In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topo...In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.展开更多
In this note, we state some refinements of conjectures of Gan-Gross-Prasad and Kudla concerning the central derivatives of L-series and special cycles on Shimura varieties. The analogues of our formulation for special...In this note, we state some refinements of conjectures of Gan-Gross-Prasad and Kudla concerning the central derivatives of L-series and special cycles on Shimura varieties. The analogues of our formulation for special values of L-series are written in terms of invariant linear forms on automorphic representations defined by integrations of matrix coefficients.展开更多
We study the evolution of a gynodioecious species under mixed-mating through a nucleocytoplasmic male sterility model. We consider two cytoplasmic types and a nuclear locus with two alleles. Here, the interaction betw...We study the evolution of a gynodioecious species under mixed-mating through a nucleocytoplasmic male sterility model. We consider two cytoplasmic types and a nuclear locus with two alleles. Here, the interaction between one cytoplasmic type and a recessive nuclear male-sterility factor gives rise to only one female genotype, while the remaining types correspond to hermaphroditic plants. We include two fitness paramaters: the advantageous female fitness t of females relative to that of hermaphrodites;and a silent and dominant cost of restoration, that is, a diminished fitness for plants carrying a dominant restorer gene relative to that of hermaphrodites. The parameter related to the cost of restoration is assumed to be present on outcrossing male fertility only. We find that every population converges to a stable population. We also determine the nature of the attracting stable population, which could be a nucleocytoplasmic polymorphism, a nuclear polymorphism or another population with some genotypes absent. This depends on the position of t with respect to critical values expressed in terms of the other parameters and also on the initial population.展开更多
In this paper,we find all positive squarefree integers d satisfying that the Pell equation X^2-d Y^2=±1 has at least two positive integer solutions(X,Y)and(X′,Y′)such that both X and X′have Zeckendorf represen...In this paper,we find all positive squarefree integers d satisfying that the Pell equation X^2-d Y^2=±1 has at least two positive integer solutions(X,Y)and(X′,Y′)such that both X and X′have Zeckendorf representations with at most two terms.展开更多
文摘In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.
文摘In this note, we state some refinements of conjectures of Gan-Gross-Prasad and Kudla concerning the central derivatives of L-series and special cycles on Shimura varieties. The analogues of our formulation for special values of L-series are written in terms of invariant linear forms on automorphic representations defined by integrations of matrix coefficients.
文摘We study the evolution of a gynodioecious species under mixed-mating through a nucleocytoplasmic male sterility model. We consider two cytoplasmic types and a nuclear locus with two alleles. Here, the interaction between one cytoplasmic type and a recessive nuclear male-sterility factor gives rise to only one female genotype, while the remaining types correspond to hermaphroditic plants. We include two fitness paramaters: the advantageous female fitness t of females relative to that of hermaphrodites;and a silent and dominant cost of restoration, that is, a diminished fitness for plants carrying a dominant restorer gene relative to that of hermaphrodites. The parameter related to the cost of restoration is assumed to be present on outcrossing male fertility only. We find that every population converges to a stable population. We also determine the nature of the attracting stable population, which could be a nucleocytoplasmic polymorphism, a nuclear polymorphism or another population with some genotypes absent. This depends on the position of t with respect to critical values expressed in terms of the other parameters and also on the initial population.
基金supported by the project from Universidad del Valle(Grant No.71079)supported by NRF of South Africa(Grant No.CPRR160325161141)an A-Rated Scientist Award from the NRF of South Africa and by Czech Granting Agency(Grant No.17-02804S)。
文摘In this paper,we find all positive squarefree integers d satisfying that the Pell equation X^2-d Y^2=±1 has at least two positive integer solutions(X,Y)and(X′,Y′)such that both X and X′have Zeckendorf representations with at most two terms.
