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 Lewis...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
At a rice wheat rotational free air CO 2 enrichment(FACE) platform, the effect of elevated atmospheric CO 2 on soil nematode communities in a farmland ecosystem was studied. Wheat plots were exposed to elevated atmosp...At a rice wheat rotational free air CO 2 enrichment(FACE) platform, the effect of elevated atmospheric CO 2 on soil nematode communities in a farmland ecosystem was studied. Wheat plots were exposed to elevated atmospheric CO 2(ambient 370 μl/L + 200 μl/L). 32 families and 40 genera of nematode were observed in soil suspensions during the study period. Under FACE treatment, the numbers of total nematodes, bacterivores and fungivores exhibited an increasing trend. Because of the seasonal variation of soil temperature and moisture, the effect of elevated atmospheric CO 2 on soil nematodes was only observed under favorable conditions. The response of nematode communities to elevated atmospheric CO 2 may indicate the change of soil food web.展开更多
Oxygen and nitrogen-functionalized carbon nanotubes （OCNTs and NCNTs） were applied as metal-free catalysts in selective olefin hydro- genation. A series of NCNTs was synthesized by NH3 post-treatment of OCNTs. Tempe...Oxygen and nitrogen-functionalized carbon nanotubes （OCNTs and NCNTs） were applied as metal-free catalysts in selective olefin hydro- genation. A series of NCNTs was synthesized by NH3 post-treatment of OCNTs. Temperature-programmed desorption, N2 physisorption, Raman spectroscopy, high-resolution transmission electron microscopy and X-ray photoelectron spectroscopy were employed to characterize the surface properties of OCNTs and NCNTs, aiming at a detailed analysis of the type and amount of oxygen- and nitrogen-containing groups as well as surface defects. The gas-phase treatments applied for oxygen and nitrogen functionalization at elevated temperatures up to 600 ℃ led to the increase of surface defects, but did not cause structural damages in the bulk. NCNTs showed a clearly higher activity than the pristine CNTs and OCNTs in the hydrogenation of 1,5-cyclooctadiene, and also the selectivity to cyclooctene was higher. The favorable catalytic properties are ascribed to the nitrogen-containing surface functional groups as well as surface defects related to nitrogen species. In contrast, oxygen-containing surface groups and the surface defects caused by oxygen species did not show clear contribution to the hydrogenation catalysis.展开更多
Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group rand...Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.展开更多
This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtap...This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.展开更多
We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open prob...We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.展开更多
Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposi...Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.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.
文摘At a rice wheat rotational free air CO 2 enrichment(FACE) platform, the effect of elevated atmospheric CO 2 on soil nematode communities in a farmland ecosystem was studied. Wheat plots were exposed to elevated atmospheric CO 2(ambient 370 μl/L + 200 μl/L). 32 families and 40 genera of nematode were observed in soil suspensions during the study period. Under FACE treatment, the numbers of total nematodes, bacterivores and fungivores exhibited an increasing trend. Because of the seasonal variation of soil temperature and moisture, the effect of elevated atmospheric CO 2 on soil nematodes was only observed under favorable conditions. The response of nematode communities to elevated atmospheric CO 2 may indicate the change of soil food web.
基金supported by the German Federal Ministry of Education and Research (BMBF) for the CarboKat Project (03X0204D) within the scope of the Inno.CNT Alliance
文摘Oxygen and nitrogen-functionalized carbon nanotubes （OCNTs and NCNTs） were applied as metal-free catalysts in selective olefin hydro- genation. A series of NCNTs was synthesized by NH3 post-treatment of OCNTs. Temperature-programmed desorption, N2 physisorption, Raman spectroscopy, high-resolution transmission electron microscopy and X-ray photoelectron spectroscopy were employed to characterize the surface properties of OCNTs and NCNTs, aiming at a detailed analysis of the type and amount of oxygen- and nitrogen-containing groups as well as surface defects. The gas-phase treatments applied for oxygen and nitrogen functionalization at elevated temperatures up to 600 ℃ led to the increase of surface defects, but did not cause structural damages in the bulk. NCNTs showed a clearly higher activity than the pristine CNTs and OCNTs in the hydrogenation of 1,5-cyclooctadiene, and also the selectivity to cyclooctene was higher. The favorable catalytic properties are ascribed to the nitrogen-containing surface functional groups as well as surface defects related to nitrogen species. In contrast, oxygen-containing surface groups and the surface defects caused by oxygen species did not show clear contribution to the hydrogenation catalysis.
文摘Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.
文摘This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.
文摘We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.
文摘Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.
