Let G be a group.The family of all sets which are closed in every Hausdorf group topology of G form the family of closed sets of a T_(1) topology M_(G) on G called the Markov topology.Similarly,the family of all algeb...Let G be a group.The family of all sets which are closed in every Hausdorf group topology of G form the family of closed sets of a T_(1) topology M_(G) on G called the Markov topology.Similarly,the family of all algebraic subsets of G forms a family of closed sets for another T_(1)topology Z_(G) on G called the Zarski topology.A subgroup H of G is said to be Markov(resp.Zarski)embedded if the equality M_(G|H)=M_(H)(resp.Z_(G|H)=Z_(H))holds.I's proved that an abirary subgroup of a free group is both Zariski and Markov embedded in it.展开更多
A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of count...A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications,we obtain the highly ordered transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q.展开更多
Let p and q be two fixed non zero integers verifying the condition gcd(p,q) = 1. We check solutions in non zero integers a1,b1,a2,b2 and a3 for the following Diophantine equations: (B1) (B2) . The equations (B1) and (...Let p and q be two fixed non zero integers verifying the condition gcd(p,q) = 1. We check solutions in non zero integers a1,b1,a2,b2 and a3 for the following Diophantine equations: (B1) (B2) . The equations (B1) and (B2) were considered by R.C. Lyndon and J.L. Ullman in [1] and A.F. Beardon in [2] in connection with the freeness of the M?bius group generated by two matrices of namely and where .?They proved that if one of the equations (B1) or (B2) has solutions in non zero integers then the group is not free. We give algorithms to decide if these equations admit solutions. We obtain an arithmetical criteria on p and q for which (B1) admits solutions. We show that for all p and q the equations (B1) and (B2) have only a finite number of solutions.展开更多
How to rationally design effective and practical CO_2 adsorbent is a great challenge. Herein, an ultra-microporous metal-organic framework(FJI-H19) with high concentration of free carboxyl groups and uncoordinated Lew...How to rationally design effective and practical CO_2 adsorbent is a great challenge. Herein, an ultra-microporous metal-organic framework(FJI-H19) with high concentration of free carboxyl groups and uncoordinated Lewis basic sites has been synthesized from a multi-dental ligand with a high proportion of polar CO_2-philic atoms. FJI-H19 displays a relatively high CO_2 volumetric uptake(120 cm^3?cm^(–3)) with high selectivity under practical atmosphere(298 K and 1 bar). Further researches demonstrate that such high adsorption results from an unusual synergistic effect from free carboxyl group and uncoordinated N atoms. This result will provide a potential strategy for developing more effective and pratical CO_2 adsorbent based on MOFs.展开更多
Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Similar to free-standing pile groups, piled raft foundations are conventionally designed in which the piles carry the total load of structure and the raft bearing capacity is not taken into account. Numerous studies i...Similar to free-standing pile groups, piled raft foundations are conventionally designed in which the piles carry the total load of structure and the raft bearing capacity is not taken into account. Numerous studies indicated that this method is too conservative. Only when the pile cap is elevated from the ground level,the raft bearing contribution can be neglected. In a piled raft foundation, pileesoileraft interaction is complicated. Although several numerical studies have been carried out to analyze the behaviors of piled raft foundations, very few experimental studies are reported in the literature. The available laboratory studies mainly focused on steel piles. The present study aims to compare the behaviors of piled raft foundations with free-standing pile groups in sand, using laboratory physical models. Cast-in-place concrete piles and concrete raft are used for the tests. The tests are conducted on single pile, single pile in pile group, unpiled raft, free-standing pile group and piled raft foundation. We examine the effects of the number of piles, the pile installation method and the interaction between different components of foundation. The results indicate that the ultimate bearing capacity of the piled raft foundation is considerably higher than that of the free-standing pile group with the same number of piles. With installation of the single pile in the group, the pile bearing capacity and stiffness increase. Installation of the piles beneath the raft decreases the bearing capacity of the raft. When the raft bearing capacity is not included in the design process, the allowable bearing capacity of the piled raft is underestimated by more than 200%. This deviation intensifies with increasing spacing of the piles.展开更多
The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ ...The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(Ω) ∩ L∞(Ω) and f : R2n→R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).展开更多
Natural convective boundary layer flow and heat and mass transfer of a fluid with variable viscosity and thermal radiation over a vertical stretching surface in the presence of suction/injection is investigated by Lie...Natural convective boundary layer flow and heat and mass transfer of a fluid with variable viscosity and thermal radiation over a vertical stretching surface in the presence of suction/injection is investigated by Lie group analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. The effects of fluid viscosity and thermal radiation on the dimensionless velocity, temperature and concentration profiles are shown graphically. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by these parameters.展开更多
基金Supported by the Grant-in-Aid for Scientific Research(C)by the Japan Society for the Promotion of Science(20K03615)。
文摘Let G be a group.The family of all sets which are closed in every Hausdorf group topology of G form the family of closed sets of a T_(1) topology M_(G) on G called the Markov topology.Similarly,the family of all algebraic subsets of G forms a family of closed sets for another T_(1)topology Z_(G) on G called the Zarski topology.A subgroup H of G is said to be Markov(resp.Zarski)embedded if the equality M_(G|H)=M_(H)(resp.Z_(G|H)=Z_(H))holds.I's proved that an abirary subgroup of a free group is both Zariski and Markov embedded in it.
文摘A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications,we obtain the highly ordered transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q.
文摘Let p and q be two fixed non zero integers verifying the condition gcd(p,q) = 1. We check solutions in non zero integers a1,b1,a2,b2 and a3 for the following Diophantine equations: (B1) (B2) . The equations (B1) and (B2) were considered by R.C. Lyndon and J.L. Ullman in [1] and A.F. Beardon in [2] in connection with the freeness of the M?bius group generated by two matrices of namely and where .?They proved that if one of the equations (B1) or (B2) has solutions in non zero integers then the group is not free. We give algorithms to decide if these equations admit solutions. We obtain an arithmetical criteria on p and q for which (B1) admits solutions. We show that for all p and q the equations (B1) and (B2) have only a finite number of solutions.
基金supported by the National Natural Science Foundation of China(21390392,21471148)the Youth Innovation Promotion Association CAS
文摘How to rationally design effective and practical CO_2 adsorbent is a great challenge. Herein, an ultra-microporous metal-organic framework(FJI-H19) with high concentration of free carboxyl groups and uncoordinated Lewis basic sites has been synthesized from a multi-dental ligand with a high proportion of polar CO_2-philic atoms. FJI-H19 displays a relatively high CO_2 volumetric uptake(120 cm^3?cm^(–3)) with high selectivity under practical atmosphere(298 K and 1 bar). Further researches demonstrate that such high adsorption results from an unusual synergistic effect from free carboxyl group and uncoordinated N atoms. This result will provide a potential strategy for developing more effective and pratical CO_2 adsorbent based on MOFs.
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
文摘Similar to free-standing pile groups, piled raft foundations are conventionally designed in which the piles carry the total load of structure and the raft bearing capacity is not taken into account. Numerous studies indicated that this method is too conservative. Only when the pile cap is elevated from the ground level,the raft bearing contribution can be neglected. In a piled raft foundation, pileesoileraft interaction is complicated. Although several numerical studies have been carried out to analyze the behaviors of piled raft foundations, very few experimental studies are reported in the literature. The available laboratory studies mainly focused on steel piles. The present study aims to compare the behaviors of piled raft foundations with free-standing pile groups in sand, using laboratory physical models. Cast-in-place concrete piles and concrete raft are used for the tests. The tests are conducted on single pile, single pile in pile group, unpiled raft, free-standing pile group and piled raft foundation. We examine the effects of the number of piles, the pile installation method and the interaction between different components of foundation. The results indicate that the ultimate bearing capacity of the piled raft foundation is considerably higher than that of the free-standing pile group with the same number of piles. With installation of the single pile in the group, the pile bearing capacity and stiffness increase. Installation of the piles beneath the raft decreases the bearing capacity of the raft. When the raft bearing capacity is not included in the design process, the allowable bearing capacity of the piled raft is underestimated by more than 200%. This deviation intensifies with increasing spacing of the piles.
基金This work is supported by NNSF(10471063), Hunan NSF(03JJY4002) & Hunan Education Administration Item(03A011)
文摘The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(Ω) ∩ L∞(Ω) and f : R2n→R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).
文摘Natural convective boundary layer flow and heat and mass transfer of a fluid with variable viscosity and thermal radiation over a vertical stretching surface in the presence of suction/injection is investigated by Lie group analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. The effects of fluid viscosity and thermal radiation on the dimensionless velocity, temperature and concentration profiles are shown graphically. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by these parameters.
