In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Ou...It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Our results generalize some well-known results.展开更多
It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method a...It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.展开更多
Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Inste...Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Instead of theory establishment or field data derivation,I adopted a data simulation method that used the power function of SAR to fit log-normal distribution of species abundance.Important Findings The results showed that one-step sampling caused biphasic SAR and n-step sampling could cause 2n-phasic SAR.Practical two-step sampling produced triphasic SAR due to the Preston and Pan effects in large areas.Furthermore,before exploring biological or ecological mechanisms for the nature phenomenon,we should identify or exclude potential mathematical,statistical or sampling reasons.展开更多
文摘In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
基金Supported by the Nitional Science Foundation of China !(19871073)
文摘It is known that the product of two nilpotent subgroups of a finite group is not necessarily nilpotent.In this paper, we study the influence of the Engel condition on the product of two nilpotent subgroups. Our results generalize some well-known results.
文摘It is proved that each su?ciently large integer N ≡ 5 (mod24) can be written as N = p21+p22+p23+p24+p25 with |pj? N/5| ≤ U = N 12? 135+ε, where pj are primes. This result, which is obtained by an iterative method and a hybrid estimate for Dirichlet polynomial, improves the previous results in this direction.
基金The work was supported by the National Key R&D Program of China(2018YFF0214905 and 2016YFC1200802).
文摘Aims It is important to explore the underlying mechanisms that cause triphasic species–area relationship(triphasic SAR)across different scales in order to understand the spatial patterns of biodiversity.Methods Instead of theory establishment or field data derivation,I adopted a data simulation method that used the power function of SAR to fit log-normal distribution of species abundance.Important Findings The results showed that one-step sampling caused biphasic SAR and n-step sampling could cause 2n-phasic SAR.Practical two-step sampling produced triphasic SAR due to the Preston and Pan effects in large areas.Furthermore,before exploring biological or ecological mechanisms for the nature phenomenon,we should identify or exclude potential mathematical,statistical or sampling reasons.
