All parabolic subgroups and Borel subgroups of PΩ（2m ＋ 1, F） over a linearable field F of characteristic 0 are shown to be complete groups, provided m 〉 3.
Let G be an l subgroup of a complete lattice ordered group H . For Conrad and McAlisters open question: to characterise those l subgroups of a complete l group H that have a unique completion...Let G be an l subgroup of a complete lattice ordered group H . For Conrad and McAlisters open question: to characterise those l subgroups of a complete l group H that have a unique completion in H , a necessary and sufficient condition on G is given so that G has a unique completion in H .展开更多
The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule contain...The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.展开更多
A well-known result for Vilenkin systems is the fact that for all 1 〈 p 〈 oc the n-th partial sums of Fourier series of all functions in the space Lp converge to the function in LP-norm. This statement can not be ge...A well-known result for Vilenkin systems is the fact that for all 1 〈 p 〈 oc the n-th partial sums of Fourier series of all functions in the space Lp converge to the function in LP-norm. This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups, but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way.展开更多
With one exception, the holomorph of a finite dimensional abelian connectedalgebraic group is shown to be a complete generalized algebraic group. This result on algebraic group is an analogy to that on Lie algebra.
A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a part...A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a partition of the set of all k-cycles of Kv into CS（v, k, λ）s, and is denoted by LCS（v, k, λ）. A （v - 1）-cycle in K, is called almost Hamilton. The completion of the existence problem for LCS（v, v- 1,λ） depends only on one case： all v ≥ 4 for λ=2. In this paper, it is shown that there exists an LCS（v,v - 1,2） for all v ≡ 2 （mod 4）, v ≥ 6.展开更多
文摘All parabolic subgroups and Borel subgroups of PΩ（2m ＋ 1, F） over a linearable field F of characteristic 0 are shown to be complete groups, provided m 〉 3.
文摘Let G be an l subgroup of a complete lattice ordered group H . For Conrad and McAlisters open question: to characterise those l subgroups of a complete l group H that have a unique completion in H , a necessary and sufficient condition on G is given so that G has a unique completion in H .
基金Supported partially by NSF of China (10201007)National Tianyuan Foundation of China (A0324614)
文摘The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.
基金Supported by project TAMOP-4.2.2.A-11/1/KONV-2012-0051
文摘A well-known result for Vilenkin systems is the fact that for all 1 〈 p 〈 oc the n-th partial sums of Fourier series of all functions in the space Lp converge to the function in LP-norm. This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups, but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071078).
文摘With one exception, the holomorph of a finite dimensional abelian connectedalgebraic group is shown to be a complete generalized algebraic group. This result on algebraic group is an analogy to that on Lie algebra.
基金Supported in part by the National Natural Science Foundation of China(No.10901051,11201143)the Fundamental Research Funds for the Central Universities(No.2016MS66)the Co-construction Project of Bejing Municipal Commission of Education
文摘A k-cycle system of order v with index A, denoted by CS（v, k, λ）, is a collection A of k-cycles （blocks） of Kv such that each edge in Kv appears in exactly λ blocks of A. A large set of CS（v, k, λ）s is a partition of the set of all k-cycles of Kv into CS（v, k, λ）s, and is denoted by LCS（v, k, λ）. A （v - 1）-cycle in K, is called almost Hamilton. The completion of the existence problem for LCS（v, v- 1,λ） depends only on one case： all v ≥ 4 for λ=2. In this paper, it is shown that there exists an LCS（v,v - 1,2） for all v ≡ 2 （mod 4）, v ≥ 6.
