Azido-, hydroxo-, and oxo-bridged copper(II) dimers: spin population analysis within broken-symmetry, density functional methods

Within the general context of homometallic spin-coupled Cu(II) dimers, we propose to relate the antiferromagnetic part of the exchange coupling constant, J _AF, to the quantity ΔP ²(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through J _AF≈−UΔP ²(Cu), where U is interpreted as the covalent–ionic term. This proportionality is illustrated for three “bare” Cu(II) dimers (i.e. without peripheral ligation, so as to enhance the antiferromagnetic contribution) bridged by azido, hydroxo, or oxo groups. This provides an alternative quantifier of the exchange phenomenon to that usually used, i.e. Δ², the square of the singly occupied molecular orbital splitting in the triplet state. Moreover, and quite interestingly, the quantity ΔP ²(Cu) can become negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

Algorithm of orbit determination using one or two GPS satellites

The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary state of satellite orbit with a certain precision in short time.     

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

一个新的高维向量Lie代数及其应用

构造了一个新的8维向量Lie代数,通过适当设计等谱问题,利用屠格式和扩展的迹恒等式得到了AKNS族的可积耦合及Hamilton结构.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

Induced and coinduced Banach Lie–Poisson spaces and integrability

The Poisson induction and coinduction procedures are used to construct Banach Lie–Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie–Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail.     

激光偏振性的量子理论与实验研究

本文建立了激光偏振性的全量子理论。分析了各向异性腔中多模运转下激光束的偏振特性。给出He-Ne激光器在6328振荡谱线上各模相互间角度随各向异性变化的基本方程、计算曲线及偏振组态。本文还给出了由应力导致相位各向异性对模式偏振性影响的实验结果。理论分析与实验结果相符。     

Structural characterization of silver dialkylphosphite salts using solid‐state 109Ag and 31P NMR spectroscopy,IR spectroscopy and DFT calculations

High‐resolution solid‐state ¹⁰⁹Ag and ³¹P NMR spectroscopy was used to investigate a series of silver dialkylphosphite salts, Ag(O)P(OR)₂ (R = CH₃, C₂H₅, C₄H₉ and C₈H₁₇), and determine whether they adopt keto, enol or dimer structures in the solid state. The silver chemical shift, CS, tensors and |J(¹⁰⁹Ag, ³¹P)| values for these salts were determined using ¹⁰⁹Ag (Ξ = 4.652%) NMR spectroscopy. The magnitudes of J(¹⁰⁹Ag, ³¹P) range from 1250 ± 10 to 1318 ± 10 Hz and are the largest reported so far. These values indicate that phosphorus is directly bonded to silver for all these salts and thus exclude the enol structure. All ³¹P NMR spectra exhibit splittings due to indirect spin–spin coupling to ¹⁰⁷Ag (I = 1/2, NA = 51.8%) and ¹⁰⁹Ag (I = 1/2, NA = 48.2%). The ¹J(¹⁰⁹Ag, ³¹P) values measured by both ¹⁰⁹Ag and ³¹P NMR spectroscopy agree within experimental error. Analysis of ³¹P NMR spectra of stationary samples for these salts allowed the determination of the phosphorus CS tensors. The absence of characteristic P?O stretching absorption bands near 1250 cm^?1 in the IR spectra for these salts exclude the simple keto tautomer. Thus, the combination of solid‐state NMR and IR results indicate that these silver dialkylphosphite salts probably have a dimer structure. Values of silver and phosphorus CS tensors as well as ¹J(¹⁰⁹Ag, ³¹P) values for a dimer model calculated using the density functional theory (DFT) method are in agreement with the experimental observations. Copyright © 2010 John Wiley & Sons, Ltd.     

SQSQh: 1H‐detected SQ–SQ experiment for determination of signed silicon–carbon coupling constants

A new variant of SQ–SQ pulse sequence (SQSQh) for relative sign determination and detection of small silicon–carbon couplings over more than one bond is presented. In the SQSQh sequence, proton detection replaces carbon detection used in the original SQ–SQ pulse sequence (SQSQc). The theoretical gain in sensitivity was experimentally tested on two samples (trimethylsiloxyethane, 1, and 1,2,4‐tris(trimethylsiloxy)benzene, 2), the experimentally found gain provided by the SQSQh over the SQSQc method varied between 6 and 8. The method can be applied to linear spin systems, i.e. to systems where the silicon is coupled to the carbon in question and to any hydrogen not necessarily bonded to the carbon. Copyright © 2010 John Wiley & Sons, Ltd.