Let $alpha$ be a prime Hurwitz integer. $mathcal{H}_{alpha}$, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of $mathcal{H},$ which is the set of all Hurwitz integers. In this study, we present an algebraic construction technique, which is a modulo function formed depending on two modulo operations, for codes over Hurwitz integers. We consider left congruent modulo $alpha,$ and the domain of related modulo function is $mathbb{Z}_{N(alpha)},$ which is residual class ring of ordinary integers with $N(alpha)$ elements. Therefore, we obtain the residue class rings of Hurwitz integers with $N(alpha)$ size. In addition, we present some results for mathematical notations used in two modulo functions, and for the algebraic construction technique formed depending upon two modulo functions. Moreover, we presented graphs obtained by graph layout methods, such as spring, high-dimensional, and spiral embedding, for the set of the residual class obtained with respect to the related modulo function in the rings of Hurwitz integers.
{"title":"An algebraic construction technique for codes over Hurwitz integers","authors":"Murat GÜZELTEPE>, Ramazan DURAN>","doi":"10.15672/hujms.1137425","DOIUrl":"https://doi.org/10.15672/hujms.1137425","url":null,"abstract":"Let $alpha$ be a prime Hurwitz integer. $mathcal{H}_{alpha}$, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of $mathcal{H},$ which is the set of all Hurwitz integers. In this study, we present an algebraic construction technique, which is a modulo function formed depending on two modulo operations, for codes over Hurwitz integers. We consider left congruent modulo $alpha,$ and the domain of related modulo function is $mathbb{Z}_{N(alpha)},$ which is residual class ring of ordinary integers with $N(alpha)$ elements. Therefore, we obtain the residue class rings of Hurwitz integers with $N(alpha)$ size. In addition, we present some results for mathematical notations used in two modulo functions, and for the algebraic construction technique formed depending upon two modulo functions. Moreover, we presented graphs obtained by graph layout methods, such as spring, high-dimensional, and spiral embedding, for the set of the residual class obtained with respect to the related modulo function in the rings of Hurwitz integers.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"277 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135478554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The intersection graph of quasinormal subgroups of a group $G$, denoted by $Gamma_{mathrm{q}}(G)$, is a graph defined as follows: the vertex set consists of all nontrivial, proper quasinormal subgroups of $G$, and two distinct vertices $H$ and $K$ are adjacent if $Hcap K$ is nontrivial. In this paper, we show that when $G$ is an arbitrary nonsimple group, the diameter of $Gamma_{mathrm{q}}(G)$ is in ${0,1,2,infty}$. Besides, all general skew linear groups $mathrm{GL}_n(D)$ over a division ring $D$ can be classified depending on the diameter of $Gamma_{mathrm{q}}(mathrm{GL}_n(D))$.
{"title":"Intersection graphs of quasinormal subgroups of general skew linear groups","authors":"Le QUİ DANH","doi":"10.15672/hujms.1249433","DOIUrl":"https://doi.org/10.15672/hujms.1249433","url":null,"abstract":"The intersection graph of quasinormal subgroups of a group $G$, denoted by $Gamma_{mathrm{q}}(G)$, is a graph defined as follows: the vertex set consists of all nontrivial, proper quasinormal subgroups of $G$, and two distinct vertices $H$ and $K$ are adjacent if $Hcap K$ is nontrivial. In this paper, we show that when $G$ is an arbitrary nonsimple group, the diameter of $Gamma_{mathrm{q}}(G)$ is in ${0,1,2,infty}$. Besides, all general skew linear groups $mathrm{GL}_n(D)$ over a division ring $D$ can be classified depending on the diameter of $Gamma_{mathrm{q}}(mathrm{GL}_n(D))$.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"60 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75011701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we improve the results of [1] and solve one of the open problems of [1]. First, we have shown that all subvarieties of the variety of rectangular bands are closed in the variety of n-nilpotent extension of bands. Further, we gave the new, simple and shorter proof of closedness of the variety of regular bands and lastly, we have shown that all subvarieties of the variety of normal bands are closed in the variety of left semiregular bands.
{"title":"Dominions and closed varieties of bands","authors":"Shabnam Abbas, W. Ashraf, N. M. Khan","doi":"10.15672/hujms.1217130","DOIUrl":"https://doi.org/10.15672/hujms.1217130","url":null,"abstract":"In this paper, we improve the results of [1] and solve one of the open problems of [1]. First, we have shown that all subvarieties of the variety of rectangular bands are closed in the variety of n-nilpotent extension of bands. Further, we gave the new, simple and shorter proof of closedness of the variety of regular bands and lastly, we have shown that all subvarieties of the variety of normal bands are closed in the variety of left semiregular bands.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77187140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Ayazoğlu, G. Alisoy, Sezgin Akbulut, Tuba AĞIRMAN AYDIN
In this paper, we consider an initial boundary value problem for a class of p(⋅)-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. We obtain the global and decay of existence of the solutions for small initial data and for some suitable conditions on the parameter λ. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.
{"title":"Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity.","authors":"R. Ayazoğlu, G. Alisoy, Sezgin Akbulut, Tuba AĞIRMAN AYDIN","doi":"10.15672/hujms.1106985","DOIUrl":"https://doi.org/10.15672/hujms.1106985","url":null,"abstract":"In this paper, we consider an initial boundary value problem for a class of p(⋅)-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. We obtain the global and decay of existence of the solutions for small initial data and for some suitable conditions on the parameter λ. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76841682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study several generalized metric properties of the space $mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. In particular, we consider such properties $(P)$ for which $mathcal F(X)$ has $(P)$ if and only if $X$ has $(P)$. Also, we obtain some results related to the images of metric spaces under some kinds of continuous mappings.
{"title":"The Vietoris hyperspace $mathcal F(X)$ and certain generalized metric properties","authors":"L. Kočinac, L. Q. Tuyen, Tuyen ONG VAN","doi":"10.15672/hujms.1203236","DOIUrl":"https://doi.org/10.15672/hujms.1203236","url":null,"abstract":"In this paper, we study several generalized metric properties of the\u0000space $mathcal F(X)$ of finite subsets of a space $X$ endowed with\u0000the Vietoris topology. In particular, we consider such properties\u0000$(P)$ for which $mathcal F(X)$ has $(P)$ if and only if $X$ has\u0000$(P)$. Also, we obtain some results related to the images of metric\u0000spaces under some kinds of continuous mappings.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80142113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a recent paper, Mao has studied min-pure injective modules to investigate the existence of min-injective covers. A min-pure injective module is one that is injective relative only to min-pure exact sequences. In this paper, we study the notion of min-pure projective modules which is the projective objects of min-pure exact sequences. Various ring characterizations and examples of both classes of modules are obtained. Along this way, we give conditions which guarantee that each min-pure projective module is either injective or projective. Also, the rings whose injective objects are min-pure projective are considered. The commutative rings over which all injective modules are min-pure projective are exactly quasi-Frobenius. Finally, we are interested with the rings all of its modules are min-pure projective. We obtain that a ring R is two-sided Kothe if all right R-modules are min-pure projective. Also, a commutative ring over which all modules are min-pure projective is quasi-Frobenius serial. As consequence, over a commutative indecomposable ring with J(R)^2 = 0, it is proven that all R-modules are min-pure projective if and only if R is either a field or a quasi-Frobenius ring of composition length 2.
{"title":"HOMOLOGICAL OBJECTS OF MIN-PURE EXACT SEQUENCES","authors":"Yusuf Alagöz, A. MORADZADEH-DEHKORDI","doi":"10.15672/hujms.1186239","DOIUrl":"https://doi.org/10.15672/hujms.1186239","url":null,"abstract":"In a recent paper, Mao has studied min-pure injective modules to investigate the existence of min-injective covers. A min-pure injective module is one that is injective relative only to min-pure exact sequences. In this paper, we study the notion of min-pure projective modules which is the projective objects of min-pure exact sequences. Various ring characterizations and examples of both classes of modules are obtained. Along this way, we give conditions which guarantee that each min-pure projective module is either injective or projective. Also, the rings whose injective objects are min-pure projective are considered. The commutative rings over which all injective modules are min-pure projective are exactly quasi-Frobenius. Finally, we are interested with the rings all of its modules are min-pure projective. We obtain that a ring R is two-sided Kothe if all right R-modules are min-pure projective. Also, a commutative ring over which all modules are min-pure projective is quasi-Frobenius serial. As consequence, over a commutative indecomposable ring with J(R)^2 = 0, it is proven that all R-modules are\u0000min-pure projective if and only if R is either a field or a quasi-Frobenius ring of composition length 2.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"41 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76224864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A subgroup H of a finite group G is said to be “semi-cover-avoiding in G”, if there exists a chief series of G such that H covers or avoids every chief factor of the chief series. In this article, we will consider some 2-maximal subgroups with the property of semi-cover-avoiding of a group G and explore the structure of G.
{"title":"On Semi-Cover-Avoiding 2-Maximal Subgroups of Finite Groups","authors":"Tingting Qiu, Xindan Chen, Juping Tang","doi":"10.15672/hujms.1112482","DOIUrl":"https://doi.org/10.15672/hujms.1112482","url":null,"abstract":"A subgroup H of a finite group G is said to be “semi-cover-avoiding in G”, if there exists a chief series of G such that H covers or avoids every chief factor of\u0000the chief series. In this article, we will consider some 2-maximal subgroups with the property of semi-cover-avoiding of a group G and explore the structure of G.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88377946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we shall investigate a characterization for the boundedness of the $B$-Riesz potential and its commutators on the generalized weighted $B$-Morrey spaces. We also give a characterization for the generalized weighted $B$-Morrey spaces via the boundedness of the Riesz potential and its commutators generated by generalized translate operators associated with Laplace Bessel differential operator.
{"title":"On the boundedness of $B$-Riesz potential and its commutators on generalized weighted $B$-Morrey spaces","authors":"I. Ekincioğlu, J. Hasanov, C. Keskin","doi":"10.15672/hujms.1221556","DOIUrl":"https://doi.org/10.15672/hujms.1221556","url":null,"abstract":"In the present paper, we shall investigate a characterization for the boundedness of the $B$-Riesz potential and its commutators on the generalized weighted $B$-Morrey spaces. We also give a characterization for the generalized weighted $B$-Morrey spaces via the boundedness of the Riesz potential and its commutators generated by generalized translate operators associated with Laplace Bessel differential operator.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"22 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78476257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we consider the Sturm–Liouville equation with nonlocal boundary conditions depending polynomially on the parameter. We obtain a result and give an algorithm for the reconstruction of the coefficients of the problem using asymptotics of the nodal points.
{"title":"Reconstruction of the Nonlocal Sturm-Liouville operator with boundary conditions depending on the parameter","authors":"İ. Adalar, A. S. Özkan","doi":"10.15672/hujms.1244992","DOIUrl":"https://doi.org/10.15672/hujms.1244992","url":null,"abstract":"In the present paper, we consider the Sturm–Liouville equation with nonlocal boundary conditions depending polynomially on the parameter. We obtain a result and give an algorithm for the reconstruction of the coefficients of the problem using asymptotics of the nodal points.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75515363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chung-chuan Chen, A. Bagheri Salec, S. M. Tabatabaie
In this paper, we study the spaces ${mathcal X}^Phi$ as Banach algebras, where $mathcal X$ is a quasi-Banach space and $Phi$ is a Young function, and extend some well-known facts regarding Lebesgue and Orlicz spaces on this new structure. Also, for each $pgeq 1$, we give some necessary condition for the space $mathcal{X}^p$ to be a Banach algebra under the pointwise product.
{"title":"Orlicz Algebras Associated to a Banach Function Space","authors":"Chung-chuan Chen, A. Bagheri Salec, S. M. Tabatabaie","doi":"10.15672/hujms.1018098","DOIUrl":"https://doi.org/10.15672/hujms.1018098","url":null,"abstract":"In this paper, we study the spaces ${mathcal X}^Phi$ as Banach algebras, where $mathcal X$ is a quasi-Banach space and $Phi$ is a Young function, and extend some well-known facts regarding Lebesgue and Orlicz spaces on this new structure. Also, for each $pgeq 1$, we give some necessary condition for the space $mathcal{X}^p$ to be a Banach algebra under the pointwise product.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"24 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83955085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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