In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusfor...In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusforμ>0,s=1,2,...andμs∈Z^(+).In addition,the composition of x^(-s)ln|x|andis also defined for r,s∈Z^(+).展开更多
Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（...Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（r） of R in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn＇t be discussed respectively.展开更多
In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationsh...In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.展开更多
Let G be a finite abelian group and S be a sequence with elements of G.We say that S is a regular sequence over G if|SH|≤|H|-1 holds for every proper subgroup H of G,where SH denotes the subsequence of S consisting o...Let G be a finite abelian group and S be a sequence with elements of G.We say that S is a regular sequence over G if|SH|≤|H|-1 holds for every proper subgroup H of G,where SH denotes the subsequence of S consisting of all terms of S contained in H.We say that S is a zero-sum free sequence over G if 0■Σ(S),where Σ(S)■G denotes the set of group elements which can be expressed as a sum of a nonempty subsequence of S.In this paper,we study the inverse problems associated with Σ(S)when S is a regular sequence or a zero-sum free sequence over G=Cp■Cp,where p is a prime.展开更多
In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.
基金Tubitak(Scientific and Technological Research Council of Turkey).
文摘In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusforμ>0,s=1,2,...andμs∈Z^(+).In addition,the composition of x^(-s)ln|x|andis also defined for r,s∈Z^(+).
文摘Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1（r） of R in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn＇t be discussed respectively.
文摘In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.
基金supported in part by the Fundamental Research Funds for the Central Universities(No.3122019152)the National Natural Science Foundation of China(Grant Nos.11701256,11871258)+2 种基金the Youth Backbone Teacher Foundation of Henan's University(No.2019GGJS196)the China Scholarship Council(Grant No.201908410132)was also supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN 2017-03903).
文摘Let G be a finite abelian group and S be a sequence with elements of G.We say that S is a regular sequence over G if|SH|≤|H|-1 holds for every proper subgroup H of G,where SH denotes the subsequence of S consisting of all terms of S contained in H.We say that S is a zero-sum free sequence over G if 0■Σ(S),where Σ(S)■G denotes the set of group elements which can be expressed as a sum of a nonempty subsequence of S.In this paper,we study the inverse problems associated with Σ(S)when S is a regular sequence or a zero-sum free sequence over G=Cp■Cp,where p is a prime.
基金Supported by the Grant No.144031 by Ministary of Science of Republic of Serbia
文摘In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.
