Because the grinding temperature is high when grinding using conventional disordered grinding wheels,the grinding quality improvement is limited when using single abrasive ordered grinding wheels,and the wheel prepara...Because the grinding temperature is high when grinding using conventional disordered grinding wheels,the grinding quality improvement is limited when using single abrasive ordered grinding wheels,and the wheel preparation process is complex and costly when using microstructured grinding wheels,abrasive groups ordered grinding wheels are widely investigated.However,there is a paucity of systematic analyses and comprehensive reviews focused on abrasive groups ordered grinding wheels.Therefore,this paper defines abrasive groups ordered grinding wheels and classifies them,based on their unique characteristics,into groups such as abrasive blocks ordered grinding wheel,fine grain structured grinding wheel,abrasive clusters ordered grinding wheel,and abrasive fibers ordered grinding wheel.We provide an overview of the latest advances in wheel structures,preparation methods,and abrasive selection for various types of abrasive groups ordered grinding wheels.Furthermore,we conduct a comparative analysis of the existing types,significant advantages,and challenges associated with the four types of abrasive groups ordered grinding wheels.Looking ahead,given the potential of abrasive groups ordered grinding wheels in reducing grinding force and temperature,we recommend further exploration of their application in combination with special processing techniques.This could pave the way for the development of machining processes that are more environmentally friendly,energy-efficient,and precise.展开更多
Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney Ja...Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.展开更多
Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft gr...Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.展开更多
Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg<sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;">h...Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg<sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;">hg<sub>2 </sub>whenever <em style="white-space:normal;">g<sub style="white-space:normal;">1</sub><span style="white-space:normal;"> <span style="white-space:normal;">≤ g<sub>2</sub>. G is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg<sub style="white-space:normal;">1</sub><span style="white-space:normal;"> <span style="white-space:normal;">≤ hg<sub>2</sub> whenever <span style="white-space:nowrap;">g<sub>1</sub> ≤ g<sub>2</sub> and <em style="white-space:normal;">g<sub style="white-space:normal;">1</sub><em style="white-space:normal;">h<span style="white-space:normal;"> ≤ <em style="white-space:normal;">g<sub style="white-space:normal;">2</sub><em style="white-space:normal;">h whenever g<sub>1</sub> ≤ g<sub>2</sub>. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.展开更多
The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commuta...The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commutativity of finite p-groups, and the structure of the generators of its automorphism groups is obtained. Then the orders of automorphism groups are determined through some properties of equivalence in number theory.展开更多
In this paper, maximal above and below pairs of fully ordered groups (o groups) are studied. It is shown that maximal above and below pairs of an divisible abelian o group have some specific properties, and by using...In this paper, maximal above and below pairs of fully ordered groups (o groups) are studied. It is shown that maximal above and below pairs of an divisible abelian o group have some specific properties, and by using these properties another embedding method of an abelian o group to real valued functions is discussed.展开更多
The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the ...The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).展开更多
For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G i...For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.展开更多
Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] ...Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.展开更多
This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of el...This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.展开更多
This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and gene...This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.展开更多
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract ...Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.展开更多
A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.Th...A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.展开更多
With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Ya...With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.展开更多
In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describin...Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].展开更多
We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for ...We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for every n, K0（A） is weakly unperforated too. Furthermore, the Riesz interpolation property of K0（An） can be transmitted to K0（A）.展开更多
Linear wave theory and Longuet-Higgins and Steward’s (1964) group-induced second-order longweve (GSLW) theory ware used in this study on the grouping effect on wave forces acting on a verticalbreakwater. The calculat...Linear wave theory and Longuet-Higgins and Steward’s (1964) group-induced second-order longweve (GSLW) theory ware used in this study on the grouping effect on wave forces acting on a verticalbreakwater. The calculated variance of total wave pressure on the vertical breakwater was closer tothe measured value if the wave grouping effect was considered.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
基金Supported by National Natural Science Foundation of China(Grant No.52175401)Hunan Provincial Postgraduate Scientific Research Innovation Project(Grant No.QL20230244)+1 种基金Enterprise Innovation and Development Joint Program of National Natural Science Foundation of China(Grant No.U20B2032)Hunan Provincial Science and Technology Innovation Program(Grant No.2022RC1050).
文摘Because the grinding temperature is high when grinding using conventional disordered grinding wheels,the grinding quality improvement is limited when using single abrasive ordered grinding wheels,and the wheel preparation process is complex and costly when using microstructured grinding wheels,abrasive groups ordered grinding wheels are widely investigated.However,there is a paucity of systematic analyses and comprehensive reviews focused on abrasive groups ordered grinding wheels.Therefore,this paper defines abrasive groups ordered grinding wheels and classifies them,based on their unique characteristics,into groups such as abrasive blocks ordered grinding wheel,fine grain structured grinding wheel,abrasive clusters ordered grinding wheel,and abrasive fibers ordered grinding wheel.We provide an overview of the latest advances in wheel structures,preparation methods,and abrasive selection for various types of abrasive groups ordered grinding wheels.Furthermore,we conduct a comparative analysis of the existing types,significant advantages,and challenges associated with the four types of abrasive groups ordered grinding wheels.Looking ahead,given the potential of abrasive groups ordered grinding wheels in reducing grinding force and temperature,we recommend further exploration of their application in combination with special processing techniques.This could pave the way for the development of machining processes that are more environmentally friendly,energy-efficient,and precise.
基金The Science Research Foundation of Chongqing Municipal Education Commission of China(KJ050611)
文摘Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.
文摘Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.
文摘Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg<sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;">hg<sub>2 </sub>whenever <em style="white-space:normal;">g<sub style="white-space:normal;">1</sub><span style="white-space:normal;"> <span style="white-space:normal;">≤ g<sub>2</sub>. G is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg<sub style="white-space:normal;">1</sub><span style="white-space:normal;"> <span style="white-space:normal;">≤ hg<sub>2</sub> whenever <span style="white-space:nowrap;">g<sub>1</sub> ≤ g<sub>2</sub> and <em style="white-space:normal;">g<sub style="white-space:normal;">1</sub><em style="white-space:normal;">h<span style="white-space:normal;"> ≤ <em style="white-space:normal;">g<sub style="white-space:normal;">2</sub><em style="white-space:normal;">h whenever g<sub>1</sub> ≤ g<sub>2</sub>. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.
基金The Science Research Foundation of Chongqing Municipal Education Commission of China(KJ050611)
文摘The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commutativity of finite p-groups, and the structure of the generators of its automorphism groups is obtained. Then the orders of automorphism groups are determined through some properties of equivalence in number theory.
文摘In this paper, maximal above and below pairs of fully ordered groups (o groups) are studied. It is shown that maximal above and below pairs of an divisible abelian o group have some specific properties, and by using these properties another embedding method of an abelian o group to real valued functions is discussed.
文摘The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).
基金This work has been supported by the Research Institute for Fundamental Sciences Tabriz,Iran.
文摘For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.
基金This work is Supported by NSF of Heilongjiang Provice
文摘Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.
文摘This paper aims at treating a study on the order of every element for addition and multiplication composition in the higher order of groups for different algebraic structures as groups;order of a group and order of element of a group in real numbers. Here we discuss the higher order of groups in different types of order which will give us practical knowledge to see the applications of the addition and multiplication composition. If G is a finite group, n is a positive integer and a ⋴G, then the order of the products na. When G is a finite group, every element must have finite order. However, the converse is false: there are infinite groups where each element has finite order. For example, in the group of all roots of unity in C<sup>×</sup> each element has finite order. Finally, we find out the order of every element of a group in different types of higher order of group.
文摘This paper aims to treat a study of generators of the cyclic group of higher even, odd, and prime order for composition being multiplication. In fact we developed order of a group, order of element of a group and generators of the cyclic group in real numbers. Also we express cyclic and generators of the group for composition in real numbers. Here we discuss the higher order of groups in different types of order, and generators of the cyclic group which will give us practical knowledge to see the applications of the composition. In order to find out the order of an element am∈Gin which an=e= identity element, then find Highest Common Factor i.e. (H.C.F) of mand n. When Gis a finite group, every element must have finite order but the converse is false. There are infinite groups where each element has a finite order. There may be more than one generator of a cyclic group. Also every cyclic group is necessarily abelian. But show that every infinite cyclic group contains only two generators. Finally, we find out the generators of the cyclic group of higher even, odd and prime order in different types of the group for composition being multiplication.
基金supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)
文摘Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
基金supported by National Natural Science Funds for Young Scholar(No.50903027)the Natural Science Foundation of Hebei Province(No.E2010000058)Education Department Science Research Plan of Hebei Province(No.2007307).
文摘A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.
基金supported by the National Natural Science Foundation of China (10872192)
文摘With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117136411271301)+2 种基金the Natural Science Foundation Project of CQ CSTC(Grant No.2014jcyjA00004)the Science and Technology Project of Chongqing Education Committee(Grant No.KJ1400520)the Foundation Project of Chongqing Normal University(Grant No.14XYY026)
文摘In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
文摘Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].
基金The NNSF (10271090) of China and Shanghai Priority Academic Discipline.
文摘We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for every n, K0（A） is weakly unperforated too. Furthermore, the Riesz interpolation property of K0（An） can be transmitted to K0（A）.
文摘Linear wave theory and Longuet-Higgins and Steward’s (1964) group-induced second-order longweve (GSLW) theory ware used in this study on the grouping effect on wave forces acting on a verticalbreakwater. The calculated variance of total wave pressure on the vertical breakwater was closer tothe measured value if the wave grouping effect was considered.
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.
