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.

Ab initio study of C-9 and LaC9+ clusters

The energies and geometries of C-9 and LaC9+ clusters were calculated at HF, MP2 and DFT levels. For C-9, all theoretical levels show that the linear chain is the most stable structure. For LaC9+, two isomers were considered. In the first case La has two single bonds (A), while it forms a double bond in the second (B). Our results showed that in HF calculation, B is marginally more stable than A, while for MP2 and DFT, A is favored. Our results also revealed that there is not enough space for C-9 ring to accommodate lanthanum. Our conclusion agrees well with experiment.

Heterogenization of heteropolyacids: A general discussion on the preparation of supported acid catalysts

Heteropolyacids (HPAs) possess both acidic and redox catalytic properties and held extensive promise of practical application. These type of compound display a great potential of specific synthesis reactions for replacing sulfuric acid to satisfy the requirements of environmental protection. Heterogenizing HPAs would not only make them more useful in liquid phase oxidation with oxygen and in acid-catalyzed reaction, as the catalyst is often difficult to separate from the reaction products, but also create favorable factors for realizing heterogenization of homogeneous reaction and even utilizing new technology of catalytic distillation. In this paper, different kinds of porous materials which are well characterized, including oxides such as Al2O3, SiO2, TiO2, diatomite, bentonite, and active carbon of different sources, were used as support for heterogenizing HPAs (in different media), and the obtained results, the intrinsic characters of supports which may influence both the nature of the interaction between HPAs and supports in the heterogenization and the activity in the catalytic reaction, are explored. It is expected that these can provide a referential model for preparing supported acid catalyst used in liquid phase.

Electron collision cross sections and rate coefficients for the Na-like Cu ion

Collision cross sections are calculated using the R-matrix method for excitations between the three lowest LS states for Na-like Cu ion. The complex resonance structures are investigated. The collision rate coefficients have been calculated assuming a Maxwellian distribution of electron-impact energies. The results of the collision cross sections are in good agreement with those of the other theory.

THE APPLICATION OF AN ULTRAMICROELECTRODE IN HOMOGENEOUS CATALYTIC REACTION .1. GENERAL CHARACTERISTIC OF A HOMOGENEOUS CATALYTIC REACTION AT AN ULTRAMICROELECTRODE WITH ARBITRARY GEOMETRY UNDER STEADY-STATE

A general characteristic of the electrochemical process coupling with a homogeneous catalytic reaction at an ultramicroelectrode under steady state is described. It was found that the electrochemical process coupling with homogeneous catalytic reaction has a similar steady state voltammetric wave at an ultramicroelectrode with arbitrary geometry. A method of determination for the kinetic constant of homogeneous catalytic reaction at an ultramicroelectrode with arbitrary geometry is proposed.

THE GENERAL AN INDEX AND ITS APPLICATION .4. THE APPLICATION OF GENERAL AN INDEX TO HYDROCARBONS

The general a(N) index (GAI) was used to characterize the cis, trans isomers of hydrocarbons. The best one-variable equations were obtained with GAI for several physicochemical properties of seven pairs of olefin cis, trans isomers. The linear correlation coefficients are in the range of 0.975 to 0.997. GAI was also compared with the other five topological indices, Randic connectivity index chi, Wiener number W, Hosoya index Z, the average distance sum connectivity J proposed by Balaban and a(N) index introduced by Yang, in correlating with the octane number (MON) of heptanes and octanes.

AN ALGEBRAIC METHOD TO ESTIMATE GENERAL TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

ADVANCED ELECTROANALYTICAL CHEMISTRY IN CHINA .1. GENERAL ASPECT AND SOME METHODOLOGIES

The Research on Electroanalytical chemistry in China started mainly from the beginning of new China in 1949. It has already good basis and development nowadays. A review with references to the end of seventies has been published in "Reviews in Analytical Chemistry" 1) and in a book titled "Fifty years of Chinese Chemistry" edited by the Chinese Chemical Society in 1985 2). Since then more than thousand papers have been published, and it is impossible and also not necessary to describe all of them. This review only deals with the main progress of electroanalytical chemistry in China in recent years. Some new developed methodologies will be reviewed by S. Dong in the next article.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .2. THE CORRELATION BETWEEN THE GENERAL ALPHA-N INDEX AND PHYSICAL-PROPERTIES OF NEUTRAL PHOSPHORUS-COMPOUNDS

The relationship between the alpha-N index and physical properties of neutral phosphorus extractants is studied. Using the general alpha-N index which could describe extractants with minute difference in structure, the good correlation between it and various physical properties of the neutral phosphorus extractants (e.g., densities, refractive index, shift ratio of paper chromatography and IR frequencies of bond P = O) is obtained. The result indicates that general alpha-N index is a good topological index of organic compounds.

GENERAL ALPHA-N INDEX AND ITS APPLICATION .1. GENERAL ALPHA-N INDEX AND ITS APPLICATION IN THE EXTRACTION OF Y, CE, U, AND TH BY NEUTRAL PHOSPHORUS EXTRACTANCTS

The general a(N) index is established for molecules containing heteroatoms, rings, and multiple bonds. The general a(N) index is able to describe molecules with minute differences in structure and can also reveal the properties of molecules. This theory is successfully applied to the case of neutral phosphorus extractants. Both the molecular polarity and steric effect are characterized by the general a(N) index. The relationships between these properties and the distribution ratios for extracting Y, Ce, U, and Th are also shown by the general a(N) index.

Dielectric response of graded composites having general power-law-graded cylindrical inclusions

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation epsilon(i)(r)=c(b+r)(k) (where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile epsilon(i)(r) = cr(k) and a linear dielectric profile epsilon(i)(r) = c(b + r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b -> 0 and k -> 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, epsilon(i)(r)=c(b+r)(k)e(beta r). (c) 2005 American Institute of Physics.

Effective dielectric responses of graded composites of the particles with a general power-law gradation profile

The effective dielectric response of graded spherical composites having general power-law gradient inclusions is investigated under a uniform applied electric field, where the dielectric gradation profile of the spherical inclusions is modeled by the equation epsilon(i) (r) = c(b+r)(k). Analytical solutions of the local electrical potentials are derived in terms of hyper-geometric function and the effective dielectric response of the graded composites is predicted in the dilute limit. From our result, the local potentials of graded spherical composites having both simple power-law dielectric profile epsilon(i)(r) = cr(k) and linear dielectric profile epsilon(i) (r) = c(b+r) are derived exactly by taking the limits b --> 0 and k --> 1, respectively. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites, and it is shown that the DEDA is in excellent agreement with exact result. (C) 2005 Elsevier B.V. All rights reserved.

Viewing DVM via general behaviors of zooplankton: A way bridging the success of individual and population

In this paper, we viewed the diel vertical migration (DVM) of copepod in the context of the animal's immediate behaviors of everyday concerns and constructed an instantaneous behavioral criterion effective for DVM and non-DVM behaviors. This criterion employed the function of 'venturous revenue' (VR), which is the product of the food intake and probability of the survival, to evaluate the gains and losses of the behaviors that the copepod could trade-off. The optimal behaviors are to find the optimal habitats to maximize VR. Two types of VRs are formulated and tested by the theoretical analysis and simulations. The sensed VR, monitoring the real-time changes of trade-offs and thereby determining the optimum habitat, is validated to be the effective objective function for the optimization of the behavior; whereas, the realized VR, quantifying the actual profit obtained by an optimal copepod in the sensed-VR-determined habitat, defines the life history of a specific age cohort. The achievement of a robust copepod overwintering stock through integrating the dynamics of the constituent age cohorts subjected to the instantaneous behavioral criterion for DVM clearly exemplified a possible way bridging the immediate pursuit of an individual and the end success of the population. (c) 2005 Published by Elsevier Ltd.