结构相角二阶代数式的应用：Ⅱ.正交空间群二阶式及其应用

以作者在前文中提出的单相角二阶代数式的推导方法为依据,在完成三斜、单斜空间群推导结果的基础上,进而又完成了正交晶系59个空间群二阶式的推导,从而提供了低级晶系(三斜、单斜和正交)全部74个空间群的简明、完备的二阶代数式运算用表。对三个晶体结构进行了相角估算,结果较好。文中提出了代数法应用的新特点,即“一种类型相角可用多种二阶式求得,多种类型相角也可用一种二阶式求算”。     

Criticality and phase transitions in ionic fluids

Recent experimental investigations of criticality and phase separation in ionic fluids have revealed behavior of great theoretical interest. In seeking to understand the experiments, some of which appear to exhibit argonlike criticality and some of which exhibit classical (mean-field) criticality, a convenient starting point is the restricted primitive model (RPM) of symmetrically charged hard spheres, all of equal diameter , each sphere bearing a positive or negative charge of magnitudeq. There is overall charge neutrality, so that the expected number densities of the anions and cations are equal, ₊= _-. Studies of RPM charge-charge and density-density correlation functions indicate that the fluctuation-suppressing mechanism that yields mean-field critical behavior in nonionic systems with long-range interparticle potentials is not operative in the RPM. On the basis of plausible assumptions, Ising-like behavior is instead expected. The above work is summarized. New work of Zhang and the author is outlined, showing that when one loses the RPM symmetry (through, e.g., different valence, diameter, or dipole moment of anions and cations) a strong coupling between charge-charge and density-density correlation ensues. The way in which this can be expected to give rise to mean-field or mean-field-like behavior is noted. Other new observations concern the mean-field analogy found by Høye and the author between the parameter 2/(d–2) (d is the dimensionality) in that model and the monomer number in high polymers, with respect to the coexistence-curve shape dependence on those parameters.     

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.     

Small Changes,Big Impact: Tungsten Bronzes with Extremely Large Second Harmonic Generation Achieved by the Transition Metal Doping on the B-Site

Two novel transition metal-doped tungsten bronze oxides, Pb_2.15Li_0.85Nb_4.85Ti_0.15O₁₅ (PLNT) and Pb_2.15Li_0.55Nb_4.85W_0.15O₁₅ (PLNW), are synthesized by high-temperature solid-state reactions. The Rietveld method using the high-resolution synchrotron radiation indicates that PLNT and PLNW crystallize in the orthorhombic polar noncentrosymmetric space group, Pmn2₁ (no. 31). As a class of tungsten bronze oxide, PLNT and PLNW retain a unique rigid framework composed of d⁰ transition metal cation (Ti⁴⁺ or W⁶⁺)-doped highly distorted NbO₆ octahedra along with the subsequently generated Pb/LiO₁₂ and PbO₁₅ polyhedra. Interestingly, the d⁰ transition metal-doped tungsten bronzes, PLNT and PLNW, exhibit extremely large second-harmonic generation (SHG) responses of 56 and 67 × KH₂PO₄, respectively. The observed immeasurably strong SHG is mainly attributed to a net polarization originating from the alignment of highly distorted NbO₆ octahedra with doped transition metals in the frameworks. It is believed that doping transition metal cations at the B-site of the tungsten bronze structures should be an innovative strategy to develop novel high-performance nonlinear optical materials.     

一种宽带注入锁定三倍频器

文章提出了一种宽带注入锁定三倍频器。在传统注入方式基础上,倍频器采用了推-推差分对输入信号进行二倍频,并将产生的二次谐波通过变压器耦合至注入管的源极共模点,增强了注入管源极共模点二次谐波。由于注入电流是由注入信号与源极共模点二次谐波进行混频而产生,因此注入电流也被增强,从而增大了锁定范围。除此之外,三倍频采用了四阶谐振器,谐振阻抗的相位在过零点被平坦化,锁定范围进一步被增大。采用标准CMOS 65 nm工艺设计三倍频,芯片面积为720×670 μm²,1.2-V供电时的功耗为15.2 mW。0 dBm注入功率下三倍频的锁定范围为19.2~27.6 GHz,对应的基波抑制比大于25 dB,二次谐波抑制大于35 dB。注入锁定三倍频器可满足5G收发机中本振源的要求。     

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。     

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.