In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary ...In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.展开更多
This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we ...This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.展开更多
Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and ide...Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and identify the weakest subsystem to optimize products and improve their reliabilities.However,traditional ranking methods based on failure mode effect and critical analysis(FMECA)does not consider the complex maintenance of products.Herein,a weakness ranking method for the subsystems of heavy-duty machine tools is proposed based on generalized FMECA information.In this method,eight reliability indexes,including maintainability and maintenance cost,are considered in the generalized FMECA information.Subsequently,the cognition best worst method is used to calculate the weight of each screened index,and the weaknesses of the subsystems are ranked using a technique for order preference by similarity to an ideal solution.Finally,based on the failure data collected from certain domestic heavy-duty horizontal lathes,the weakness ranking result of the subsystems is obtained to verify the effectiveness of the proposed method.An improved weakness ranking method that can comprehensively analyze and identify weak subsystems is proposed herein for designing and improving the reliability of complex electromechanical products.展开更多
A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e+u+(1-e)rx or x=-e+uq-(1-e)rx where e is an idempotent and u is a invertible element. These ringsare shown to...A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e+u+(1-e)rx or x=-e+uq-(1-e)rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H(R) andT(R,a). The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent: that is R is pseudo weakly clean; there is an integer n such thatR[x]/(x^n) is pseudo weakly clean; there is an integer n such that R[[x]]/(x^n) is pseudo weakly clean.展开更多
In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, th...In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.展开更多
Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R...Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R and 0 ≠ ab ∈ √I, we have a ∈√I or b ∈ √I. In this paper, we introduce a new class of ideals that is closely related to the class of (weakly) semiprimary ideals. Let I(R) be the set of all ideals of R and let δ : I(R) → I(R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J I, we have L δ(L) and δ(J) δ(I). Let δ be an expansion function of ideals of R. Then a proper ideal I of R is called a δ-semiprimary (weakly δ-semiprimary) ideal of R if ab ∈ I (0 ≠ ab ∈ I) implies a ∈ δ(I) or b∈ δ(I). A number of results concerning weakly δ-semiprimary ideals and examples of weakly δ-semiprimary ideals are given.展开更多
The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and a...The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.展开更多
Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if wh...Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if whenevernonunit elements a,b,c∈R and O≠abc∈I,we have ab∈I or c∈√I.A number of results concerning weakly 1-absorbing primary ideals are given,as well as examples of weakly 1-absorbing primary ideals.Furthermore,we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.展开更多
Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakl...Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.展开更多
文摘In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.
文摘This paper aims to introduce new notions of (fuzzy) n-fold P-ideals and (fuzzy) n-fold weak P-ideals in BCI-algebras, and investigate several properties of the foldness theory of P-ideals in BCI-algebras. Finally, we construct a computer-program for studying the foldness theory of P-ideals in BCI-algebras.
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.
基金Supported by National Nat ural Science Foundation of China(Grant Nos.51675227,51975249)Jilin Province Science and Technology Development Funds(Grant Nos.20180201007GX,20190302017GX)+2 种基金Technology Development and Research of Jilin Province(Grant No.2019C037-01)Changchun Science and Technology Planning Project(Grant No.19SS011)National Science and technology Major Project(Grant No.2014ZX04015031).
文摘Heavy-duty machine tools are composed of many subsystems with different functions,and their reliability is governed by the reliabilities of these subsystems.It is important to rank the weaknesses of subsystems and identify the weakest subsystem to optimize products and improve their reliabilities.However,traditional ranking methods based on failure mode effect and critical analysis(FMECA)does not consider the complex maintenance of products.Herein,a weakness ranking method for the subsystems of heavy-duty machine tools is proposed based on generalized FMECA information.In this method,eight reliability indexes,including maintainability and maintenance cost,are considered in the generalized FMECA information.Subsequently,the cognition best worst method is used to calculate the weight of each screened index,and the weaknesses of the subsystems are ranked using a technique for order preference by similarity to an ideal solution.Finally,based on the failure data collected from certain domestic heavy-duty horizontal lathes,the weakness ranking result of the subsystems is obtained to verify the effectiveness of the proposed method.An improved weakness ranking method that can comprehensively analyze and identify weak subsystems is proposed herein for designing and improving the reliability of complex electromechanical products.
文摘A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e+u+(1-e)rx or x=-e+uq-(1-e)rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H(R) andT(R,a). The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent: that is R is pseudo weakly clean; there is an integer n such thatR[x]/(x^n) is pseudo weakly clean; there is an integer n such that R[[x]]/(x^n) is pseudo weakly clean.
基金Foundationitem:The NNSP(19971073) of China and the NSF of Yangzhou University
文摘In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.
文摘Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R and 0 ≠ ab ∈ √I, we have a ∈√I or b ∈ √I. In this paper, we introduce a new class of ideals that is closely related to the class of (weakly) semiprimary ideals. Let I(R) be the set of all ideals of R and let δ : I(R) → I(R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J I, we have L δ(L) and δ(J) δ(I). Let δ be an expansion function of ideals of R. Then a proper ideal I of R is called a δ-semiprimary (weakly δ-semiprimary) ideal of R if ab ∈ I (0 ≠ ab ∈ I) implies a ∈ δ(I) or b∈ δ(I). A number of results concerning weakly δ-semiprimary ideals and examples of weakly δ-semiprimary ideals are given.
基金supported by the State Key Program of National Natural Science Foundation of China(Grants No.11731008)the National Natural Science Foundation of China(Grants No.10771087)。
文摘The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.
文摘Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if whenevernonunit elements a,b,c∈R and O≠abc∈I,we have ab∈I or c∈√I.A number of results concerning weakly 1-absorbing primary ideals are given,as well as examples of weakly 1-absorbing primary ideals.Furthermore,we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
文摘Herzog,Hibi,Hreinddttir et al.introduced the class of closed graphs,and they proved that the binomial edge ideal JG of a graph G has quadratic GrSbner bases if G is closed.In this paper,we introduce the class of weakly closed graphs as a generalization of the closed graph,and we prove that the quotient ring S/JG of the polynomial ring S=K[x1,...,xn,y1,...,yn]with K a field and n=|V(G)|is F-pure if G is weakly closed.This fact is a generalization of Ohtani's theorem.