On the trivectors of a 6-dimensional symplectic vector space. II

Let V be a 6-dimensional vector space over a field $\mathbb{F}$, let f be a nondegenerate alternating bilinear form on V and let $\mathit{Sp}(V\text{,}f)?{\mathit{Sp}}_6(\mathbb{F})$ denote the symplectic group associated with $(V\text{,}f)$. The group $\mathit{GL}(V)$ has a natural action on the third exterior power ${?}^{3}V$ of V and this action defines five families of nonzero trivectors of V. Four of these families are orbits for any choice of the field $\mathbb{F}$. The orbits of the fifth family are in one-to-one correspondence with the quadratic extensions of $\mathbb{F}$ that are contained in a fixed algebraic closure $\overline{\mathbb{F}}$ of $\mathbb{F}$. In this paper, we divide the orbits corresponding to the separable quadratic extensions into suborbits for the action of $\mathit{Sp}(V\text{,}f)?\mathit{GL}(V)$ on ${?}^{3}V$.     

Diastereoselective allylation of N-glyoxyloyl-(2R)-bornane-10,2-sultam and (1R)-8-phenylmenthyl glyoxylate: synthesis of (2S,4S)-2-hydroxy-4-hydroxymethyl-4-butanolide

The diastereoselective addition of allylsilanes and allylstannanes to N-glyoxyloyl-(2R)-bornane-10,2-sultam 1 and (1R)-8-phenylmenthyl glyoxylate 7 in the presence of Lewis acids has been studied. We obtained diastereoselectivities up to 84% and 94% for the allylation of 2 and 7, respectively. The application of the allylation products of 1 or 2 in the synthesis of 4-butanolides, for example (2S,4S)-2-hydroxy-4-hydroxymethyl-4-butanolide 13 is presented.     

High-throughput kinase profiling: a more efficient approach toward the discovery of new kinase inhibitors

Selective protein kinase inhibitors have only been developed against a small number of kinase targets. Here we demonstrate that "high-throughput kinase profiling" is an efficient method for the discovery of lead compounds for established as well as unexplored kinase targets. We screened a library of 118 compounds constituting two distinct scaffolds (furan-thiazolidinediones and pyrimido-diazepines) against a panel of 353 kinases. A distinct kinase selectivity profile was observed for each scaffold. Selective inhibitors were identified with submicromolar cellular activity against PIM1, ERK5, ACK1, MPS1, PLK1-3, and Aurora A,B kinases. In addition, we identified potent inhibitors for so far unexplored kinases such as DRAK1, HIPK2, and DCAMKL1 that await further evaluation. This inhibitor-centric approach permits comprehensive assessment of a scaffold of interest and represents an efficient and general strategy for identifying new selective kinase inhibitors.     

Catalytic asymmetric allylation of aldehydes using the chiral (salen)chromium(III) complexes

The enantioselective addition of allylstannanes to glyoxylates and glyoxals, as well as simple aromatic and aliphatic aldehydes, catalyzed by chiral (salen)Cr(III) complexes, has been studied. The reaction proceeded smoothly for the reactive 2-oxoaldehydes and allyltributyltin in the presence of small amounts (1-2 mol %) of (salen)Cr(III)BF₄ (1b) under mild, undemanding conditions. However, in the case of other simple aldehydes, the use of high-pressure conditions is required to obtain good yields. Classic chromium catalyst 1b, easily prepared from the commercially available chloride complex 1a, affords homoallylic alcohols usually in good yield and with enantiomeric purity of 50-79% ee. The stereochemical results are rationalized on the basis of the proposed model.     

New Heteroaromatic Complexing Agents and Luminescence of Their Europium(III) and Terbium(III) Chelates

Twelve heteroaromatic complexing agents 9a–I were synthesized with the purpose to develop suitable labels for time-resolved luminescence-based bioaffinity assays. The relative luminescence yields, excitation maxima, and emission decay constants of their europium(III) and terbium(III) chelates were determined. According to these results, 2,2′,2″,2?-[(2,2′-bipyridine-6,6′-diyl)bis(methylenenitrilo)]tetrakis (acetic acid) ( 9e ) and 2,2′,2″,2?-[(2,2′:6′,2″-terpyridine-6,6″-diyl)bis(methylenenitrilo)] tetrakis(acetic acid) ( 91 ) are the most promising agents.     

Unitary operators with discrete spectrum induced by measure preserving transformations

The purpose of this paper is to prove the following theorem.Theorem. Given a countable subset Λ on the circle K and an integer-valued function n(λ) on Λ, there exists a dynamical system with discrete spectrum (X,$\text{F}$,μ,T) such that Λ is the set of all eigenvalues of T and n(λ) is the multiplicity function of T if and only if there exist two systems of subgroups {G_i}_i∈N and $\text{{S}{}_{\mathrm{j}}\text{}}{}_{\mathrm{j\in M}}\text{(}\text{N}\text{??}{}_0\text{,}\text{M}\text{??}{}_0\text{)}$ of the circle such that Λ = G ∪ S and

$\text{n(λ)=}\text{∞}\text{for}\text{λ∈S,}\text{{i∈N; λ∈G}{}_{\mathrm{i}}\text{}}\text{for}\text{λ∈G?S,}$

where $\text{G =}\text{?}\text{i∈N}\text{G}{}_{\mathrm{i}}\text{, S =}\text{?}\text{j∈M}\text{S}{}_{\mathrm{j}}$.     

Q-switched Er:YAG lasers resonantly pumped by Erbium fiber laser

The study describes efficient, acousto-optic Q-switching of Er:YAG laser at the 1645 nm eye-safe wavelength. For longitudinal pumping at wavelength 1532 nm, linear-polarized 10 W Erbium fiber laser radiation was used. The investigated Er:YAG crystals were 25 and 40 mm long and their Erbium concentration was 0.20 and 0.25%, respectively. For giant pulse generation, a fused silica acousto-optic modulator was inserted inside the Er:YAG laser oscillator. For a maximum incident pump power of 7.95 W, pulse energy up to 4.1 mJ was generated with pulse duration 34 ns at 500-Hz repetition rate; the corresponding peak power was 119 kW.     

Deposition of bulk GaN from solution in gallium under high N2 pressure on silicon carbide and sapphire substrates

Results of high-pressure directional growth of GaN on foreign substrates: SiC, sapphire and GaN/sapphire MOCVD templates are presented. The role of nitrogen pressure and supersaturation in the growth process is discussed. The conditions for stable growth of the nitride are determined. The results of the crystallization process are compared with those obtained for directional growth on pressure grown GaN crystals.     

High-pressure accelerated asymmetric organocatalytic Friedel-Crafts alkylation of indoles with enones: application to quaternary stereogenic centers construction

An organocatalytic Friedel-Crafts alkylation of indoles with α,β-unsaturated ketones was found to be efficiently accelerated under high-pressure conditions with a low loading of chiral primary amine salts with good yield and enantioselectivity up to 90%. This approach also allows, for the first time, selected indole derivatives containing quaternary stereogenic centers to be obtained from prochiral β,β-disubstituted enones with an enantioselectivity up to 80%.