This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semil...This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).展开更多
Computer-generated aesthetic patterns arewidely used as design materials in various fields. Themost common methods use fractals or dynamicalsystems as basic tools to create various patterns. Toenhance aesthetics and c...Computer-generated aesthetic patterns arewidely used as design materials in various fields. Themost common methods use fractals or dynamicalsystems as basic tools to create various patterns. Toenhance aesthetics and controllability, some researchershave introduced symmetric layouts along with thesetools. One popular strategy employs dynamical systemscompatible with symmetries that construct functionswith the desired symmetries. However, these aretypically confined to simple planar symmetries. Theother generates symmetrical patterns under theconstraints of tilings. Although it is slightly moreflexible, it is restricted to small ranges of tilingsand lacks textural variations. Thus, we proposed anew approach for generating aesthetic patterns bysymmetrizing quasi-regular patterns using general kuniformtilings. We adopted a unified strategy toconstruct invariant mappings for k-uniform tilings thatcan eliminate texture seams across the tiling edges.Furthermore, we constructed three types of symmetriesassociated with the patterns: dihedral, rotational, andreflection symmetries. The proposed method can beeasily implemented using GPU shaders and is highlyefficient and suitable for complicated tiling with regularpolygons. Experiments demonstrated the advantages of our method over state-of-the-art methods in terms offlexibility in controlling the generation of patterns withvarious parameters as well as the diversity of texturesand styles.展开更多
The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite...The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.展开更多
In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups ...In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.展开更多
A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approx...A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.展开更多
Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak converge...Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.展开更多
引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是...引入拟正则Armendariz环并研究其性质。证明弱Armendariz环是拟正则Armendariz环,直积∏i∈I R i是拟正则Armendariz环当且仅当每个环R i(i∈I)是拟正则Armendariz环,同时证明R是拟正则Armendariz环当且仅当上三角矩阵环T n(R)(n≥2)是拟正则Armendariz环,并通过例子说明任意环R上的全矩阵环M n(R)(n≥2)不是拟正则Armendariz环。展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).
基金supported by the Key R&D Programs of Zhejiang Province(Nos.2023C01224 and 2022C01220)the National Natural Science Foundation of China(No.61702458)+1 种基金Yun Zhang was partially supported by Zhejiang Province Public Welfare Technology Application Research(No.LGG22F020009)Key Lab of Film and TV Media Technology of Zhejiang Province(No.2020E10015).
文摘Computer-generated aesthetic patterns arewidely used as design materials in various fields. Themost common methods use fractals or dynamicalsystems as basic tools to create various patterns. Toenhance aesthetics and controllability, some researchershave introduced symmetric layouts along with thesetools. One popular strategy employs dynamical systemscompatible with symmetries that construct functionswith the desired symmetries. However, these aretypically confined to simple planar symmetries. Theother generates symmetrical patterns under theconstraints of tilings. Although it is slightly moreflexible, it is restricted to small ranges of tilingsand lacks textural variations. Thus, we proposed anew approach for generating aesthetic patterns bysymmetrizing quasi-regular patterns using general kuniformtilings. We adopted a unified strategy toconstruct invariant mappings for k-uniform tilings thatcan eliminate texture seams across the tiling edges.Furthermore, we constructed three types of symmetriesassociated with the patterns: dihedral, rotational, andreflection symmetries. The proposed method can beeasily implemented using GPU shaders and is highlyefficient and suitable for complicated tiling with regularpolygons. Experiments demonstrated the advantages of our method over state-of-the-art methods in terms offlexibility in controlling the generation of patterns withvarious parameters as well as the diversity of texturesand styles.
文摘The uniqueness of the Beurling-Deny first formula in quasi-regular Dirichlet spaces is verified in terms of the strictly strong local property. An extension of the Beurling-Deny second formula is obtained in infinite dimensional spaces.
文摘In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.
文摘A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.
基金Project partially supported by the National Natural Science Foundation of ChinaTianyuan Mathematics Foundation.
文摘Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.
