collected at sites beyond the refinery limits. Carbon and collodion membranes were used as a support for collection of dust particles straight on transmission electron microscopy (TEM) grids. Micrographs of the dust particles were taken at magnifications from ×4,000 to ×80,000 with a Tesla BS500 transmission electron microscope. Four parameters were defined on the basis of the micrographs: surface area, Feret diameter, circumference, and shape coefficient. The micrographs and literature data were used to classify the atmospheric dusts into six groups: particles with an irregular shape and rounded edges; particles with an irregular shape and sharp edges; soot and its aggregates; spherical particles; singly occurring, ultrafine dust particles; and particles not allocated to any of the previous five groups. The types of dusts found in all the samples were similar, although differences did exist between the various morphological parameters. Dust particles with the largest Feret diameter were present in sample 3 (mean, 0.739 μm)—these were collected near the refinery's effluent treatment plant. The particles with the smallest diameter were found in the sample that had been intended to be a reference sample for the remaining results (mean, 0.326 μm). The dust particles collected in the refinery had larger mean Feret diameters, even 100% larger, than those collected beyond it. Particles with diameters from 0.1 to 0.2 μm made up the most numerous group in all the samples collected in the refinery.     

Analysis of airborne metal containing particles with EDX/EDS detectors in electron microscopes

In years 2006–2010 particulate matter analysis was undertaken for dust samples collected from Gdansk and London area in order to compare their morphology and composition. Part of those studies was devoted to analysis of particulate matter (PM) bearing metals. Characterization of the morphology and size of the particles collected onto the filters was performed using a scanning electron microscope (SEM) and transmission electron microscope (TEM). Both electron microscopes were equipped with energy dispersive X-ray spectrometers to identify the elemental composition of the particles. On analysis of the X-ray spectra acquired by both TEM and SEM, the particles were divided into 10 groups as follows: Al-rich, Ba-rich, C-rich, Ca-rich, Cl-rich, Fe-rich, Mg-rich, Na-rich, S-rich, Si-rich. Speciation of the particles based on the major element and accompanying minor elements yielded 34 particle types. However, some pairs of elements repeat, for instance: Na-Cl and Cl-Na, Al-S and S-Al, Si-Al and Al-Si, S-Ca and Ca-S. These are undoubtedly the same types of particles; variation in peak heights of the major and minor elements is normal in a mixed particle population.     

Equivalent conditions for generalized contractions on (ordered) metric spaces

We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252].