The abundance of neutral hydrogen（HI）in satellite galaxies in the local group is important for studying the formation history of our local group.In this work,we generated mock HI satellite galaxies in the Local Grou...The abundance of neutral hydrogen（HI）in satellite galaxies in the local group is important for studying the formation history of our local group.In this work,we generated mock HI satellite galaxies in the Local Group using the high mass-resolution hydrodynamic APOSTLE simulation.The simulated HI mass function agrees with the ALFALFA survey very well above 10~6M_⊙,although there is a discrepancy below this scale because of the observed flux limit.After carefully checking various systematic elements in the observations,including fitting of line width,sky coverage,integration time and frequency drift due to uncertainty in a galaxy’s distance,we predicted the abundance of HI in galaxies in a future survey that will be conducted by FAST.FAST has a larger aperture and higher sensitivity than the Arecibo telescope.We found that the HI mass function could be estimated well around 10~5M_⊙ if the integration time is 40 minutes.Our results indicate that there are 61 HI satellites in the Local Group and 36 in the FAST field above 10~5M_⊙.This estimation is one order of magnitude better than the current data,and will put a strong constraint on the formation history of the Local Group.Also more high resolution simulated samples are needed to achieve this target.展开更多
The lack of Birkhoff theorem in finite-range gravitation reveals nonzero acceleration of the test body inside the massive spherical shell, as well as breakdown of screening inside the charged conductor gives rise to a...The lack of Birkhoff theorem in finite-range gravitation reveals nonzero acceleration of the test body inside the massive spherical shell, as well as breakdown of screening inside the charged conductor gives rise to acceleration of the test charge. An application of this effect to the motion of galaxies in Local Group allows to constraint quintessence parameter in some massive gravitational theories.展开更多
Let R be an associative ring with identity. R is said to be semilocal if R/J（R） is （semisimple） Artinian, where J（R） denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions ...Let R be an associative ring with identity. R is said to be semilocal if R/J（R） is （semisimple） Artinian, where J（R） denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.展开更多
For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amena...For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.展开更多
The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity ...The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.展开更多
By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry gro...By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.展开更多
In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Ha...In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.展开更多
Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give...Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.展开更多
All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting ...All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.展开更多
Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to...Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.展开更多
In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, ...In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.展开更多
A novel synthetic aperture radar(SAR)image de-noising method based on the local pixel grouping(LPG)principal component analysis(PCA)and guided filter is proposed.This method contains two steps.In the first step,we pro...A novel synthetic aperture radar(SAR)image de-noising method based on the local pixel grouping(LPG)principal component analysis(PCA)and guided filter is proposed.This method contains two steps.In the first step,we process the noisy image by coarse filters,which can suppress the speckle effectively.The original SAR image is transformed into the additive noise model by logarithmic transform with deviation correction.Then,we use the pixel and its nearest neighbors as a vector to select training samples from the local window by LPG based on the block similar matching.The LPG method ensures that only the similar sample patches are used in the local statistical calculation of PCA transform estimation,so that the local features of the image can be well preserved after coefficients shrinkage in the PCA domain.In the second step,we do the guided filtering which can effectively eliminate small artifacts left over from the coarse filtering.Experimental results of simulated and real SAR images show that the proposed method outstrips the state-of-the-art image de-noising methods in the peak signalto-noise ratio(PSNR),the structural similarity(SSIM)index and the equivalent number of looks(ENLs),and is of perceived image quality.展开更多
A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl...A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.展开更多
The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two c...The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.展开更多
In this work, we focus on assessing the group effect of localized corrosion on the ultimate strength of the marine structural plates and study the load-deformation behaviors of plates of various slenderness and uniaxi...In this work, we focus on assessing the group effect of localized corrosion on the ultimate strength of the marine structural plates and study the load-deformation behaviors of plates of various slenderness and uniaxial compression.Meanwhile, we investigate different corroded patterns from a single circular pit to 25 circular pits distributed over the plate and carry out hundreds of nonlinear finite element simulations by combining the number, depth, distribution of pits with imperfections and slenderness of plate. The distribution of multiple pits causes scattering of stress concentration on the plate, then the plastic section of plate changes with wider distribution of damage simultaneously. The ultimate strength arises when un-loading zone comprised of the yielding strips and holes extends across the plate. It can be concluded that the corroded condition defined as group effect of pits manipulates the deformation state and the loading capacity of plate at the ultimate strength mode that coincides with the proportion of effective loading area and section in the process of post-buckling. To validate the effect of pits group, we perform the numerical experiments of the post-buckling of steel plates containing pits in a row with different orientation.展开更多
A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to ...A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question： If G is a locally finite group or a cyclic group of order 3, then when is RG semiclean？ Some known results on clean group rings are generalized.展开更多
Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two...Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.展开更多
Six kinds of nonclassical periodic lattices with locally 10-fold rotational symmetries are proposed. They can be delineated via nonclassical plane-crystallographic groups. The projections on the planes of correspondin...Six kinds of nonclassical periodic lattices with locally 10-fold rotational symmetries are proposed. They can be delineated via nonclassical plane-crystallographic groups. The projections on the planes of corresponding unit cells consisting of embedding polyhedra generate the periodic lattices, respectively. The Fourier-transform patterns of the periodiclattices have almost perfect 10-fold rotational symmetries, which are very similar to those displaying in the electron-diffraction patterns of so-called quasicrystals.展开更多
In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a ...In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.展开更多
基金support by China Program of International S&T Cooperation(2016YFE0100300)support by the National Natural Science Foundation of China(NSFC,Grant Nos.11633004,11390372,11303008 and 11773034)+1 种基金the 973 program grant 2015CB857005the NSFC(No.11373029)
文摘The abundance of neutral hydrogen（HI）in satellite galaxies in the local group is important for studying the formation history of our local group.In this work,we generated mock HI satellite galaxies in the Local Group using the high mass-resolution hydrodynamic APOSTLE simulation.The simulated HI mass function agrees with the ALFALFA survey very well above 10~6M_⊙,although there is a discrepancy below this scale because of the observed flux limit.After carefully checking various systematic elements in the observations,including fitting of line width,sky coverage,integration time and frequency drift due to uncertainty in a galaxy’s distance,we predicted the abundance of HI in galaxies in a future survey that will be conducted by FAST.FAST has a larger aperture and higher sensitivity than the Arecibo telescope.We found that the HI mass function could be estimated well around 10~5M_⊙ if the integration time is 40 minutes.Our results indicate that there are 61 HI satellites in the Local Group and 36 in the FAST field above 10~5M_⊙.This estimation is one order of magnitude better than the current data,and will put a strong constraint on the formation history of the Local Group.Also more high resolution simulated samples are needed to achieve this target.
文摘The lack of Birkhoff theorem in finite-range gravitation reveals nonzero acceleration of the test body inside the massive spherical shell, as well as breakdown of screening inside the charged conductor gives rise to acceleration of the test charge. An application of this effect to the motion of galaxies in Local Group allows to constraint quintessence parameter in some massive gravitational theories.
基金Foundation item:The NNSF(10571026)of China,the NSF(BK2005207)of Jiangsu Provincethe Specialized Research Fund(20060286006)for the Doctoral Program of Higher Education.
文摘Let R be an associative ring with identity. R is said to be semilocal if R/J（R） is （semisimple） Artinian, where J（R） denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.
文摘For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.
基金financially supported by the National Key Research and Development Program of China(Grant No.2017YFC1404200)the Tianjin Key Program of Applied Foundation and Advanced-Tech Research,China(Grant No.18JCZDJC40200)+1 种基金the National High Technology Research and Development Program of China(863 Program,Grant No.2012AA051709)the National Natural Science Foundation of China(Grant No.51509183)
文摘The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.
基金Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014the National Natural Science Foundation of China under Grant Nos 11326164,11401528,11435005 and 11375090+4 种基金the Global Change Research Program of China(No 2015CB953904)the Research Fund for the Doctoral Program of Higher Education of China(No 20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No 61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(No ZF1213)Shanghai Minhang District Talents of High Level Scientific Research Project
文摘By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.
文摘In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.
文摘Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.
基金The NSF (60776810,10871205) of Chinathe NSF (08JCYBJC13900) of Tianjin
文摘All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11175092)the Scientific Research Fund of Education Department of Zhejiang Province of China (Grant No. Y201017148)K. C. Wong Magna Fund in Ningbo University
文摘In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.
基金supported by the National Natural Science Foundation of China(6200220861572063+1 种基金61603225)the Natural Science Foundation of Shandong Province(ZR2016FQ04)。
文摘A novel synthetic aperture radar(SAR)image de-noising method based on the local pixel grouping(LPG)principal component analysis(PCA)and guided filter is proposed.This method contains two steps.In the first step,we process the noisy image by coarse filters,which can suppress the speckle effectively.The original SAR image is transformed into the additive noise model by logarithmic transform with deviation correction.Then,we use the pixel and its nearest neighbors as a vector to select training samples from the local window by LPG based on the block similar matching.The LPG method ensures that only the similar sample patches are used in the local statistical calculation of PCA transform estimation,so that the local features of the image can be well preserved after coefficients shrinkage in the PCA domain.In the second step,we do the guided filtering which can effectively eliminate small artifacts left over from the coarse filtering.Experimental results of simulated and real SAR images show that the proposed method outstrips the state-of-the-art image de-noising methods in the peak signalto-noise ratio(PSNR),the structural similarity(SSIM)index and the equivalent number of looks(ENLs),and is of perceived image quality.
文摘A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.
基金supported by the Program for Changjiang Scholars and Innovative Research Team in University of China under contract No,IRT0420the National Natural Science Foundation of China under contract No.50409015.
文摘The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51490670 and 11572300)R&D Plan(Grant No.2017GHY15120)Fundamental Research Fund for Central Universities(Ocean University of China)
文摘In this work, we focus on assessing the group effect of localized corrosion on the ultimate strength of the marine structural plates and study the load-deformation behaviors of plates of various slenderness and uniaxial compression.Meanwhile, we investigate different corroded patterns from a single circular pit to 25 circular pits distributed over the plate and carry out hundreds of nonlinear finite element simulations by combining the number, depth, distribution of pits with imperfections and slenderness of plate. The distribution of multiple pits causes scattering of stress concentration on the plate, then the plastic section of plate changes with wider distribution of damage simultaneously. The ultimate strength arises when un-loading zone comprised of the yielding strips and holes extends across the plate. It can be concluded that the corroded condition defined as group effect of pits manipulates the deformation state and the loading capacity of plate at the ultimate strength mode that coincides with the proportion of effective loading area and section in the process of post-buckling. To validate the effect of pits group, we perform the numerical experiments of the post-buckling of steel plates containing pits in a row with different orientation.
基金Supported by the National Natural Science Foundation of China(Grant No.11401009)the Natural Science Foundation of Ahui Province(Grant No.1408085QA01)
文摘A ring R with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question： If G is a locally finite group or a cyclic group of order 3, then when is RG semiclean？ Some known results on clean group rings are generalized.
基金the Key Projects in the National Science & Technology Pillar Program during the Twelfth Five-year Plan Period(Grant No.2015BAK17B01)Science Foundation of Institute of Engineering Mechanics,CEA under Grant No.2014B10+1 种基金Natural Science Foundation of Heilongjiang Province of China under Grant No.LC201403National Natural Science Foundation under Grant No.51378479 and No.51108431
文摘Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.
文摘Six kinds of nonclassical periodic lattices with locally 10-fold rotational symmetries are proposed. They can be delineated via nonclassical plane-crystallographic groups. The projections on the planes of corresponding unit cells consisting of embedding polyhedra generate the periodic lattices, respectively. The Fourier-transform patterns of the periodiclattices have almost perfect 10-fold rotational symmetries, which are very similar to those displaying in the electron-diffraction patterns of so-called quasicrystals.
基金Supported by the National Natural Science Foundation of China(11201414,11471153)
文摘In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.
