General expression for probabilistic estimation of multiphase structure invariants in the case of a native protein and multiple derivatives. Application to estimates of the three-phase structure invariants

Concise probabilistic formulae with definite crystallographic implications are obtained from the distribution for eight three-phase structure invariants (3PSIs) in the case of a native protein and a heavy-atom derivative [Hauptman (1982). Acta Cryst. A38, 289-294] and from the distribution for 27 3PSIs in the case of a native and two derivatives [Fortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646-651]. The main results of the probabilistic formulae for the four-phase structure invariants are presented and compared with those for the 3PSIs. The analysis directly leads to a general formula of probabilistic estimation for the n-phase structure invariants in the case of a native and m derivatives. The factors affecting the estimated accuracy of the 3PSIs are examined using the diffraction data from a moderate-sized protein. A method to estimate a set of the large-modulus invariants, each corresponding to one of the eight 3PSIs, that has the largest \Delta\ values and relatively large structure-factor moduli between the native and derivative is suggested, which remarkably improves the accuracy, and thus a phasing procedure making full use of all eight 3PSIs is proposed.

Aharonov-Bohm oscillation and chirality effect in optical activity of single-wall carbon nanotubes

We study the Aharonov-Bohm effect in the optical phenomena of single-wall carbon nanotubes (SWCN) and also their chirality dependence. Especially, we consider the natural optical activity as a proper observable and derive its general expression based on a comprehensive symmetry analysis, which reveals the interplay between the enclosed magnetic flux and the tubule chirality for arbitrary chiral SWCN. A quantitative result for this optical property is given by a gauge invariant tight-binding approximation calculation to stimulate experimental measurements.

Nitrogen vacancy scattering in GaN grown by metal-organic vapor phase epitaxy

Electron mobility limited by nitrogen vacancy scattering was taken into account to evaluate the quality of n-type GaN grown by metal-organic vapor phase epitaxy. Two assumptions were made for this potential for the nitrogen vacancy (1) it acts in a short range, and (2) does not diverge at the vacancy core. According to the above assumptions, a general expression to describe the scattering potential U(r) = - U-0 exp[- (r/beta)(n)], (n = 1, 2,...,infinity) was constructed, where beta is the potential well width. The mobilities for n = 1, 2, and infinity were calculated based on this equation, corresponding to the simple exponential, Gaussian and square well scattering potentials, respectively. In the limiting case of kbeta << 1 (where k is the wave vector), all of the mobilities calculated for n = 1, 2, and infinity showed a same result but different prefactor. Such difference was discussed in terms of the potential tail and was found that all of the calculated mobilities have T-1/2 temperature and beta(-6) well width dependences. A mobility taking account of a spatially complicate scattering potential was studied and the same temperature dependence was also found. A best fit between the calculated results and experimental data was obtained by taking account of the nitrogen vacancy scattering. (C) 2002 Elsevier Science Ltd. All rights reserved.

General Relationship Between Contact Stiffness, Contact Depth, and Mechanical Properties for Indentation in Linear Viscoelastic Solids Using Axisymmetric Indenters of Arbitrary Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. Although the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. Furthermore, the same expression holds true for both fast loading and unloading. These results should provide a sound basis for using the relationship for determining properties of viscoelastic solids using indentation techniques.

Signal bandwidth of general N x N multimode interference couplers

Analytical expression of signal bandwidth of general straight and tapered N x N multimode interference (MMI) couplers is presented. The signal bandwidth is characterized as a function of mode relative energy, mode propagation delay time, and mode pulse broadening in the multimode section of MMI coupler. The model is used to evaluate the signal bandwidth of specific couplers. Results indicate that the signal bandwidth decreases seriously with the increase of channel number and channel guide space. Compared with the straight MMI coupler, the tapered MMI coupler has an improved signal bandwidth.

Faddeev-Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

Study on the apoptosis and Bcl-2/Bax expression of human hepatoma SMMC-7721 cells after exposure to heavy-ion and X-ray irradiations

This study is aimed at observing the apoptosis and Bcl-2/Bax gene expression of mammalian cells following heavy-ion and X-ray irradiations. Exponentially growing human hepatoma SMMC-7721 cells cultured in vitro were irradiated with a C-12 ion beam of 50 MeV/u (corresponding to a LET value of 44.56 keV/mu m) from Heavy Ion Research Facility in Lanzhou (HIRFL) at doses varying from 0 to 3 Gy. The X-ray irradiation (8 MV) was performed in the therapy unit of the General Hospital of the Lanzhou Military Area. Survival fractions of irradiated cells at various doses were measured by means of MTT assay. Apoptotic cells after irradiation were analyzed with fluorescence microscope and flow cytometer (FCM). Immuno-histological assay were applied to detect the expression of Bcl-2/Bax genes in the irradiated cells. The survival fraction of SMMC-7721 cells decreased gradually (vs. control p<0.05) with increasing the dose of the carbon ion beam more obviously than X-ray irradiation, and the carbon ion irradiation efficiently induced cell apoptosis and significantly promoted the expression of Bax gene while Bcl-2 gene expression was restrained. High-LET heavy ion beam would induce cell apoptosis effectively than low-LET X-ray, and the apoptosis rate is correlated with the transcription of Bcl-2/Bax and the ratio of Bcl-2/Bax in human hepatoma SMMC-7721 cells after irradiation to heavy ion beam.