Local Energy Statistics in Spin Glasses

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E _N < β _c N, where β _c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies. Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from Physics and Biology” and by the European Science Foundation in the Programme RDSES.     

Efficient synthetic route toward biologically active γ-carboline derivatives

An efficient and short route was established for the synthesis of anti-bovine viral diarrhea virus agents, namely 4-methyl-γ-carboline (SK4M) 1, 3-methyl-γ-carboline (SK3M) 2, 5-methyl-γ-carboline (SK5M) 3, and a new γ-carboline derivative 4, using thermal electrocyclization reaction as a key step. The evaluation of cytotoxicity of compound 4 against human cervical cancer cell line HeLa and leukemic cell line HL-60 furnished CC₅₀ value of 19.5 and 18.8 µM respectively.     

Fifth-Order Alice-Bob Systems and Their Abundant Periodic and Solitary Wave Solutions*

The study on the nonlocal systems is one of the hot topics in nonlinear science. In this paper, the well-known fifth-order integrable systems including the Sawada-Kotera (SK) equation, the Kaup-Kupershmidt (KK) equation and the fifth-order Koterweg-de Vrise (FOKdV) equation are extended to a generalized two-place nonlocal form, the generalised fifth-order Alice-Bob system. The Lax integrability of two sets of Alice-Bob systems for all the SK, KK and FOKdV type systems are explicitly given via matrix Lax pairs. The $\hat{P}\hat{T}$ symmetry breaking and symmetry invariant periodic and solitary waves for one set of nonlocal SK, KK and FOKdV system are investigated via a special travelling wave solution ansatz.     

Lie symmetries of soliton equations with self-consistent sources via source generation procedure

In this paper, the ‘source generation’ procedure (SGP) proposed by Hu and Wang [X.B. Hu, H.Y. Wang, Construction of dKP and BKP equation with self-consistent sources, Inverse Problems 22 (2006) 1903-1920] is utilized to derive Lie symmetries of bilinear soliton equations with self-consistent sources (SESCS) such as KPESCS, BKPESCS, and differential-difference KPESCS. Furthermore, it is shown that these Lie symmetries constitute generators of the corresponding Lie symmetry algebras.     

Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.     

Pharmacokinetic studies of a novel tubulin inhibitor SK1326 in rat plasma by UPLC–MS/MS

A sensitive method for quantitation of SK1326 in rat plasma has been established using ultra-performance liquid chromatography–electrospray ionization tandem mass spectrometry (UPLC–ESI/MS/MS). SK1326 and the internal standard (tramadol) in plasma sample were extracted using acetonitrile. A centrifuged upper layer was then evaporated and reconstituted with a mobile phase of 0.5% formic acid–acetonitrile (35:65, v/v). The reconstituted samples were injected into a C₁₈ reversed-phase column. Using MS/MS in the multiple reaction monitoring mode, SK1326 and tramadol were detected without severe interference from the rat plasma matrix. SK1326 produced a protonated precursor ion ([M + H]⁺) at m/z 432.3 and a corresponding product ion at m/z 114.4. The internal standard produced a protonated precursor ion ([M + H]⁺) at m/z 264.4 and a corresponding product ion at m/z 58.1. Detection of SK1326 in rat plasma by the UPLC–ESI/MS/MS method was accurate and precise with a quantitation limit of 1.0 ng/mL. The validation, reproducibility, stability and recovery of the method were evaluated. The method has been successfully applied to pharmacokinetic studies of SK1326 in rat plasma. The pharmacokinetic parameters of SK1326 were evaluated after intravenous (at a dose of 10 mg/kg) and oral (at a dose of 20 mg/kg) administration of SK1326 in rats. After oral administration (20 mg/kg) of SK1326, the F (fraction absorbed) value was ~77.1%.     

Electrosynthesis of Poly(3,4-ethylenedioxythiophene) and Its Composite with a Polymer Perfluorinated Sulfo-Cationite from Water–Acetonitrile Solutions

Films of poly(3,4-ethylenedioxythiophene) (PEDT) are synthesized during anodic polarization from a water-acetonitrile mixture containing sulfo-cationite MF-4SK and without it. A comparison of electrochemical and spectroelectrochemical characteristics of the films and an elemental analysis evidence the formation of composite PEDT–MF-4SK. The immobilization of the polymer anion in the PEDT matrix is shown to alter its oxidation mechanism. For a neutral composite film, this mechanism includes the exit of sulfo-cationite cations and the entering of supporting anions.     

On mean field equations for spin glasses

In this paper we study rigorously the random Ising model on a Cayley tree in the limit of infinite coordination numberz 8. An iterative scheme is developed relating mean magnetizations and mean square magnetizations of successive shells far removed from the surface of the lattice. In this way we obtain local properties of the model in the (thermodynamic) limit of an infinite number of shells. When the coupling constants are independent Gaussian random variables the SK expressions emerge as stable fixed points of our scheme and provide a valid local mean-field theory of spin glasses in which negative local entropy (at low temperatures) while perfectly possible mathematically may still perhaps be physically undesirable. Finally we examine the TAP equations and show that if the average over bond disorder and the limitz 8 are actually performed, one recovers our iterative scheme and hence the SK equations also in the thermodynamic limit.On leave from Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia.     

基于FLUENT的水平管道稠油掺稀均质化流场模拟

掺稀降黏输送是常用的稠油管道输送工艺,稀油通过分散和溶解作用降低稠油黏度。然而,稠油黏度较高,稀稠油是否混合均匀将直接影响降黏效果。国内外学者对竖直井筒中稠油掺稀举升的混合方式和效果多有研究,但针对水平管道掺稀方式及入口速度和掺稀比对混合效果的影响却鲜有报道,故本文基于计算流体动力学理论,建立了水平管道稠油掺稀模型,着重分析了稠油入口速度、掺稀比以及加装静态混合器对混合效果的影响,研究结果表明:水平管道稠油掺稀流动过程中,稠油、稀油混合不均匀,形成稠油、混合油、稀油的分层流动形态;稠油进口速度不能改善分层流动现象,对稠油、稀油的混合均匀性影响较小;改变掺稀比不能有效改善稠油、稀油的混合效果;在管道内加装3组SK组件能实现稠油、稀油的最优混合;SK静态混合组件能极大程度地提高混合油品在管道内的湍动能,促进稠油、稀油均匀混合。本文的研究成果对改善稠油水平掺稀的混合均匀性,提高降黏效率有重要意义。