Characterization of partially transesterified poly(beta-hydroxyalkanoate)s using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used for the characterization of a partially transesterified poly(beta-hydroxyalkanoate), PHA, polymer produced by the bacterial strain Alcaligenes eutrophus using saponified vegetable oils as the sole carbon sources. The transesterification was carried out separately under acidic and basic conditions to obtain PHA oligomers weighing less than 10 kDa. The intact oligomers were detected in their cationized [M + Na](+) and [M + K](+) forms by MALDI-TOFMS. A composition analysis, using the MALDI-TOF spectra, indicate that the oligomers obtained via acid catalysis were terminated with a methyl 3-hydroxybutyrate end group, and those obtained by base catalysis had a methyl crotonate (olefinic) termination. In addition to HB (hydroxy butyrate), the oligomers were found to contain a small percentage of HV (hydroxy valerate). This was independently confirmed using gas chromatography/mass spectrometry (GC/MS). In comparison, the analysis of a commercial PHA polymer, transesterified under identical conditions, only showed the presence of HB, i.e. a pure PHB homopolymer. Copyright 1999 John Wiley & Sons, Ltd.     

Phase transitions in electron systems with short-range pairing interactions: Ground state

We propose a real-space, tight-binding model of electrons with short-range pairing interactions. The model involves a competition between the ordinary single particle hoppingt and an attractive interactionV between the singlet electronic pairs formed on neighboring lattice sites. The Hamiltonian effectively describes a mechanism for pair formation. We study the ground-state properties of its onedimensional version using numerically exact finite chain calculations for up toN= 10 sites. The ground-state wave functions, the energy spectrum, and various ground-state correlation functions are calculated with the help of an exactly equivalent system of two coupledS=1/2 spin chains. The results indicate the existence of a transition between the band and the localized pairs situation. The transition takes place forV/t= 1.4–0.1 and appears to be of essential singularity type. Comparison with other models used for pairing phenomena, like the negativeU-Hubbard model is made.     

More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) ⁿ , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt ², where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.     

A three-parameter Hopf deformation of the algebra of Feynman-like diagrams*

We construct a three-parameter deformation of the Hopf algebra LDIAG. This is the algebra that appears in an expansion in terms of Feynman-like diagrams of the product formula in a simplified version of quantum field theory. This new algebra is a true Hopf deformation which reduces to LDIAG for some parameter values and to the algebra of matrix quasi-symmetric functions (MQSym) for others, and thus relates LDIAG to other Hopf algebras of contemporary physics. Moreover, there is an onto linear mapping preserving products from our algebra to the algebra of Euler–Zagier sums.     

Combinatorial Coherent States via Normal Ordering of Bosons

We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to be moments of positive functions. Consequently, the resulting coherent states automatically satisfy the resolution of unity condition. In addition they display such non-classical fluctuation properties as super-Poissonian statistics and squeezing.     

漫谈有效数字和计算器

介绍了有效数字的概念及其计算规则,介绍了计算器的一般特性及使用技巧,并给出计算实例.     

速度算符和电子的颤动

指出了国外某些量子力学教材中关于速度算符的概念错误和相对论自由电子进行颤动的错误,分析了错误的原因.