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
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 <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;&...Let <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;"><em>hg</em><sub>2 </sub></span></span>whenever <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <i>g</i><sub>2</sub></span>. <em>G</em> is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <em>hg</em><sub>2</sub></span> whenever <span style="white-space:nowrap;"><em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub></span> and <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><em style="white-space:normal;">h</em><span style="white-space:normal;"> ≤ </span><em style="white-space:normal;">g</em><sub style="white-space:normal;">2</sub><em style="white-space:normal;">h</em> whenever <em>g</em><sub>1</sub> ≤ <em>g</em><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
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
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
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
Let R be a ring with an identity element.R∈IBN means that R<sup>m</sup>■R<sup>n</sup> implies m=n,R ∈IBN<sub>1</sub> means that R<sup>m</sup> ■R<sup>n</sup&...Let R be a ring with an identity element.R∈IBN means that R<sup>m</sup>■R<sup>n</sup> implies m=n,R ∈IBN<sub>1</sub> means that R<sup>m</sup> ■R<sup>n</sup>⊕K implies m≥n,and R ∈IBN<sub>2</sub> means that R<sup>m</sup>■R<sup>m</sup>⊕K implies K=0.In this paper we give some characteristic properties of IBN<sub>1</sub> and IBN<sub>2</sub>,with orderings o the Grothendieck groups.In addition,we obtain the following results:(1)If R ∈IBM<sub>1</sub> and all finitely generated projective left R-modules are stably free,then the Grothendieck group K<sub>o</sub>(R)is a totally ordered abelian group.(2)If the pre-ordering of the Grothendieck group K<sub>o</sub>(R)of a ring R is a partial ordering,then R ∈IBM<sub>1</sub> or K<sub>o</sub>(R)=0.展开更多
Bearing unique redox nature and high oxygen storage capacity,ceria(CeO_(2))has always been a promising CO oxidation catalyst support for gold(Au)catalysts and the like.Herein,a series of Au-CeO_(2)-P(P stands for pH v...Bearing unique redox nature and high oxygen storage capacity,ceria(CeO_(2))has always been a promising CO oxidation catalyst support for gold(Au)catalysts and the like.Herein,a series of Au-CeO_(2)-P(P stands for pH value)samples was prepared by a co-precipitation method with the assistance of an alkaline environment and amino groups functionalized ordered mesoporous polymer(OMP-NH_(2)).Afterward,all samples described above were characterized that the Au-CeO_(2)-P catalysts are made of Au-Ce-O solid solution and Au nanoparticles(NPs)supported on CeO_(2).It turns out that OMP-NH_(2) is not just a simple sacrificial template for mesoporous structure,but also plays an important role as an amino source,explaining the presence of rich oxygen vacancies.Due to the concentration of oxygen vacancies in Au-Ce-O solid solution is the key factor for the oxygen mobility of CO oxidation,the catalytic results also demonstrate that the catalytic activity of Au-CeO_(2)-P catalysts is related to the concentration of their oxygen vacancies.Moreover,Au-CeO_(2)-9.6 with a highest concentration of oxygen vacancies(as high as 13.98%)in Au-CeO_(2)-P catalysts exhibits the best catalytic activity(complete conversion at 10℃).展开更多
In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.
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 <em>G</em> be a group. <em>G</em> is right-orderable provided it admits a total order ≤ satisfying <em>hg</em><sub>1</sub> <span style="white-space:normal;">≤ <span style="white-space:normal;"><em>hg</em><sub>2 </sub></span></span>whenever <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <i>g</i><sub>2</sub></span>. <em>G</em> is orderable provided it admits a total order ≤ satisfying both: <em style="white-space:normal;">hg</em><sub style="white-space:normal;">1</sub><span style="white-space:normal;"> </span><span style="white-space:normal;">≤ <em>hg</em><sub>2</sub></span> whenever <span style="white-space:nowrap;"><em>g</em><sub>1</sub> ≤ <em>g</em><sub>2</sub></span> and <em style="white-space:normal;">g</em><sub style="white-space:normal;">1</sub><em style="white-space:normal;">h</em><span style="white-space:normal;"> ≤ </span><em style="white-space:normal;">g</em><sub style="white-space:normal;">2</sub><em style="white-space:normal;">h</em> whenever <em>g</em><sub>1</sub> ≤ <em>g</em><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).
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.
基金Supported by National Nature Science Foundation of China.
文摘Let R be a ring with an identity element.R∈IBN means that R<sup>m</sup>■R<sup>n</sup> implies m=n,R ∈IBN<sub>1</sub> means that R<sup>m</sup> ■R<sup>n</sup>⊕K implies m≥n,and R ∈IBN<sub>2</sub> means that R<sup>m</sup>■R<sup>m</sup>⊕K implies K=0.In this paper we give some characteristic properties of IBN<sub>1</sub> and IBN<sub>2</sub>,with orderings o the Grothendieck groups.In addition,we obtain the following results:(1)If R ∈IBM<sub>1</sub> and all finitely generated projective left R-modules are stably free,then the Grothendieck group K<sub>o</sub>(R)is a totally ordered abelian group.(2)If the pre-ordering of the Grothendieck group K<sub>o</sub>(R)of a ring R is a partial ordering,then R ∈IBM<sub>1</sub> or K<sub>o</sub>(R)=0.
基金Project supported by the National Natural Science Foundation of China(22002056,21663016,21961021)the Key Laboratory of Jiangxi Province for Environment and Energy Catalysis(20181BCD40004)the Research Project on Teaching Reform of Degree and Graduate Education of Jiangxi Province(JXYJG-2018-007)。
文摘Bearing unique redox nature and high oxygen storage capacity,ceria(CeO_(2))has always been a promising CO oxidation catalyst support for gold(Au)catalysts and the like.Herein,a series of Au-CeO_(2)-P(P stands for pH value)samples was prepared by a co-precipitation method with the assistance of an alkaline environment and amino groups functionalized ordered mesoporous polymer(OMP-NH_(2)).Afterward,all samples described above were characterized that the Au-CeO_(2)-P catalysts are made of Au-Ce-O solid solution and Au nanoparticles(NPs)supported on CeO_(2).It turns out that OMP-NH_(2) is not just a simple sacrificial template for mesoporous structure,but also plays an important role as an amino source,explaining the presence of rich oxygen vacancies.Due to the concentration of oxygen vacancies in Au-Ce-O solid solution is the key factor for the oxygen mobility of CO oxidation,the catalytic results also demonstrate that the catalytic activity of Au-CeO_(2)-P catalysts is related to the concentration of their oxygen vacancies.Moreover,Au-CeO_(2)-9.6 with a highest concentration of oxygen vacancies(as high as 13.98%)in Au-CeO_(2)-P catalysts exhibits the best catalytic activity(complete conversion at 10℃).
文摘In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.