In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
Let G be a 2 connected graph with n vertices. In this paper, we prove that if there exist two vertices of any there independent vertices in G such that the sum of whose degree is at least n , then G ...Let G be a 2 connected graph with n vertices. In this paper, we prove that if there exist two vertices of any there independent vertices in G such that the sum of whose degree is at least n , then G is pancyclic, or G is K n/2,n/2 , or G is K n/2,n/2 -e , or G is a cycle of length 5.展开更多
Let G be a 2 connected simple graph of order n ( n ≥5) and minimum degree δ . In this paper, we show that if for any two nonadjacent vertices u , v of G there holds | N(u)∪N(v)|≥n-δ , t...Let G be a 2 connected simple graph of order n ( n ≥5) and minimum degree δ . In this paper, we show that if for any two nonadjacent vertices u , v of G there holds | N(u)∪N(v)|≥n-δ , then G is {3,4} - vertex pancyclic unless G≌K n2,n2 .展开更多
Intercellular interactions play a significant role in a wide range of biological functions and processes at both the cellular and tissue scales, for example, embryogenesis, organogenesis, and cancer invasion. In this ...Intercellular interactions play a significant role in a wide range of biological functions and processes at both the cellular and tissue scales, for example, embryogenesis, organogenesis, and cancer invasion. In this paper, a dynamic cellular vertex model is presented to study the morphomechanics of a growing epithelial monolayer. The regulating role of stresses in soft tissue growth is revealed. It is found that the cells originating from the same parent cell in the monolayer can orchestrate into clustering patterns as the tissue grows. Collective cell migration exhibits a feature of spatial correlation across multiple cells. Dynamic intercellular interactions can engender a variety of distinct tissue behaviors in a social context. Uniform cell proliferation may render high and heterogeneous residual compressive stresses, while stress-regulated proliferation can effectively release the stresses, reducing the stress heterogeneity in the tissue. The results highlight the critical role of mechanical factors in the growth and morphogenesis of epithelial tissues and help understand the development and invasion of epithelial tumors.展开更多
Large-volume liquid scintillator detectors with ultra-low background levels have been widely used to study neutrino physics and search for dark matter.Event vertex and event time are not only useful for event selectio...Large-volume liquid scintillator detectors with ultra-low background levels have been widely used to study neutrino physics and search for dark matter.Event vertex and event time are not only useful for event selection but also essential for the reconstruction of event energy.In this study,four event vertex and event time reconstruction algorithms using charge and time information collected by photomultiplier tubes were analyzed comprehensively.The effects of photomultiplier tube properties were also investigated.The results indicate that the transit time spread is the main effect degrading the vertex reconstruction,while the effect of dark noise is limited.In addition,when the event is close to the detector boundary,the charge information provides better performance for vertex reconstruction than the time information.展开更多
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints....Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.展开更多
The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, dampi...The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.展开更多
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
The precise vertex reconstruction for large liquid scintillator detectors is essential.A novel machine learning-based method was successfully developed to reconstruct an event vertex in JUNO.In this study,the performa...The precise vertex reconstruction for large liquid scintillator detectors is essential.A novel machine learning-based method was successfully developed to reconstruct an event vertex in JUNO.In this study,the performance of machine learning-based vertex reconstruction was further improved by optimizing the input images of neural networks.By separating the information of different types of PMTs and adding the information of the second hit of PMTs,the vertex resolution was improved by approximately 9.4% at 1 MeV and 9.8% at 11 MeV.展开更多
Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as ...Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
文摘Let G be a 2 connected graph with n vertices. In this paper, we prove that if there exist two vertices of any there independent vertices in G such that the sum of whose degree is at least n , then G is pancyclic, or G is K n/2,n/2 , or G is K n/2,n/2 -e , or G is a cycle of length 5.
文摘Let G be a 2 connected simple graph of order n ( n ≥5) and minimum degree δ . In this paper, we show that if for any two nonadjacent vertices u , v of G there holds | N(u)∪N(v)|≥n-δ , then G is {3,4} - vertex pancyclic unless G≌K n2,n2 .
基金Supports from the National Natural Science Foundation of China(Grants 11432008,11542005,11672161,and 11620101001)Tsinghua University(Grant 20151080441)Thousand Young Talents Program of China are acknowledged
文摘Intercellular interactions play a significant role in a wide range of biological functions and processes at both the cellular and tissue scales, for example, embryogenesis, organogenesis, and cancer invasion. In this paper, a dynamic cellular vertex model is presented to study the morphomechanics of a growing epithelial monolayer. The regulating role of stresses in soft tissue growth is revealed. It is found that the cells originating from the same parent cell in the monolayer can orchestrate into clustering patterns as the tissue grows. Collective cell migration exhibits a feature of spatial correlation across multiple cells. Dynamic intercellular interactions can engender a variety of distinct tissue behaviors in a social context. Uniform cell proliferation may render high and heterogeneous residual compressive stresses, while stress-regulated proliferation can effectively release the stresses, reducing the stress heterogeneity in the tissue. The results highlight the critical role of mechanical factors in the growth and morphogenesis of epithelial tissues and help understand the development and invasion of epithelial tumors.
基金supported by the National Natural Science Foundation of China(Nos.11805294 and 11975021)the China Postdoctoral Science Foundation(2018M631013),the Strategic Priority Research Program of Chinese Academy of Sciences(XDA10010900)+1 种基金the Fundamental Research Funds for the Central Universities,Sun Yatsen University(19lgpy268)in part by the CAS Center for Excellence in Particle Physics(CCEPP).
文摘Large-volume liquid scintillator detectors with ultra-low background levels have been widely used to study neutrino physics and search for dark matter.Event vertex and event time are not only useful for event selection but also essential for the reconstruction of event energy.In this study,four event vertex and event time reconstruction algorithms using charge and time information collected by photomultiplier tubes were analyzed comprehensively.The effects of photomultiplier tube properties were also investigated.The results indicate that the transit time spread is the main effect degrading the vertex reconstruction,while the effect of dark noise is limited.In addition,when the event is close to the detector boundary,the charge information provides better performance for vertex reconstruction than the time information.
文摘Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C（x） denote the set of colors of vertex x and of the edges incident with x, we call C（x） the color set of x. If C（u） ≠ C（v） for any two different vertices u and v of V （G）, then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by Хvt^e（G） and is called the VDE T chromatic number of G. The VDET coloring of complete bipartite graph K7,n （7 ≤ n ≤ 95） is discussed in this paper and the VDET chromatic number of K7,n （7 ≤ n ≤ 95） has been obtained.
基金the National Outstanding Youth Science Foundation of China (10425208)111 Project (B07009) FanZhou Science and Research Foundation for Young Scholars (No. 20080503)
文摘The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
基金supported by the National Natural Science Foundation of China(Nos.11975021,12175257,12175321,11675275,and U1932101)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515012039)+3 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA10010900)the National College Students Science and Technology Innovation Projectthe Undergraduate Base Scientific Research Project of Sun Yat-sen Universitythe CAS Center for Excellence in Particle Physics(CCEPP).
文摘The precise vertex reconstruction for large liquid scintillator detectors is essential.A novel machine learning-based method was successfully developed to reconstruct an event vertex in JUNO.In this study,the performance of machine learning-based vertex reconstruction was further improved by optimizing the input images of neural networks.By separating the information of different types of PMTs and adding the information of the second hit of PMTs,the vertex resolution was improved by approximately 9.4% at 1 MeV and 9.8% at 11 MeV.
文摘Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.
