Enumeration of one-nodal rational curves in projective spaces

We give a formula computing the number of one-nodal rational curves that pass through an appropriate collection of constraints in a complex projective space. The formula involves intersections of tautological classes on moduli spaces of stable rational maps. We combine the methods and results from three different papers.     

Singularities and semistable degenerations for symplectic topology

We overview our work [7], [8], [9], [10], [11], [6] defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary and sufficient condition for smoothing normal crossings symplectic varieties. In addition, we explain some connections with other areas of mathematics and discuss a few directions for further research.     

Mechanistic study of multi-step nucleophilic substitution for trifluoromethylated styrenes

The key steps of the reactions of nitrogen nucleophiles with β-halogen-β-trifluoromethylstyrenes have been studied by ¹⁹F and ¹H NMR monitoring and quantum-chemical calculations. In contrast to the mechanism proposed earlier for nucleophilic vinylic substitution of captodative carbonyl-bearing haloalkenes, this reaction proceeds via either E–Ad or Ad–E sequence depending on the nature of aromatic substituents of the parent styrenes.     

Insights into the mechanism of O₂ formation and release from the Mn₄O₄L₆ "cubane" cluster

To probe photoinduced water oxidation catalyzed by the Mn?O?L? cubane clusters, we have computationally studied the mechanism and controlling factors of the O? formation from the [Mn?O?L?] catalyst, 6. It was demonstrated that dissociation of an L = H?PO?? ligand from 6 facilitates the direct O-O bond formation that proceeds with a 28.3 (33.4) kcal/mol rate-determining energy barrier at the transition state TS1. This step (the O-O single bond formation) of the reaction is a two-electron oxidation/reduction process, during which two oxo ligands are transformed into to μ2:η2-O?2? unit, and two ("distal") Mn centers are reduced from the 4+ to the 3+ oxidation state. Next two-electron oxidation/reduction occurs by "dancing" of the resulted O?2? fragment between the Mn1 and Mn2/Mn(2')-centers, keeping its strong coordination to the Mn(1')-center. As a result of this four-electron oxidation/reduction process Mn centers of the Mn?-core of I transform from {Mn1(III)-Mn(1')(III)-Mn2(IV)-Mn(2')(IV)} to {Mn1(II)-Mn(1')(II)-Mn2(III)-Mn(2')(III)} in IV. In other words, upon O? formation in cationic complex [Mn?O?L?](+), I, all four Mn-centers are reduced by one electron each. The overall reaction I → TS1 → II → III → TS2 → IV → TS3 → V → VI + O? is found to be exothermic by 15.4 (10.5) kcal/mol. We analyze the lowest spin states and geometries of all reactants, intermediates, transition states, and products of the targeted reaction.     

Synthesis and structure of new 1,3,5-triazine-pyrazole derivatives

We have studied the reaction of methylenedicarbonyl compounds with 4,6-disubstituted 2-hydrazinyl-1,3,5-triazine in order to obtain novel coupled biheterocyclic aromatic systems with potential bioactivity. Reaction conditions were studied and optimized, and a series of 4,6-disubstituted 2-(1H-pyrazolyl)-1,3,5-triazines were obtained with good yield.     

Nanocrystalline aerogel VOx/MgO as a catalyst for oxidative dehydrogenation of propane

Nanocrystalline aerogel VO_x/MgO catalysts for the oxidative dehydrogenation of propane with high surface area and uniform vanadium distribution were synthesized by co-gelation followed by supercritical drying. The catalysts were shown to have superior performance compared to nanocrystalline VO_x/MgO catalysts prepared by impregnation.     

Collisional activation of ions in RF ion traps and ion guides: The effective ion temperature treatment

Ion transfer and storage using inhomogeneous radio frequency (RF) electric fields in combination with gas-assisted ion cooling and focusing constitutes one of the basic techniques in mass spectrometry today. The RF motion of ions in the bath gas environment involves a large number of ion-neutral collisions that leads to the internal activation of ions and their effective "heating" (when a thermal distribution of internal energies results). The degree of ion activation required in various applications may range from a minimum level (e.g., slightly raising the average internal energy) to an intense level resulting in ion fragmentation. Several research groups proposed using the effective temperature as a measure of ion activation under conditions of multiple ion-neutral collisions. Here we present approximate relationships for the effective ion temperature relevant to typical operation modes of RF multipole devices. We show that RF ion activation results in near-thermal energies for ions occupying an equilibrium position at the center of an RF trap, whereas increased ion activation can be produced by shifting ions off-center, e.g., by means of an external DC electric field. The ion dissociation in the linear quadrupole ion trap using the dipolar DC ion activation has been observed experimentally and interpreted in terms of the effective ion temperature.     

Thin-Layer Chromatography with an Isolated Support and Forced Flow of the Mobile Phase

JPC – Journal of Planar Chromatography – Modern TLC -