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 i...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.)展开更多
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 an...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.展开更多
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 con...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.展开更多
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 quasi...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.展开更多
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 mol...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.展开更多
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 molecule...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.展开更多
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 (...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.展开更多
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 Henn...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.展开更多
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, ...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.展开更多
文摘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.)
基金Supported by the National Programfor the BasicScience Researches of China(G19990751)
文摘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.
文摘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.
文摘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.
文摘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.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0402300)the National Natural Science Foundation of China(Grant No.U1732133)the Science Fund from Chinese Academy of Sciences(Grant No.11320101003)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1332204,11274291,and 11320101003)
文摘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.
文摘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.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos. 61572335, 61472263, 61402312 and 61402313, the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20151223, and the Collaborative Innovation Center of Novel Software Technology and Industrialization, Jiangsu, China.
文摘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.