In this paper, we introduce two new classes of groups that are described as weakly nilpotent and weakly solvable groups. A group G is weakly nilpotent if its derived subgroup does not have a supplement except G and a group G is weakly solvable if its derived subgroup does not have a normal supplement except G. We present some examples and counter-examples for these groups and characterize a finitely generated weakly nilpotent group. Moreover, we characterize the nilpotent and solvable groups in terms of weakly nilpotent and weakly solvable groups. Finally, we prove that if F is a free group of rank n such that every normal subgroup of F has rank n, then F is weakly solvable.
{"title":"Groups whose derived subgroup is not supplemented by any proper subgroup","authors":"Shiv Narain, Sunil Kumar, Gaurav Mittal, Surinder Kumar","doi":"10.52737/18291163-2022.14.10-1-13","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.10-1-13","url":null,"abstract":"In this paper, we introduce two new classes of groups that are described as weakly nilpotent and weakly solvable groups. A group G is weakly nilpotent if its derived subgroup does not have a supplement except G and a group G is weakly solvable if its derived subgroup does not have a normal supplement except G. We present some examples and counter-examples for these groups and characterize a finitely generated weakly nilpotent group. Moreover, we characterize the nilpotent and solvable groups in terms of weakly nilpotent and weakly solvable groups. Finally, we prove that if F is a free group of rank n such that every normal subgroup of F has rank n, then F is weakly solvable.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44958535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-13DOI: 10.52737/18291163-2022.14.7-1-18
Raúl Pachón
In this paper, we define and study the ⋄-connected spaces as a generalization of the connectedness, and thus of the Ekici-Noiri and Modak-Noiri notions, through ideals.
{"title":"A generalization of connectedness via ideals","authors":"Raúl Pachón","doi":"10.52737/18291163-2022.14.7-1-18","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.7-1-18","url":null,"abstract":"In this paper, we define and study the ⋄-connected spaces as a generalization of the connectedness, and thus of the Ekici-Noiri and Modak-Noiri notions, through ideals.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-30DOI: 10.52737/18291163-2022.14.6-1-10
Grigor Kirakosyan
The present paper considers an integral operator defined on the entire real axis, which differs from the Hilbert transform with terms where kernels are constructed using integral exponential functions. The considered operator has similar properties with respect to the Hilbert transform. The form of the inverse operator is obtained.
{"title":"On the invertibility of one integral operator","authors":"Grigor Kirakosyan","doi":"10.52737/18291163-2022.14.6-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.6-1-10","url":null,"abstract":"The present paper considers an integral operator defined on the entire real axis, which differs from the Hilbert transform with terms where kernels are constructed using integral exponential functions. The considered operator has similar properties with respect to the Hilbert transform. The form of the inverse operator is obtained.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48344289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.52737/18291163-2022.14.5-1-15
Carlos Granados, A. Das
In this paper, we prove two new Tauberian theorems via statistical Cesàro summability mean of a continuous function of three variables by using oscillating behavior and De la Vallée Poussin means of a triple integral over a locally convex space. Moreover, some remarks and corollaries are provided here to support our results.
本文利用振荡行为和局部凸空间上三积分的De la Vallée Poussin均值，通过三元连续函数的统计Cesàro可和性均值，证明了两个新的Tauberian定理。此外，这里提供了一些评论和推论，以支持我们的结果。
{"title":"New Tauberian theorems for statistical Cesàro summability of a function of three variables over a locally convex space","authors":"Carlos Granados, A. Das","doi":"10.52737/18291163-2022.14.5-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.5-1-15","url":null,"abstract":"In this paper, we prove two new Tauberian theorems via statistical Cesàro summability mean of a continuous function of three variables by using oscillating behavior and De la Vallée Poussin means of a triple integral over a locally convex space. Moreover, some remarks and corollaries are provided here to support our results.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49121120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-18DOI: 10.52737/18291163-2022.14.8-1-40
L. Khachatryan
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss possible applications of the considered systems.
{"title":"Description of random fields by systems of conditional distributions","authors":"L. Khachatryan","doi":"10.52737/18291163-2022.14.8-1-40","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.8-1-40","url":null,"abstract":"In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss possible applications of the considered systems.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45003016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-10DOI: 10.52737/18291163-2022.14.4-1-9
A. Kumar, Z. Manzoor, B. Zargar
{"title":"Annular region containing all the zeros of lacunary-type polynomials","authors":"A. Kumar, Z. Manzoor, B. Zargar","doi":"10.52737/18291163-2022.14.4-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.4-1-9","url":null,"abstract":"","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48277785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-10DOI: 10.52737/18291163-2022.14.1-1-9
R. Khats
In this paper, we study an integral representation of one class of entire functions. Conditions for the existence of this representation in terms of certain solutions of some differential equations are found. We obtain asymptotic estimates of entire functions from the considered class of functions. We also give examples of entire functions from this class
{"title":"Integral representation of one class of entire functions","authors":"R. Khats","doi":"10.52737/18291163-2022.14.1-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.1-1-9","url":null,"abstract":"In this paper, we study an integral representation of one class of entire functions. Conditions for the existence of this representation in terms of certain solutions of some differential equations are found. We obtain asymptotic estimates of entire functions from the considered class of functions. We also give examples of entire functions from this class","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45254325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-10DOI: 10.52737/18291163-2022.14.2-1-10
O. Maphane
. In this paper, we determine, in terms of the Sullivan models, rational evaluation subgroups of the inclusion C P ( n ) (cid:44) → C P ( n + k ) between complex projective spaces and, more generally, the G -sequence of the homotopy monomorphism ι : X (cid:44) → Y between simply connected formal homogeneous spaces for which π ∗ ( Y ) ⊗ Q is finite dimensional.
{"title":"Evaluation subgroups of a map and the rationalized G-sequence","authors":"O. Maphane","doi":"10.52737/18291163-2022.14.2-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.2-1-10","url":null,"abstract":". In this paper, we determine, in terms of the Sullivan models, rational evaluation subgroups of the inclusion C P ( n ) (cid:44) → C P ( n + k ) between complex projective spaces and, more generally, the G -sequence of the homotopy monomorphism ι : X (cid:44) → Y between simply connected formal homogeneous spaces for which π ∗ ( Y ) ⊗ Q is finite dimensional.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43470155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-10DOI: 10.52737/18291163-2022.14.3-1-23
A. Ahmima, A. Fareh
{"title":"Exponential decay for a strain gradient porous thermoelasticity with second sound","authors":"A. Ahmima, A. Fareh","doi":"10.52737/18291163-2022.14.3-1-23","DOIUrl":"https://doi.org/10.52737/18291163-2022.14.3-1-23","url":null,"abstract":"","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47245445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-28DOI: 10.52737/18291163-2021.13.13-1-18
Prasenjit Ghosh, T. Samanta
We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.
{"title":"Controlled generalized fusion frame in the tensor product of Hilbert spaces","authors":"Prasenjit Ghosh, T. Samanta","doi":"10.52737/18291163-2021.13.13-1-18","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.13-1-18","url":null,"abstract":"We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42306176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：