The scalar of Japanese yew （Taxus cuspidata） population and the relationship between individual distribution and site factors were analyzed according to investigating data in 74 sample belts with a total sampled are...The scalar of Japanese yew （Taxus cuspidata） population and the relationship between individual distribution and site factors were analyzed according to investigating data in 74 sample belts with a total sampled area of 436.872 hm2 in Muling Nature Reserve. The result showed that the distribution rules of Japanese yew population were correlated to elevation, slope position, slope aspect and slope gradient. The optimal distribution range in elevation for the natural Japanese yew population is at the attitudes of 700-800 m. The amounts of Japanese yew individuals on shady slope were more than those on sunny slope. On top slope and mid-slope, the individual amounts of Japanese yew are more than those on toe slope. Most of Japanese yew individuals occurred on slope gradient of less than 15. The scalar of the population was decreased with the slope gradient increasing.展开更多
We prove a converse theorem for split even special orthogonal groups over finite fields.This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism...We prove a converse theorem for split even special orthogonal groups over finite fields.This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.展开更多
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach.For example,matrix coefficients of supercuspidal representations can be used as test ...Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach.For example,matrix coefficients of supercuspidal representations can be used as test functions for this.However,they kill a large class of interesting cuspidal automorphic representations.For the case of number fields,multipliers of the Schwartz algebra are used in the recent work(see Beuzart-Plessis et al.(2021))to isolate all the cuspidal spectrum.In particular,they are suitable for the comparison of orbital integrals.These multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups(see Beuzart-Plessis et al.(2021,2022)).In this article,we prove the similar result on isolating the cuspidal spectrum in Beuzart-Plessis et al.(2021)for the function field case.展开更多
We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace f...We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.展开更多
In this paper, we investigate the limit cycle bifurcations in a cubic near-Hamiltonian system by perturbing a cuspidal loop and prove that 5 limit cycles can appear in a neighborhood of the cuspidal loop.
基金This work was supported by Northeast Forestry University fund Program from Science and Technology Department of Heilongjiang Province (LC05C14)
文摘The scalar of Japanese yew （Taxus cuspidata） population and the relationship between individual distribution and site factors were analyzed according to investigating data in 74 sample belts with a total sampled area of 436.872 hm2 in Muling Nature Reserve. The result showed that the distribution rules of Japanese yew population were correlated to elevation, slope position, slope aspect and slope gradient. The optimal distribution range in elevation for the natural Japanese yew population is at the attitudes of 700-800 m. The amounts of Japanese yew individuals on shady slope were more than those on sunny slope. On top slope and mid-slope, the individual amounts of Japanese yew are more than those on toe slope. Most of Japanese yew individuals occurred on slope gradient of less than 15. The scalar of the population was decreased with the slope gradient increasing.
基金partially supported by the NSF Grants DMS-1848058partially supported by the NSF Grants DMS-1702218, DMS-1848058start-up funds from the Department of Mathematics at Purdue University.
文摘We prove a converse theorem for split even special orthogonal groups over finite fields.This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.
基金supported by National Natural Science Foundation of China(Grant No.11971254)supported by National Natural Science Foundation of China(Grant No.11501382)。
文摘Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach.For example,matrix coefficients of supercuspidal representations can be used as test functions for this.However,they kill a large class of interesting cuspidal automorphic representations.For the case of number fields,multipliers of the Schwartz algebra are used in the recent work(see Beuzart-Plessis et al.(2021))to isolate all the cuspidal spectrum.In particular,they are suitable for the comparison of orbital integrals.These multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups(see Beuzart-Plessis et al.(2021,2022)).In this article,we prove the similar result on isolating the cuspidal spectrum in Beuzart-Plessis et al.(2021)for the function field case.
文摘We show that the cuspidal component of the stable trace formula of a split special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the r-stable trace formula, when r is the standard or the second fundamental representation of the dual group, and show that they satisfy a similar kind of beyond endoscopic decomposition. The results are consequences of Arthur's works(2013) on endoscopic classification of automorphic representations, together with known results concerning a class of Langlands L-functions for special odd orthogonal groups.
基金supported by Foundation of Shanghai Municipal Education Commission(10YZ74)
文摘In this paper, we investigate the limit cycle bifurcations in a cubic near-Hamiltonian system by perturbing a cuspidal loop and prove that 5 limit cycles can appear in a neighborhood of the cuspidal loop.
