Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

Perturbation analysis of theGI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.     

Analytic expression of the second derivatives of electronic energy for full configuration interaction wave functions

Summary A new analytic second derivative expression of the electronic energy is derived for full configuration interaction (CI) wave functions. This formula is shown to be free from the derivative terms of both CI and MO coefficients. The second-order relationships between CI and MO coefficients for full CI wave functions are also presented.     

富勒烯及其衍生物的质谱研究

本文制备了一系列富勒烯及其衍生物，并利用多种质谱技术进行了鉴定、表征、揭示了它们在离子源条件下的稳定性及解规律。这些富勒烯及其省生物在ＦＤＭＳ、ＩＳＭＳ中均得到了较强的准分子离子峰且碎片峰很少。结果表昨ＦＤＭＳ，ＬＳＩＭＳ技术均适于富勒烯及其衍生物的定性分析，是目前富勒烯分析鉴定中较好的方法。     

Synthesis and characterization of thermally crosslinked polyimide with second-order nonlinear optical chromophore

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Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Strategies to enhance the enzymatic hydrolysis of pretreated softwood with high residual lignin content

Pretreatment of Douglas-fir by steam explosion produces a substrate containing approx 43% lignin. Two strategies were investigated for reducing the effect of this residual lignin on enzymatic hydrolysis of cellulose: mild alkali extraction and protein addition. Extraction with cold 1% NaOH reduced the lignin content by only approx 7%, but cellulose to glucose conversion was enhanced by about 30%. Before alkali extraction, addition of exogenous protein resulted in a significant improvement in cellulose hydrolysis, but this protein effect was substantially diminished after alkali treatment. Lignin appears to reduce cellulose hydrolysis by two distinct mechanisms: by forming a physical barrier that prevents enzyme access and by non-productively binding cellulolytic enzymes. Cold alkali appears to selectively remove a fraction of lignin from steam-exploded Douglas-fir with high affinity for protein. Corresponding data for mixed softwood pretreated by organosolv extraction indicates that the relative importance of the two mechanisms by which residual lignin affects hydrolysis is different according to the pre- and post-treatment method used.     

A Density Functional Theory Study on Electronic Structure and Second—order Nonlinear Optical Properties of Some Push—Pull Molecules

Time-dependent density-functional theory(TDDFT)has been applied to calculate the electronic structure and second-order nonlinear optical(NLO) properties of some organic molecules.The two-dimensional(2-D)charge transfer charateristics of calculated molecules were studied and compared with corresponding experimental results.All the theoretical results agree well with the measurement.For 2-D molecule with two-fold symmetry,the dominant charge transfer is off-diagonal,while for three-fold symmetry 2-D molecule,the dominant charge transfer is not only between branches and central group but also among branches.