Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this pape...Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.展开更多
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
Let G be a finite group.A subgroup H of G is called an H-subgroup in G if NG(H) ∩Hg≤H for all g∈G.A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G=HK and H∩...Let G be a finite group.A subgroup H of G is called an H-subgroup in G if NG(H) ∩Hg≤H for all g∈G.A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G=HK and H∩K is an H-subgroup in G.In this paper,we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G.Our results improve and generalize several recent results in the literature.展开更多
In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab...In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.展开更多
Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subg...Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.展开更多
The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as cont...The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as control were treated by pure moxa stick. After treatment, the serum gastrin, urinary D - xylose excretory rate and T cell subgroups in patients with spleen deficiency have been greatly improved as compared with those before treatment in two groups (P< 0.01 or 0.05). Comparing the changes of the indexes between treatment group and control group, there were significant(P<0.05), or markedly significant(P<0.01) differences. It indicated that the medicinal moxibustion could improve the secreting and absorbing functions of digestive tract and the cellular immune function in patients with spleen deficiency.展开更多
The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case ...The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.展开更多
Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairmen...Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairment was ex-plored with a sample of 113 participants with CFS. Subgroups were created based on past and current psychiatric status including those whose psychiatric history was premorbid and current, postmorbid and current, past but not current, and those with no lifetime diagnosis. Results from a one-way MANOVA revealed that patients with a premorbid and current psychiat-ric disorder reported significantly higher pain severity, more somatic symptoms, poorer sleep quality, and poorer quality of life than those with no psychiatric history. Levels of fatigue and physical functioning among patients with CFS were unrelated to the four subgroups in this study. Although those with a premorbid and current psychiatric disorder were differentiated from those with no psychiatric history on some markers of impairment, the sample as a whole had severe fatigue-related impairment, which is the cardinal symptom of CFS. Implications for research are discussed.展开更多
In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.
Suppose we have a sample of subjects in two treatment groups.To study the difference of the treatment effects,we can analyse the data using all subjects(overall analysis).We may also divide the subjects into several s...Suppose we have a sample of subjects in two treatment groups.To study the difference of the treatment effects,we can analyse the data using all subjects(overall analysis).We may also divide the subjects into several subgroups based on some covariates of interest(eg,gender),and study the treatment effects within each subgroup.The results of these two analyses may be different or even in opposite directions.In this paper,we give a general sufficient condition of consistency between the overall and subgroup analyses.展开更多
The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structur...The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.展开更多
Although modern technology has an important role in human economic and social development,it can result in significant ecological damage.Thus,research has begun to focus on so-called"ecological technologies"...Although modern technology has an important role in human economic and social development,it can result in significant ecological damage.Thus,research has begun to focus on so-called"ecological technologies"to repair the degraded land and fragmented ecological environment and build a green mode of production and development.However,the concept of"ecological technology"is currently ill-defined,given the many different research fields involved.Therefore,here we divide ecological technologies into broad versus narrow technologies in terms of their impact on economic and social development and the related needs of production and ecological governance.We redefine each concept and clarify their aims and extensions,before further dividing them into three groups and seven subgroups,and clarifying the functions of each.The grouping and subgrouping of ecological technology will lay a foundation for the technology selection,collocation,implementation,promotion,monitoring and evaluation of ecological engineering planning and design.展开更多
Cancer trials often start investigational therapy at diagnosis or after a selected number of relapses.These are the usual core inclusion criteria in clinical trials.Hence it is helpful when planning a trial to know th...Cancer trials often start investigational therapy at diagnosis or after a selected number of relapses.These are the usual core inclusion criteria in clinical trials.Hence it is helpful when planning a trial to know the likely percentages of patients receiving standard therapy at clinics and hospitals who meet this key inclusion criteria of being newly diagnosed during a period or having just had their first,second or third relapse during an anticipated enrollment time frame.Often regulatory agencies will have approvals tied to the use of a therapy in a relapsed context or in a newly diagnosed context.We provide details on calculations to help those in clinical trial operations make realistic assessments on the number of sites and likely enrollment at clinical trial sites,and the enrollment time frames that might be needed to complete planned total patient enrollment.The estimates complement site feasibility questionnaires which are often sent to gauge patient availability and site interest.展开更多
基金Yibin University Pre-research Project,Research on the coupling and coordinated development ofmanufacturing and logistics industry under the background of intelligentmanufacturing,(2022YY001)Sichuan ProvincialDepartment of EducationWater Transport EconomicResearch Center,Research on the Development Path and Countermeasures of the Advanced Manufacturing Industry in the Sanjiang New District of Yibin under a“dual circulation”development pattern(SYJJ2020A06).
文摘Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group.A subgroup H of G is called an H-subgroup in G if NG(H) ∩Hg≤H for all g∈G.A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G=HK and H∩K is an H-subgroup in G.In this paper,we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G.Our results improve and generalize several recent results in the literature.
文摘In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.
文摘Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.
文摘The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as control were treated by pure moxa stick. After treatment, the serum gastrin, urinary D - xylose excretory rate and T cell subgroups in patients with spleen deficiency have been greatly improved as compared with those before treatment in two groups (P< 0.01 or 0.05). Comparing the changes of the indexes between treatment group and control group, there were significant(P<0.05), or markedly significant(P<0.01) differences. It indicated that the medicinal moxibustion could improve the secreting and absorbing functions of digestive tract and the cellular immune function in patients with spleen deficiency.
文摘The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.
文摘Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairment was ex-plored with a sample of 113 participants with CFS. Subgroups were created based on past and current psychiatric status including those whose psychiatric history was premorbid and current, postmorbid and current, past but not current, and those with no lifetime diagnosis. Results from a one-way MANOVA revealed that patients with a premorbid and current psychiat-ric disorder reported significantly higher pain severity, more somatic symptoms, poorer sleep quality, and poorer quality of life than those with no psychiatric history. Levels of fatigue and physical functioning among patients with CFS were unrelated to the four subgroups in this study. Although those with a premorbid and current psychiatric disorder were differentiated from those with no psychiatric history on some markers of impairment, the sample as a whole had severe fatigue-related impairment, which is the cardinal symptom of CFS. Implications for research are discussed.
基金Supported by the Scientific Research Foundation of Kaili University(Z1519)Guizhou Province Excellence Teacher Education Program(Mathematics and Applied Mathematics)
文摘In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.
文摘Suppose we have a sample of subjects in two treatment groups.To study the difference of the treatment effects,we can analyse the data using all subjects(overall analysis).We may also divide the subjects into several subgroups based on some covariates of interest(eg,gender),and study the treatment effects within each subgroup.The results of these two analyses may be different or even in opposite directions.In this paper,we give a general sufficient condition of consistency between the overall and subgroup analyses.
文摘The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
基金National Key Research and Development Program of China(2016YFC0503702)。
文摘Although modern technology has an important role in human economic and social development,it can result in significant ecological damage.Thus,research has begun to focus on so-called"ecological technologies"to repair the degraded land and fragmented ecological environment and build a green mode of production and development.However,the concept of"ecological technology"is currently ill-defined,given the many different research fields involved.Therefore,here we divide ecological technologies into broad versus narrow technologies in terms of their impact on economic and social development and the related needs of production and ecological governance.We redefine each concept and clarify their aims and extensions,before further dividing them into three groups and seven subgroups,and clarifying the functions of each.The grouping and subgrouping of ecological technology will lay a foundation for the technology selection,collocation,implementation,promotion,monitoring and evaluation of ecological engineering planning and design.
文摘Cancer trials often start investigational therapy at diagnosis or after a selected number of relapses.These are the usual core inclusion criteria in clinical trials.Hence it is helpful when planning a trial to know the likely percentages of patients receiving standard therapy at clinics and hospitals who meet this key inclusion criteria of being newly diagnosed during a period or having just had their first,second or third relapse during an anticipated enrollment time frame.Often regulatory agencies will have approvals tied to the use of a therapy in a relapsed context or in a newly diagnosed context.We provide details on calculations to help those in clinical trial operations make realistic assessments on the number of sites and likely enrollment at clinical trial sites,and the enrollment time frames that might be needed to complete planned total patient enrollment.The estimates complement site feasibility questionnaires which are often sent to gauge patient availability and site interest.
