Notes on the Elliptic Ruijsenaars Operators

We construct the spaces that the elliptic Ruijsenaars operators act on. It is shown that they are extensible to nonnegative selfadjoint operators on a space of square integrable functions, or preserve a finite dimensional vector space of entire functions. These facts are shown in terms of the R-operators which satisfy the Yang–lBaxter equation. The elliptic Ruijsenaars operators are considered as the elliptic analogues of the Macdonald operators or the difference analogues of the Lamé operators.     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Entropic criterion for model selection

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

几种改进的CoMFA方法比较研究血小板活化因子拮抗剂

由于传统的比较分子场分析(CoMFA)方法本身存在一些缺陷，使得分子的叠合 规则以及叠合分子的空间取向和空间位置等因素对q~2的影响很大，因此相继提出 了几种改进的CoMFA方法。为了优化CoMFA结果，应用传统的CoMFA方法和交叉验证 的R~2引导的区域选择法(q~2-GRS)、全取向搜索法（AOS）、全空间搜索法（APS） 以及比较分子相似性指数(CoMSIA)等四种改进的CoMFA方法，对18个pinusolide类 衍生物这类新发现的血小板活化因子（PAF）拮抗剂进行了比较研究。结果表明四 种改进的CoMFA方法得到的q~2值均比传统CoMFA的高。q~2-GRS方法得到的q~2值有 所提高，但综合结果并不理想，AOS与APS得到的q~2较为理想，而在CoMSIA中， q~2几乎不受空间取向或空间位置的影响。同时我们引人基于样本的偏最小二乘法 （SAMPLS）取代原AOS／APS程序中的传统PLS进行统计分析，明显提高了其运行速 度。最后，根据q~2最高的CoMFA模型和CoMSIA模型设计了几个预测活性更高的 pinusolide类似物。     

PEG-PLA嵌段共聚物的合成及~(13)C NMR对平均链段长度的测定

本文报道聚乙二醇(PEG)在辛酸亚锡存在下与丙交酯(LA)反应合成PEG-PLA嵌段共聚物,用~(13)C NMR测定了共聚物的结构,估算了平均链段长度.实验结果表明,L_(PEG)在反应过程中保持不变,而L_(PLA)随反应时间和LA在原料配比中含量的增加而增加,呈逐步聚合反应特点.对聚合反应机理作了推测.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.     

A competitive (dual) simplex method for the assignment problem

Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling. - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974).A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx _ij < 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx _ij is shown to converge in at most ( ₂ ^n-1 ) pivots, and at most O(n ³) time, and it is argued that on average the number of pivots is at mostn logn. Dedicated with affection to George B. Dantzig on the occasion of his seventieth birthday.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.