Group-theoretical approach to the investigation of reaction graphs for highly degenerate rearrangements of chemical compounds I. Criterion of the connectivity of a graph

We give a necessary and sufficient condition for a reaction graph of a degenerate rearrangement to be connected. This condition is formulated in terms of vertex stabilizers of the automorphism group of a molecular graph. The condition is illustrated on several examples, including the reaction graph of bullvalene. We consider different mathematical models for the construction of reaction graphs and state the problem: which of the models is more adequate?     

The problem of small negatively ionized water clusters

Structures of the negatively charged water clusters (H₂O)⁻_n with n up to 6 were optimized at the UHF/4–31 + + G** level without any geometrical restriction. There was found a chainlike structure for the trimer anion and both chainlike and cyclic geometries for the larger clusters. According to the MP2 energy estimates, all the clusters with n ≥ 3 are more stable than the combinations of separated water molecules and a free electron. The energy of the cycles is lower than that of the chains of the same size. However, the latter species are energetically closer to the neutral oligomers of the same geometry. The energy of vertical detachment of an electron from the chainlike hexamer anion is already about zero. Addition of a diffuse s function centered equidistantly between the oxygen atoms proved metastability, in particular, of the cyclic (H₂O)⁻₄ structure. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 737–748, 1997     

Molecular and conformational properties of comb-like polymers with ionically bound side chains studied in organic solvent

Conformational and dynamo-optical properties of a homologous series of poly(cetyltrimethylammonium 2-acrylamido-2-methylpropane sulfonates) with molecular masses ranging from 80 to 700?kDa were studied in chloroform solutions by viscometry, dynamic light scattering, sedimentation, and flow birefringence. The Mark–Kuhn–Houwink Equations for this polymer in chloroform were obtained; the values of hydrodynamic diameter and the Kuhn segment length as well as the value of intrinsic anisotropy of polarizability of the monomer unit were defined.     

Pyridine Adducts of Tricyano- and Dicyanoboranes

Cyanoborane adducts of the Lewis acids B(CN)₃, BF(CN)₂, and BH(CN)₂ with pyridine and 4-cyanopyridine have been obtained in high yields. The syntheses were accomplished by oxidation of the readily available potassium salts of the cyano(hydrido)borate anions [BH(CN)₃]⁻ ( MHB ), [BFH(CN)₂]⁻ ( FHB ), and [BH₂(CN)₂]⁻ ( DHB ) with bromine in the presence of the respective pyridine derivative C₅H₅N or 4-CN-C₅H₄N as starting material. All six cyanoborane adducts have been characterized by NMR and vibrational spectroscopy, elemental analysis, and single-crystal X-ray diffraction. The reduction of the cyanoborane adducts has been investigated by cyclic voltammetry and the Lewis acidity of the different cyanoboranes has been assessed using the Gutmann-Beckett method. Selected experimental data and trends are compared to theoretical ones, for example fluoride ion affinities (FIAs).     

Products of conjugacy classes in Chevalley groups I. Extended covering numbers

This paper is concerned with products of conjugacy classes in Chevalley groups. We prove that in any quasisimple Chevalley groupG proper or twisted, over any field, the extended covering number is bounded above linearly in terms of the rank ofG, that is, for some constante, for any Chevalley groupG, the product of anye · rank(G) non-central classes covers all ofG. We give estimates for the constante in different cases. The authors gratefully acknowledge the support of EPSRC through a Visiting Fellowship number GR/M58542 and a Research grant number GR/L92174.     

Resolvent Tests for Similarity to a Normal Operator

The main result of this paper is the resolvent similarity criterionwhich says that linear growth of the resolvent towards the spectrumis sufficient for a Hilbert space contraction with finite rankdefect operators and spectrum not covering the unit disc tobe similar to a normal operator. Similar results are provedfor operators having a spectral set bounded by a Dini-smoothJordan curve; in particular, a dissipative operator with finiterank imaginary part is similar to a normal operator if and onlyif its resolvent grows linearly towards the spectrum. Relevantresults on the insufficiency of linear resolvent growth notaccompanied by smallness of defect operators are presented.Also it is proved that there is no restriction on the spectrum,other than finiteness, which together with linear resolventgrowth implies similarity to a normal operator. The constructionof corresponding examples depends on a characterization of well-knownAhlfors curves as curves of linear length growth with respectto linear fractional transformations. 1991 Mathematics SubjectClassification: 11D25, 11G05, 14G05.     

Linear optics controlled-phase gate made simple

Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach, we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.     

Fixed point formula for holomorphic functions

We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of , we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.

     

Regenerative amplification of femtosecond laser pulses in Ti:sapphire at multikilohertz repetition rates

We have generated and applied noncoherent x-ray radiation in an all-solid-state laser system operating at repetition rates up to 20 kHz. Based on a model that takes into account the strong thermal loading of the Ti:sapphire rod, a laser cavity with low sensitivity to thermal lensing was chosen. With a maximum pump power of 80 W, an output power as high as 27 W was obtained in gain-switched operation, and, with a seeding from a femtosecond oscillator, 60-fs, 0.8-mJ (8-W) pulses at 10 kHz and 0.32-mJ (6.5-W) pulses at 20 kHz were generated. High power femtosecond output was used to generate x-ray continuum radiation up to 5 keV from a liquid-gallium jet target.