In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper a conceptually simpler approach to averaging in cosmology is sugge...The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper a conceptually simpler approach to averaging in cosmology is suggested, based on the averaging of scalars within unimodular gravity. As an illustration, the example of an exact spherically symmetric dust model is considered, and it is shown that within this approach averaging introduces correlations (corrections) to the effective dynamical evolution equation in the form of a spatial curvature term.展开更多
1. Let F= Q (t^2=-1, m】0 and square free) be an imaginary quadratic field, D_m the ring of integers in F, H an n-ary positive definite Hermitian form over F(hereafter simply as H-form), and let(V, H), or simply V, de...1. Let F= Q (t^2=-1, m】0 and square free) be an imaginary quadratic field, D_m the ring of integers in F, H an n-ary positive definite Hermitian form over F(hereafter simply as H-form), and let(V, H), or simply V, denote a non-zero regular n-ary positive definite Hermitian space over F. L denotes a D_m-lattice on V, i. e. L is a finitely generated D_m-module of V and FL=V.展开更多
This paper gives a method to construct indecomposable positive definite unimodular Hermitian (?)-lattices of any rank n with m(?)3 (mod 4). It is proved that we can construct: (i) for any natural number n, an indecomp...This paper gives a method to construct indecomposable positive definite unimodular Hermitian (?)-lattices of any rank n with m(?)3 (mod 4). It is proved that we can construct: (i) for any natural number n, an indecomposable positive definite normal unimodular (?)-(resp. (?)-lattice of rank n, except n=2, 3, 4,5 (resp. n=2, 3) (in the exceptional cases there are no lattices with the desired properties), and (ⅱ) for any n=4k(resp. n=2k), an indecompoaable positive definite even unimodular (?) lattice of rank n.展开更多
For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quad...For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quadratic field (-m<sup>1/2</sup>). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R<sub>15</sub>(R<sub>11</sub>- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian R<sub>m</sub>-lattices of any rank n for each m.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
Focused energy delivery(FED) is a technique that can precisely bring energy to the specific region,which arouses wide attention in precision electronic warfare(PREW).This paper first proposes a joint optimization mode...Focused energy delivery(FED) is a technique that can precisely bring energy to the specific region,which arouses wide attention in precision electronic warfare(PREW).This paper first proposes a joint optimization model with respect to the locations of the array and the transmitted signals to improve the performance of FED.As the problem is nonconvex and NP-hard,particle swarm optimization(PSO) is adopted to solve the locations of the array,while designing the transmitted signals under a feasible array is considered as a unimodular quadratic program(UQP) subproblem to calculate the fitness criterion of PSO.In the PSO-UQP framework established,two methods are presented for the UQP subproblem,which are more efficient and more accurate respectively than previous works.Furthermore,a threshold value is set in the framework to determine which method to adopt to take full advantages of the methods above.Meanwhile,we obtain the maximum localization error that FED can tolerate,which is significant for implementing FED in practice.Simulation results are provided to demonstrate the effectiveness of the joint optimization algorithm,and the correctness of the maximum localization error derived.展开更多
In this paper we show how the transformations associated with the reduction to the Smith form of some classes of mul-tivariate polynomial matrices are computed. Using a Maple implementation of a constructive version o...In this paper we show how the transformations associated with the reduction to the Smith form of some classes of mul-tivariate polynomial matrices are computed. Using a Maple implementation of a constructive version of the Quillen-Suslin Theorem, we present two algorithms for the reduction to a particular Smith form often associated with the simplification of linear systems of multidimensional equations.展开更多
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
文摘The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper a conceptually simpler approach to averaging in cosmology is suggested, based on the averaging of scalars within unimodular gravity. As an illustration, the example of an exact spherically symmetric dust model is considered, and it is shown that within this approach averaging introduces correlations (corrections) to the effective dynamical evolution equation in the form of a spatial curvature term.
基金Project supported by the National Natural Science Foundation of China.
文摘1. Let F= Q (t^2=-1, m】0 and square free) be an imaginary quadratic field, D_m the ring of integers in F, H an n-ary positive definite Hermitian form over F(hereafter simply as H-form), and let(V, H), or simply V, denote a non-zero regular n-ary positive definite Hermitian space over F. L denotes a D_m-lattice on V, i. e. L is a finitely generated D_m-module of V and FL=V.
基金Project supported by the National Natural Science Foundation of China
文摘This paper gives a method to construct indecomposable positive definite unimodular Hermitian (?)-lattices of any rank n with m(?)3 (mod 4). It is proved that we can construct: (i) for any natural number n, an indecomposable positive definite normal unimodular (?)-(resp. (?)-lattice of rank n, except n=2, 3, 4,5 (resp. n=2, 3) (in the exceptional cases there are no lattices with the desired properties), and (ⅱ) for any n=4k(resp. n=2k), an indecompoaable positive definite even unimodular (?) lattice of rank n.
文摘For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quadratic field (-m<sup>1/2</sup>). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R<sub>15</sub>(R<sub>11</sub>- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian R<sub>m</sub>-lattices of any rank n for each m.
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Anhui Provincial Natural Science Foundation(Project for Youth:1908085QF252)Research Program of National University of Defense Technology(ZK19-10)。
文摘Focused energy delivery(FED) is a technique that can precisely bring energy to the specific region,which arouses wide attention in precision electronic warfare(PREW).This paper first proposes a joint optimization model with respect to the locations of the array and the transmitted signals to improve the performance of FED.As the problem is nonconvex and NP-hard,particle swarm optimization(PSO) is adopted to solve the locations of the array,while designing the transmitted signals under a feasible array is considered as a unimodular quadratic program(UQP) subproblem to calculate the fitness criterion of PSO.In the PSO-UQP framework established,two methods are presented for the UQP subproblem,which are more efficient and more accurate respectively than previous works.Furthermore,a threshold value is set in the framework to determine which method to adopt to take full advantages of the methods above.Meanwhile,we obtain the maximum localization error that FED can tolerate,which is significant for implementing FED in practice.Simulation results are provided to demonstrate the effectiveness of the joint optimization algorithm,and the correctness of the maximum localization error derived.
文摘In this paper we show how the transformations associated with the reduction to the Smith form of some classes of mul-tivariate polynomial matrices are computed. Using a Maple implementation of a constructive version of the Quillen-Suslin Theorem, we present two algorithms for the reduction to a particular Smith form often associated with the simplification of linear systems of multidimensional equations.
