Pub Date : 2022-12-29DOI: 10.21136/CMJ.2022.0134-22
Liyun Wu, Huihui Zhu
Let R be a unital *-ring. For any a, s, t, v, w ∈ R we define the weighted w-core inverse and the weighted dual s-core inverse, extending the w-core inverse and the dual s-core inverse, respectively. An element a ∈ R has a weighted w-core inverse with the weight v if there exists some x ∈ R such that awxvx = x, xvawa = a and (awx)* = awx. Dually, an element a ∈ R has a weighted dual s-core inverse with the weight t if there exists some y ∈ R such that ytysa = y, asaty = a and (ysa)* = ysa. Several characterizations of weighted w-core invertible and weighted dual s-core invertible elements are given when weights v and t are invertible Hermitian elements. Also, the relations among the weighted w-core inverse, the weighted dual s-core inverse, the e-core inverse, the dual f-core inverse, the weighted Moore-Penrose inverse and the (v, w)-(b, c)-inverse are considered.
{"title":"Weighted w-core inverses in rings","authors":"Liyun Wu, Huihui Zhu","doi":"10.21136/CMJ.2022.0134-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0134-22","url":null,"abstract":"Let R be a unital *-ring. For any a, s, t, v, w ∈ R we define the weighted w-core inverse and the weighted dual s-core inverse, extending the w-core inverse and the dual s-core inverse, respectively. An element a ∈ R has a weighted w-core inverse with the weight v if there exists some x ∈ R such that awxvx = x, xvawa = a and (awx)* = awx. Dually, an element a ∈ R has a weighted dual s-core inverse with the weight t if there exists some y ∈ R such that ytysa = y, asaty = a and (ysa)* = ysa. Several characterizations of weighted w-core invertible and weighted dual s-core invertible elements are given when weights v and t are invertible Hermitian elements. Also, the relations among the weighted w-core inverse, the weighted dual s-core inverse, the e-core inverse, the dual f-core inverse, the weighted Moore-Penrose inverse and the (v, w)-(b, c)-inverse are considered.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"581 - 602"},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48651620","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}
Pub Date : 2022-12-28DOI: 10.21136/CMJ.2022.0057-22
Y. Mao, Christopher Melekian, E. Cheng
for a connected graph G = (V, E) and a set S ⊆ V(G) with at least two vertices, an S-Steiner tree is a subgraph T = (V′, E′) of G that is a tree with S ⊆ V′. If the degree of each vertex of S in T is equal to 1, then T is called a pendant S-Steiner tree. Two S-Steiner trees are internally disjoint if they share no vertices other than S and have no edges in common. For S ⊆ V(G) and |S| ≽ 2, the pendant tree-connectivity τG(S) is the maximum number of internally disjoint pendant S-Steiner trees in G, and for k ≽ 2, the k-pendant tree-connectivity τk(G) is the minimum value of τG(S) over all sets S of k vertices. We derive a lower bound for τ3(G ◦ H), where G and H are connected graphs and ◦ denotes the lexicographic product.
{"title":"A lower bound for the 3-pendant tree-connectivity of lexicographic product graphs","authors":"Y. Mao, Christopher Melekian, E. Cheng","doi":"10.21136/CMJ.2022.0057-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0057-22","url":null,"abstract":"for a connected graph G = (V, E) and a set S ⊆ V(G) with at least two vertices, an S-Steiner tree is a subgraph T = (V′, E′) of G that is a tree with S ⊆ V′. If the degree of each vertex of S in T is equal to 1, then T is called a pendant S-Steiner tree. Two S-Steiner trees are internally disjoint if they share no vertices other than S and have no edges in common. For S ⊆ V(G) and |S| ≽ 2, the pendant tree-connectivity τG(S) is the maximum number of internally disjoint pendant S-Steiner trees in G, and for k ≽ 2, the k-pendant tree-connectivity τk(G) is the minimum value of τG(S) over all sets S of k vertices. We derive a lower bound for τ3(G ◦ H), where G and H are connected graphs and ◦ denotes the lexicographic product.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"237 - 244"},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45634173","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}
Pub Date : 2022-12-15DOI: 10.21136/CMJ.2022.0225-22
Georgiana Fasolă, M. Tarnauceanu
We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.
{"title":"On a group-theoretical generalization of the Gauss formula","authors":"Georgiana Fasolă, M. Tarnauceanu","doi":"10.21136/CMJ.2022.0225-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0225-22","url":null,"abstract":"We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"311 - 317"},"PeriodicalIF":0.5,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47793387","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}
Pub Date : 2022-12-13DOI: 10.21136/CMJ.2023.0445-21
W. Burgess, R. Raphael
For k ∈ ℕ ∪ {∞} and U open in ℝ, let Ck (U) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f ∈ Ck(U) there is g ∈ C∞(ℝ) with U ⊆ coz g and h ∈ Ck(ℝ) with fg∣U = h∣U. The function f and its k derivatives are not assumed to be bounded on U. The function g is constructed using splines based on the Mollifier function. Some consequences about the ring Ck(ℝ) are deduced from this, in particular that Qcl(Ck(ℝ)) = Q(Ck(ℝ)).
{"title":"On extending Ck functions from an open set to ℝ with applications","authors":"W. Burgess, R. Raphael","doi":"10.21136/CMJ.2023.0445-21","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0445-21","url":null,"abstract":"For k ∈ ℕ ∪ {∞} and U open in ℝ, let Ck (U) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f ∈ Ck(U) there is g ∈ C∞(ℝ) with U ⊆ coz g and h ∈ Ck(ℝ) with fg∣U = h∣U. The function f and its k derivatives are not assumed to be bounded on U. The function g is constructed using splines based on the Mollifier function. Some consequences about the ring Ck(ℝ) are deduced from this, in particular that Qcl(Ck(ℝ)) = Q(Ck(ℝ)).","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"487 - 498"},"PeriodicalIF":0.5,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44316342","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}
Pub Date : 2022-12-12DOI: 10.21136/CMJ.2022.0094-22
S. Karimzadeh, J. Moghaderi
We investigate some properties of n-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an n-submodule. Also, we show that if M is a finitely generated R-module and AnnR(M)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sqrt {{rm{An}}{{rm{n}}_R}left(M right)} $$end{document} is a prime ideal of R, then M has n-submodule. Moreover, we define the notion of G.n-submodule, which is a generalization of the notion of n-submodule. We find some characterizations of G.n-submodules and we examine the way the aforementioned notions are related to each other.
We investigate some properties of n-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an n-submodule. Also, we show that if M is a finitely generated R-module and AnnR(M)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sqrt {{rm{An}}{{rm{n}}_R}left(M right)} $$end{document} is a prime ideal of R, then M has n-submodule. Moreover, we define the notion of G.n-submodule, which is a generalization of the notion of n-submodule. We find some characterizations of G.n-submodules and we examine the way the aforementioned notions are related to each other.
{"title":"On n-submodules and G.n-submodules","authors":"S. Karimzadeh, J. Moghaderi","doi":"10.21136/CMJ.2022.0094-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0094-22","url":null,"abstract":"We investigate some properties of n-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an n-submodule. Also, we show that if M is a finitely generated R-module and AnnR(M)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$sqrt {{rm{An}}{{rm{n}}_R}left(M right)} $$end{document} is a prime ideal of R, then M has n-submodule. Moreover, we define the notion of G.n-submodule, which is a generalization of the notion of n-submodule. We find some characterizations of G.n-submodules and we examine the way the aforementioned notions are related to each other.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"245 - 262"},"PeriodicalIF":0.5,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44778765","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}
Pub Date : 2022-12-05DOI: 10.21136/CMJ.2022.0149-22
T. Ohno, T. Shimomura
Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces as an extension of T. Ohno, T. Shimomura (2022). Our results are new even for the doubling metric measure spaces.
{"title":"Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form","authors":"T. Ohno, T. Shimomura","doi":"10.21136/CMJ.2022.0149-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0149-22","url":null,"abstract":"Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces as an extension of T. Ohno, T. Shimomura (2022). Our results are new even for the doubling metric measure spaces.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"263 - 276"},"PeriodicalIF":0.5,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46416371","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}
Pub Date : 2022-12-03DOI: 10.21136/CMJ.2022.0153-22
Feng Liu, G. Wang
We study the regularity properties of bilinear maximal operator. Some new bounds and continuity for the above operators are established on the Sobolev spaces, Triebel-Lizorkin spaces and Besov spaces. In addition, the quasicontinuity and approximate differentiability of the bilinear maximal function are also obtained.
{"title":"On the regularity of bilinear maximal operator","authors":"Feng Liu, G. Wang","doi":"10.21136/CMJ.2022.0153-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0153-22","url":null,"abstract":"We study the regularity properties of bilinear maximal operator. Some new bounds and continuity for the above operators are established on the Sobolev spaces, Triebel-Lizorkin spaces and Besov spaces. In addition, the quasicontinuity and approximate differentiability of the bilinear maximal function are also obtained.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"277 - 295"},"PeriodicalIF":0.5,"publicationDate":"2022-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42967089","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}
Pub Date : 2022-11-16DOI: 10.21136/CMJ.2022.0044-22
Watcharapon Pimsert, T. Srichan, Pinthira Tangsupphathawat
We use the estimation of the number of integers n such that ⌊nc⌋ belongs to an arithmetic progression to study the coprimality of integers in ℕc = {⌊nc⌋}n∈ℕ, c > 1, c ∉ ℕ.
{"title":"Coprimality of integers in Piatetski-Shapiro sequences","authors":"Watcharapon Pimsert, T. Srichan, Pinthira Tangsupphathawat","doi":"10.21136/CMJ.2022.0044-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0044-22","url":null,"abstract":"We use the estimation of the number of integers n such that ⌊nc⌋ belongs to an arithmetic progression to study the coprimality of integers in ℕc = {⌊nc⌋}n∈ℕ, c > 1, c ∉ ℕ.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"197 - 212"},"PeriodicalIF":0.5,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46467792","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}
Pub Date : 2022-11-15DOI: 10.21136/CMJ.2022.0154-22
Yanfei Feng
We show that for any given integer k there exist infinitely many consecutive square-free numbers of the type x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1. We also establish an asymptotic formula for 1 ⩽ x, y, z ⩽ H such that x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1 are square-free. The method we used in this paper is due to Tolev.
{"title":"Consecutive square-free values of the type x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1","authors":"Yanfei Feng","doi":"10.21136/CMJ.2022.0154-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0154-22","url":null,"abstract":"We show that for any given integer k there exist infinitely many consecutive square-free numbers of the type x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1. We also establish an asymptotic formula for 1 ⩽ x, y, z ⩽ H such that x2 + y2 + z2 + k, x2 + y2 + z2 + k + 1 are square-free. The method we used in this paper is due to Tolev.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"297 - 310"},"PeriodicalIF":0.5,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46491413","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}
Pub Date : 2022-11-04DOI: 10.21136/CMJ.2022.0043-22
Z. Du, C. D. da Fonseca
We analyse the roots of the polynomial xn − pxn−1 − qx − 1 for p≽ q ≽ 1. This is the characteristic polynomial of the recurrence relation Fk,p,q(n) = pFk,p,q(n − 1) + qFk,p,q(n − k + 1) + Fk,p,q(n − k) for n ≽ k, which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.
{"title":"Root location for the characteristic polynomial of a Fibonacci type sequence","authors":"Z. Du, C. D. da Fonseca","doi":"10.21136/CMJ.2022.0043-22","DOIUrl":"https://doi.org/10.21136/CMJ.2022.0043-22","url":null,"abstract":"We analyse the roots of the polynomial xn − pxn−1 − qx − 1 for p≽ q ≽ 1. This is the characteristic polynomial of the recurrence relation Fk,p,q(n) = pFk,p,q(n − 1) + qFk,p,q(n − k + 1) + Fk,p,q(n − k) for n ≽ k, which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"189 - 195"},"PeriodicalIF":0.5,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47624671","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}
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：