Objective To examine whether the selectivity of visual cortical neurons to stimulus spatial frequencies would be affected by aging in cats.Methods In vivo extracellular single-unit recording techniques were employed t...Objective To examine whether the selectivity of visual cortical neurons to stimulus spatial frequencies would be affected by aging in cats.Methods In vivo extracellular single-unit recording techniques were employed to record the tuning responses of V1 neurons to different stimulus spatial frequencies in old and young adult cats.Results Statistical analysis showed that the mean optimal spatial frequency of grating stimuli that evoked the maximal response of V1 neurons in old cats was significantly lower than that in young adult cats.Furthermore,the mean high cut-off spatial frequency of grating stimuli that evoked the half amplitude of the maximal response of V1 neurons in old cats was also significantly lower than that in young adult cats.Conclusion These results are consistent with those reported in the V1 of old monkeys,suggesting that the age-related decline in the selectivity of visual cortical cells to spatial frequency could be generalized to all mammalian species and might contribute to visual acuity reduction in senescent individuals.展开更多
A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated b...A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.展开更多
The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. Th...The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.展开更多
For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general...For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.展开更多
The concept of nestedness originated from the field of biogeography decades ago and has been widely used in metacommunities and biological interaction networks,but there is still a lack of research within local commun...The concept of nestedness originated from the field of biogeography decades ago and has been widely used in metacommunities and biological interaction networks,but there is still a lack of research within local communities.Moreover,studies on nestedness usually rarely incorporate the functional traits of the species and the environmental characteristics of the sites.In this study,we constructed a species presence–absence matrix of a 50-ha forest plot,used the simulated annealing algorithm to reveal the maximum nested structure and further tested the significance of nestedness patterns by constructing null ensembles.The nested ranks were used to represent the orders of species and quadrats in the maximum nestedness matrix.The regression tree analysis was used to reveal the relationships of nested ranks with environmental factors and functional traits.We found that the co-occurrence pattern of local plant communities was significantly nested.The regression tree results showed that the nested ranks of quadrats were determined by soil available phosphorus,soil water content,soil organic carbon and soil pH.Intraspecific variation of functional traits,including leaf C,leaf pH,leaf dry matter content and maximum photosynthetic rate rather than means of functional traits,provided a better explanation for the formation of species’nested ranks.Understanding the causes of species and quadrats nested ranks provides novel lens and useful insights into ecological processes underlying nestedness,and further improves our knowledge of how local plant communities are assembled.展开更多
Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL gen...Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.展开更多
In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-spe...In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-species competition among predators are investigated. The （local and global） asymptotic stability behavior of the corresponding non- spatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. In addition, we derive the conditions for Turing instability and the consequent parametric Turing space in spatial domain. The results of spatial pat- tern analysis through numerical simulations are depicted and analyzed. ~rthermore, we perform a series of numerical simulations and find that the proposed model dynamics exhibits complex pattern replication. The feasible results obtained in this paper indicate that the effect of diffusion in Turing instability plays an important role to understand better the pattern formation in ecosystem.展开更多
The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well...The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem.The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local one.The proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local problem.Especially when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the boundary.For the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.展开更多
基金supported by Natural Science Foundation of Anhui Province(No. 070413138)the Key Research Foundation of Education Department of Anhui Province,China(No. KJ2009A167)
文摘Objective To examine whether the selectivity of visual cortical neurons to stimulus spatial frequencies would be affected by aging in cats.Methods In vivo extracellular single-unit recording techniques were employed to record the tuning responses of V1 neurons to different stimulus spatial frequencies in old and young adult cats.Results Statistical analysis showed that the mean optimal spatial frequency of grating stimuli that evoked the maximal response of V1 neurons in old cats was significantly lower than that in young adult cats.Furthermore,the mean high cut-off spatial frequency of grating stimuli that evoked the half amplitude of the maximal response of V1 neurons in old cats was also significantly lower than that in young adult cats.Conclusion These results are consistent with those reported in the V1 of old monkeys,suggesting that the age-related decline in the selectivity of visual cortical cells to spatial frequency could be generalized to all mammalian species and might contribute to visual acuity reduction in senescent individuals.
基金supported by National Natural Science Foundation of China(Grant Nos.11271035,91430213 and 11421101)
文摘A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.
文摘The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.
基金supported by National Natural Science Foundation of China (Grants Nos. 10871175, 10931007)Zhejiang Natural Science Foundation (Grants No. Z6100217)Zhejiang University's Pao Yu-Kong International Fund
文摘For the 3D focusing cubic nonlinear SchrSdinger equation, scattering of H1 solutions inside the （scale invariant） potential well was established by Holmer and Roudenko （radial case） and Duyckaerts et al. （general case） in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.
基金This study was funded by the National Science Foundation of China(31925027)the Fundamental Research Funds for the Central Universities(20lgpy116,2021qntd18).
文摘The concept of nestedness originated from the field of biogeography decades ago and has been widely used in metacommunities and biological interaction networks,but there is still a lack of research within local communities.Moreover,studies on nestedness usually rarely incorporate the functional traits of the species and the environmental characteristics of the sites.In this study,we constructed a species presence–absence matrix of a 50-ha forest plot,used the simulated annealing algorithm to reveal the maximum nested structure and further tested the significance of nestedness patterns by constructing null ensembles.The nested ranks were used to represent the orders of species and quadrats in the maximum nestedness matrix.The regression tree analysis was used to reveal the relationships of nested ranks with environmental factors and functional traits.We found that the co-occurrence pattern of local plant communities was significantly nested.The regression tree results showed that the nested ranks of quadrats were determined by soil available phosphorus,soil water content,soil organic carbon and soil pH.Intraspecific variation of functional traits,including leaf C,leaf pH,leaf dry matter content and maximum photosynthetic rate rather than means of functional traits,provided a better explanation for the formation of species’nested ranks.Understanding the causes of species and quadrats nested ranks provides novel lens and useful insights into ecological processes underlying nestedness,and further improves our knowledge of how local plant communities are assembled.
基金supported by China Postdoctoral Science Foundation funded project(Grant No.201104383)the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56)+1 种基金National Natural Science Foundation of China(Grant No.10925106)Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
文摘Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
文摘In this paper, spatial patterns of a diffusive predator-prey model with sigmoid （Holling type III） ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-species competition among predators are investigated. The （local and global） asymptotic stability behavior of the corresponding non- spatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. In addition, we derive the conditions for Turing instability and the consequent parametric Turing space in spatial domain. The results of spatial pat- tern analysis through numerical simulations are depicted and analyzed. ~rthermore, we perform a series of numerical simulations and find that the proposed model dynamics exhibits complex pattern replication. The feasible results obtained in this paper indicate that the effect of diffusion in Turing instability plays an important role to understand better the pattern formation in ecosystem.
基金supported by the National Natural Science Foundation of China (No. 10728101)the 973 Project ofthe Ministry of Science and Technology of China+1 种基金the Doctoral Program Foundation of the Ministry of Ed-ucation of Chinathe "111" Project and the Postdoctoral Science Foundation of China (No. 20070410160)
文摘The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem.The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local one.The proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local problem.Especially when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the boundary.For the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.
