Generations of Monic Polynomials such that the Coefficients of Each Polynomial of the Next Generation Coincide with the Zeros of a Polynomial of the Current Generation,and New Solvable Many-Body Problems

The notion of generations of monic polynomials such that the coefficients of each polynomial of the next generation coincide with the zeros of a polynomial of the current generation is introduced, and its relevance to the identification of endless sequences of new solvable many-body problems “of goldfish type” is demonstrated.     

Surface diffusion of tungsten adatoms induced by low-energy bombardment with He atoms

Using low-temperature field ion microscope techniques, we studied at the atomic level the elementary events of radiation-induced surface diffusion of tungsten adatoms on the ideally pristine surface. The experiments on surface-damage formation and adatom displacements have been performed in situ with a source of neutral helium atoms with an energy of 5?keV. It was demonstrated that the low-energy He atomic bombardment at grazing incidence was able to induce a substantial surface mobility of adatoms. Most of the radiation-induced adatom displacements were oriented along the direction of irradiation. The long impact-induced jumps of adatoms, spanning more than a nearest-neighbor distance, were revealed. Performed molecular dynamics simulations reproduce the general experimental trends and conclusions.     

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.     

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.     

Parabolic contractions of semisimple Lie algebras and their invariants

Let $G$ be a connected semisimple algebraic group with Lie algebra $\mathfrak{g }$ and $P$ a parabolic subgroup of $G$ with $\mathrm{Lie\, }P=\mathfrak{p }$ . The parabolic contraction $\mathfrak{q }$ of $\mathfrak{g }$ is the semi-direct product of $\mathfrak{p }$ and a $\mathfrak{p }$ -module $\mathfrak{g }/\mathfrak{p }$ regarded as an abelian ideal. We are interested in the polynomial invariants of the adjoint and coadjoint representations of $\mathfrak{q }$ . In the adjoint case, the algebra of invariants is easily described and it turns out to be a graded polynomial algebra. The coadjoint case is more complicated. Here we found a connection between symmetric invariants of $\mathfrak{q }$ and symmetric invariants of centralisers $\mathfrak{g }_e\subset \mathfrak{g }$ , where $e\in \mathfrak{g }$ is a Richardson element with polarisation $\mathfrak{p }$ . Using this connection and results of Panyushev et al. (J Algebra 313:343–391, 2007), we prove that the algebra of symmetric invariants of $\mathfrak{q }$ is free for all parabolic subalgebras in types $\mathbf A$ and $\mathbf C$ and some parabolics in type $\mathbf B$ . This technique also applies to the minimal parabolic subalgebras in all types. For $\mathfrak{p }=\mathfrak{b }$ , a Borel subalgebra of $\mathfrak{g }$ , one gets a contraction of $\mathfrak{g }$ recently introduced by Feigin (Selecta Math 18:513–537, 2012) and studied from invariant-theoretic point of view in our previous paper (Panyushev and Yakimova in Ann Inst Fourier 62(6):2053–2068, 2012).     

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).     

A very large Rh-Rh bond shortening on excitation of the [Rh2(1,8-diisocyano-p-menthane)4]2+ ion by time-resolved synchrotron X-ray diffraction

A very large Rh-Rh contraction of approximately 0.85 A occurs on excitation of the [Rh(2)(1,8-diisocyano-p-menthane)(4)](2+) ion to its triplet state.     

How well can density functional methods describe hydrogen bonds to pi acceptors?

We employed four newly developed density functional theory (DFT) methods for the calculation of five pi hydrogen bonding systems, namely, H2O-C6H6, NH3-C6H6, HCl-C6H6, H2O-indole, and H2O-methylindole. We report new coupled cluster calculations for HCl-C6H6 that support the experimental results of Gotch and Zwier. Using the best available theoretical and experimental results for all five systems, our calculations show that the recently proposed MPW1B95, MPWB1K, PW6B95, and PWB6K methods give accurate energetic and geometrical predictions for pi hydrogen bonding interactions, for which B3LYP fails and PW91 is less accurate. We recommend the most recent DFT method, PWB6K, for investigating larger pi hydrogen bonded systems, such as those that occur in molecular recognition, protein folding, and crystal packing.