On the derived algebra of a centraliser

Let g be a classical Lie algebra, e∈g a nilpotent element and ge⊂g the centraliser of e. We prove that ge=[ge,ge] if and only if e is rigid. It is also shown that if e∈[ge,ge], then the nilpotent radical of ge coincides with [ge(1),ge], where ge(1)⊂ge is an eigenspace of a characteristic of e corresponding to the eigenvalue 1.     

Cage-like structure formation during sol–gel polymerization of glycidyloxypropyltrimethoxysilane

The sol–gel polymerization of 3-glycidyloxypropyltrimethoxysilane (GTMS) was followed by size exclusion chromatography and ²⁹Si NMR. Extensive non-random cyclization under formation of polyhedral cycles – cubic cages – predominates at the beginning of the reaction. Structure growth of polysilsesquioxanes proceeds by combining the incompletely condensed cage frameworks. The extent of the cage formation increases with dilution and the amount of water and depends appreciably on a catalyst. The cage fraction was isolated from a reaction mixture using preparative size exclusion chromatography and identified by ²⁹Si NMR spectroscopy and electrospray ionization mass spectrometry (ESI-MS). High content of polyhedral cages prevents gelation of the trifunctional GTMS monomer. Reaction of pendant epoxy groups is much slower; however, at a late reaction stage the epoxy hydrolysis can be significant. Under some conditions, like base catalysis, polysilsesquioxane clusters are crosslinked by intermolecular condensation of SiOH with hydrolyzed epoxy groups and the system gels. The cage with epoxide functionalities may serve as a rigid precursor of crosslinking.     

Structural and magnetic studies of tetranuclear heterometallic M/Cr (M = Co,Mn) complexes self-assembled from zerovalent cobalt or manganese,Reineckes salt and diethanolamine

Four novel heterometallic complexes [Co₂Cr₂(NCS)₄(HDea)₂(Dea)₂]·4dmf (1), [Co₂Cr₂(NCS)₄(HDea)₂(Dea)₂]·4dmso (2), [Mn₂Cr₂(NCS)₄(HDea)₂(Dea)₂(dmf)₂]·2dmf (3) and [Mn₂Cr₂(NCS)₄(HDea)₂(Dea)₂(dmso)₂]·4dmso (4) have been prepared using zerovalent cobalt (1, 2) or manganese (3, 4), Reineckes salt, ammonium thiocyanate and a non-aqueous solution of diethanolamine (H₂Dea) in air. The single X-ray analysis reveals that all compounds have similar centrosymmetric crystal structures based on a tetranuclear {M₂Cr₂(μ₃-O)₂(μ-O)₄} (M = Co, Mn) core. Variable-temperature magnetic susceptibility measurements of 1, 2 and 4 show antiferromagnetic coupling between the magnetic centers, while 3 exhibits a ferromagnetic behavior.     

Alteration of the Axial Met Ligand to Electron Acceptor A0 in Photosystem I: Effect on the Generation of P 700 ·+ A 1 ·− Radical Pairs as Studied by W-band Transient EPR

Photosystem I (PS I) mutants from the cyanobacterium Synechocystis sp. PCC 6803 bearing point mutations to the axial ligands of A_0A (M688N_PsaA) and A_0B (M668N_PsaB) were studied by high-field W-band electron paramagnetic resonance (EPR) spectroscopy. It was found that the EPR observables of PS I from the M668N_PsaB mutant were virtual identical to that of the wild type (WT), and are clearly distinct from the M688N_PsaA mutant. In particular, the P ₇₀₀ ^·+ decay kinetics in the M688N_PsaA mutant is significantly slower than in the WT or the M668N_PsaB mutant. The analysis of the out-of-phase electron–electron dipolar electron spin echo envelope modulation shows that in the M668N_PsaB mutant, the estimated distance of 26.0 ± 0.3 Å agrees well with the 25.8 Å distance for the P ₇₀₀ ^·+ A _1A ^·? radical pair measured in the X-ray crystal structure. In the M688N_PsaA mutant, two populations are found with estimated distances of 26.0 ± 0.3 and 25.0 ± 0.3 Å in a ratio of 0.7–0.3, which agree well with the 25.8 Å distance for the P ₇₀₀ ^·+ A _1A ^·? radical pair and the 24.6 Å distance for the P ₇₀₀ ^·+ A _1B ^·? radical pair measured in the X-ray crystal structure. The data confirm that under the experimental conditions employed in this work, which involve dark-adapted samples without the pre-reduction of the iron–sulfur clusters, electron transport in cyanobacterial PS I is asymmetrical at 100 K, with the majority of electron transfer taking place through the A-branch of cofactors.     

Optimizing the performance of the multiconfiguration molecular mechanics method

Multiconfiguration molecular mechanics (MCMM) is a general algorithm for constructing potential energy surfaces for reactive systems (Kim, Y.; Corchado, J. C.; Villà, J.; Xing, J.; Truhlar, D. G. J. Chem. Phys. 2000, 112, 2718). This paper illustrates how the performance of the MCMM method can be improved by adopting improved molecular mechanics parameters. We carry out calculations of reaction rate constants using variational transition state theory with optimized multidimensional tunneling on the MCMM PESs for three hydrogen transfer reactions, and we compare the results to direct dynamics. We find that the MCMM method with as little as one electronic structure Hessian can describe the dynamically important regions of the ground-electronic state PES, including the corner-cutting-tunneling region of the reaction swath, with practical accuracy.     

Polynomials whose coefficients coincide with their zeros

In this paper we consider monic polynomials such that their coefficients coincide with their zeros. These polynomials were first introduced by S. Ulam. We combine methods of algebraic geometry and dynamical systems to prove several results. We obtain estimates on the number of Ulam polynomials of degree N. We provide additional methods to obtain algebraic identities satisfied by the zeros of Ulam polynomials, beyond the straightforward comparison of their zeros and coefficients. To address the question about the existence of orthogonal Ulam polynomial sequences, we show that the only Ulam polynomial eigenfunctions of hypergeometric type differential operators are the trivial Ulam polynomials \(\{x^N\}_{N=0}^\infty \). We propose a family of solvable N-body problems such that their stable equilibria are the zeros of certain Ulam polynomials.     

Unexpected behaviour of tosylated and acetylated imidazolinium salts

Tosylated and acetylated imidazolinium salts revealed an unexpected reactivity when treated with methyl iodide or benzyl bromide. Moreover an unprecedented acid-catalysed rearrangement for an acetylated imidazolinium salt was observed during an anion metathesis.     

Isobornylchalcones as Scaffold for the Synthesis of Diarylpyrazolines with Antioxidant Activity

The pyrazoline ring is defined as a “privileged structure” in medicinal chemistry. A variety of pharmacological properties of pyrazolines is associated with the nature and position of various substituents, which is especially evident in diarylpyrazolines. Compounds with a chalcone fragment show a wide range of biological properties as well as high reactivity which is primarily due to the presence of an α, β-unsaturated carbonyl system. At the same time, bicyclic monoterpenoids deserve special attention as a source of a key structural block or as one of the pharmacophore components of biologically active molecules. A series of new diarylpyrazoline derivatives based on isobornylchalcones with different substitutes (MeO, Hal, NO₂, N(Me)₂) was synthesized. Antioxidant properties of the obtained compounds were comparatively evaluated using in vitro model Fe²⁺/ascorbate-initiated lipid peroxidation in the substrate containing brain lipids of laboratory mice. It was demonstrated that the combination of the electron-donating group in the para-position of ring B and OH-group in the ring A in the structure of chalcone fragment provides significant antioxidant activity of synthesized diarylpyrazoline derivatives.     

Failure of immunocompetitive capillary electrophoresis assay to detect disease-specific prion protein in buffy coat from humans and chimpanzees with Creutzfeldt-Jakob disease

The emergence of a new environmentally caused variant of Creutzfeldt-Jakob disease (vCJD), the result of food-born infection by the causative agent of bovine spongiform encephalopathy (BSE), has stimulated research on a practical diagnostic screening test. The immunocompetitive capillary electrophoresis (ICCE) assay has been reported to detect disease-specific, proteinase-resistant prion protein (PrPres) in the blood of scrapie-infected sheep. We have applied this method to blood from CJD-infected chimpanzees and humans. The threshold of detection achieved with our ICCE was 0.6 nM of synthetic peptide corresponding to the prion protein (PrP) C-terminus, and 2 nM of recombinant human PrP at the optimized conditions. However, the test was unable to distinguish between extracts of leucocytes from healthy and CJD-infected chimpanzees, and from healthy human donors and patients affected with various forms of CJD. Thus, the ICCE assay as presently performed is not suitable for use as a screening test in human transmissible spongiform encephalopathies (TSEs).