Point Groups and Single Forms of Quasicrystals with Eightfold and Twelvefold Symmetry

This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.

Plane Elasticity and Dislocation of One-Dimensional Hexagonal Quasicrystals with Point Group 6

Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)

Morita Equivalent Blocks in Subgroups of Finite Groups

Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.

Late Palaeogene palynoflora from Point Hennequin of the Admiralty Bay,King George Island,Antarctica with reference to its stratigraphical significance

The present paper is to discuss the geological age and sedimentary environment based mainly on the characteristics of the palynological assemblage in the intercalated tuffaceous sand mudstones of the Upper Point Hennequin Group in the Admirelty Bay, King George Island, Antarctica. More than 40 species, mainly the Late Paleogene plant community in Gondwana and belonging to Weddellian biogeographic Province, were encountered within the volcano sedimentary rocks of the Upper Point Hennequin Group. The index member is the genus Nothofagidites . The occurrence of N. cf. saraensis and N. cf. flemingii and the absence of Proteacidites spp. indicates that the sporopollen bearing rocks is of Oligocene age, which were deposited in a limnetic zone near medium lower mountains environment with warm and humid climate.

A new group contribution-based method for estimation of flash point temperature of alkanes

Flash point is a primary property used to determine the fire and explosion hazards of a liquid. New group contribution-based models were presented for estimation of the flash point of alkanes by the use of multiple linear regression(MLR)and artificial neural network(ANN). This simple linear model shows a low average relative deviation(AARD) of 2.8% for a data set including 50(40 for training set and 10 for validation set) flash points. Furthermore, the predictive ability of the model was evaluated using LOO cross validation. The results demonstrate ANN model is clearly superior both in fitness and in prediction performance.ANN model has only the average absolute deviation of 2.9 K and the average relative deviation of 0.72%.

New Exact Solutions and Conservation Laws to （3＋1）-Dimensional Potential-YTSF Equation

Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.

NOTE ON CALCULATING WIENER NUMBERS OF MOLECULAR GRAPHS WITH SYMMETRY

The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.

Selection rules for electric multipole transition of triatomic molecule in scattering experiments

In the electron or x-ray scattering experiment,the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions,while the corresponding selection rules for triatomic molecules have not been clearly elucidated.In this work,based on the molecular point group,the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered.Based on the summarized selection rules,the electron energy loss spectra of H2O,CO2,and N2O are identified,and the momentum transfer dependence behaviors of their valence-shell excitations are explained.

AN IMPLEMENTATION OF FAST ALGORITHM FOR ELLIPTIC CURVE CRYPTOSYSTEM OVER GF(p)

The design and implementation of fast algorithms related to Elliptic Curve Cryptography (ECC) over the field GF(p), such as modular addition, modular subtraction, point addition, point production, choice of embedding plaintext to a point, etc. are given. A practical software library has been produced which supports variable length implementation of the ECCbased ElGamal cryptosystem. More importantly, this scalable architecture of the design enables the ECC being used in restricted platforms as well as high-end servers based on Intel Pentium CPU. Applications such as electronic commerce security, data encryption communication, etc.are thus made possible for real time and effective ECC.

Selection rules for electric multipole transition of diatomic molecule in scattering experiments

The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules （also known as optical selection rules）. However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.

General Formulations of Finite-field Method Classifiedby Symmetry for Molecular Linear and Nonlinear Polarizabilities

The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.

Topological entropy of sets of generic points for actions of amenable groups

Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).

Discovering Functional Organized Keyword Recommendation Point of Interest Groups for Spatial

A point of interest （POI） is a specific point location that someone may find useful. With the development of urban modernization, a large number of functional organized POI groups （FOPGs）, such as shopping malls, electronic malls, and snacks streets, are springing up in the city. They have a great influence on people＇s lives. We aim to discover functional organized POI groups for spatial keyword recommendation because FOPGs-based recommendation is superior to POIs-based recommendation in efficiency and flexibility. To discover FOPGs, we design clustering algorithms to obtain organized POI groups （OPGs） and utilize OPGs-LDA （Latent Dirichlet Allocation） model to reveal functions of OPGs for further recommendation. To the best of our knowledge, we are the first to study functional organized POI groups which have important applications in urban planning and social marketing.

Homochirality in Ferroelectrochemistry

What is the most favorite and original chemistry developed in your research group?We originally proposed the design principle for molecular ferroelectrics:ferroelectrochemistry,including quasi-spherical theory,the introduction of homochirality,and H/F substitution.Ferroelectrochemistry changed the blind search for molecular ferroelectrics into targeted chemical design,which will develop into a new discipline.