New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is presented. Finally, the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.     

（2＋2）-Dimensional Discrete Soliton Equations and Integrable Coupling System

In this paper, we extend a （2＋2）-dimensional continuous zero curvature equation to （2＋2）-dimensional discrete zero curvature equation, then a new （2＋2）-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the （2＋2）-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl（4）.     

Higher-Dimensional Lie Algebra and New Integrable Coupling of Discrete KdV Equation

Based on semi-direct sums of Lie subalgebra \tilde{G}, a higher-dimensional 6 x 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derivedfrom a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity --- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we provethat the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.     

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.     

NMR Reveals Non‐Distributed and Uniform Character of Network Chain Dynamics

Results of different NMR investigations of elastomers are reviewed with respect to their significance for statistical models of rubber elasticity. In contrast to earlier work based on lineshape analysis and relaxometry, results of recent multiple‐quantum experiments indicate that the NMR‐detected dynamic chain order parameter, which reflects the conformational space of individual monomer units at which the signal is detected locally, is a rather narrowly distributed quantity. Constraints to the dynamics and the conformations of a network chain thus act uniformly and appear as a dynamic average over chains of different length and with different end‐to‐end separations. All our findings are in good agreement with large‐scale computer simulations. Anomalies on swelling such as chain desinterspersion at the early stages and the appearance of heterogeneities, are also discussed.

     

残留偶极耦合及其在蛋白质结构研究中的应用

近年来溶液中残留偶极耦合常数被用来获取生物大分子化学键之间相对取向等长程构象约束条件,用于计算或优化蛋白质及其复合物的三维空间结构. 介绍了用异核多维NMR技术测量残留偶极耦合常数的方法,及其在蛋白质结构计算中的一些应用：优化蛋白质溶液结构,评价蛋白质结构质量,确定蛋白质结构域取向,获取有关配体的构象和取向的信息,在缺乏NOE数据时构建蛋白质结构等.      

Integrable Couplings of the Coupled Burgers Hierarchy

In this letter, a new loop algebra G is constructed, from which a new isospectral problem is established. It follows that integrable couplings of the well-known coupled Burgers hierarchy are obtained.     

Multi-component SC Lax Integrable Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System with Two Arbitrary Functions

A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy.     

Sensitivity- and Gradient-Enhanced Hetero (ω1) Half-Filtered TOCSY Experiment for Measuring Long-Range Heteronuclear Coupling Constants

An enhanced version of the X(ω₁) half-filtered TOCSY experiment for measurement of long-range heteronuclear coupling constants is proposed which yields high-quality spectra with substantially increased sensitivity and resolution. The modified method features gradient-enhanced X filtering sequences, broadband homonuclear decoupling duringt₁, optional¹J_XHscaling in theF₁domain, and gradient coherence selection in combination with the sensitivity-enhanced protocol for the TOCSY transfer. These modifications extend the applicability of the method—coupling constants can be measured accurately for natural abundance samples at low concentrations and for compounds yielding complex spectra. Computer-aided analysis of E.COSY-type multiplets is applied for the determination of heteronuclear long-range coupling constants.     

Hyperfine coupling tensors of the benzosemiquinone radical anion from Car-Parrinello molecular dynamics.

Based on Car-Parrinello ab initio molecular dynamics simulations of the benzosemiquinone radical anion in both aqueous solution and the gas phase, density functional calculations provide the currently most refined EPR hyperfine coupling (HFC) tensors of semiquinone nuclei and solvent protons. For snapshots taken at regular intervals from the molecular dynamics trajectories, cluster models with different criteria for inclusion of water molecules and an additional continuum solvent model are used to analyse the HFCs. These models provide a detailed picture of the effects of dynamics and of different intermolecular interactions on the spin-density distribution and HFC tensors. Comparison with static calculations allows an assessment of the importance of dynamical effects, and of error compensation in static DFT calculations. Solvent proton HFCs depend characteristically on the position relative to the semiquinone radical anion. A point-dipolar model works well for in-plane hydrogen-bonded protons but deviates from the quantum chemical values for out-of-plane hydrogen bonding.