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Carpathian Mathematical Publications最新文献

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$mu$-statistical convergence and the space of functions $mu$-stat continuous on the segment $mu$-统计收敛性和函数$mu$-stat在段上连续的空间
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-10-04 DOI: 10.15330/cmp.13.2.433-451
S. Sadigova
{"title":"$mu$-statistical convergence and the space of functions $mu$-stat continuous on the segment","authors":"S. Sadigova","doi":"10.15330/cmp.13.2.433-451","DOIUrl":"https://doi.org/10.15330/cmp.13.2.433-451","url":null,"abstract":"In this work, the concept of a point $mu$-statistical density is defined. Basing on this notion, the concept of $mu$-statistical limit, generated by some Borel measure $muleft(cdot right)$, is defined at a point. We also introduce the concept of $mu$-statistical fundamentality at a point, and prove its equivalence to the concept of $mu$-stat convergence. The classification of discontinuity points is transferred to this case. The appropriate space of $mu$-stat continuous functions on the segment with sup-norm is defined. It is proved that this space is a Banach space and the relationship between this space and the spaces of continuous and Lebesgue summable functions is considered.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89733204","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}
引用次数: 3
Viability result for semilinear functional differential inclusions in Banach spaces Banach空间中半线性泛函微分包涵的生存性结果
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-09-16 DOI: 10.15330/cmp.13.2.395-404
M. Aitalioubrahim
{"title":"Viability result for semilinear functional differential inclusions in Banach spaces","authors":"M. Aitalioubrahim","doi":"10.15330/cmp.13.2.395-404","DOIUrl":"https://doi.org/10.15330/cmp.13.2.395-404","url":null,"abstract":"We show the existence result of a mild solution for a semilinear functional differential inclusion, with viability, governed by a family of linear operators. We consider the case when the constraint is moving.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81618628","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}
引用次数: 0
Extreme points of ${mathcal L}_s(^2l_{infty})$ and ${mathcal P}(^2l_{infty})$ ${mathcal L}_s(^2l_{infty})$和的极值点 ${mathcal P}(^2l_{infty})$
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-07-24 DOI: 10.15330/cmp.13.2.289-297
Sung Guen Kim
{"title":"Extreme points of ${mathcal L}_s(^2l_{infty})$ and ${mathcal P}(^2l_{infty})$","authors":"Sung Guen Kim","doi":"10.15330/cmp.13.2.289-297","DOIUrl":"https://doi.org/10.15330/cmp.13.2.289-297","url":null,"abstract":"For $ngeq 2,$ we show that every extreme point of the unit ball of ${mathcal L}_s(^2l_{infty}^n)$ is extreme in ${mathcal L}_s(^2l_{infty}^{n+1})$, which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of ${mathcal L}_s(^2l_{infty}^n)$ is extreme in ${mathcal L}_s(^2l_{infty})$. We also show that every extreme point of the unit ball of ${mathcal P}(^2l_{infty}^2)$ is extreme in ${mathcal P}(^2l_{infty}^n).$ As a corollary we show that every extreme point of the unit ball of ${mathcal P}(^2l_{infty}^2)$ is extreme in ${mathcal P}(^2l_{infty})$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85468926","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}
引用次数: 0
Application of slice regularity to functions of a dual-quaternionic variable 片正则性在双四元数变量函数中的应用
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-07-24 DOI: 10.15330/cmp.13.2.298-304
Ji Eun Kim
{"title":"Application of slice regularity to functions of a dual-quaternionic variable","authors":"Ji Eun Kim","doi":"10.15330/cmp.13.2.298-304","DOIUrl":"https://doi.org/10.15330/cmp.13.2.298-304","url":null,"abstract":"In this paper, we present the algebraic properties of dual quaternions and define a slice regularity of a dual quaternionic function. Since the product of dual quaternions is non-commutative, slice regularity is derived in two ways. Thereafter, we propose the Cauchy-Riemann equations and a power series corresponding to dual quaternions.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73742018","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}
引用次数: 0
Special formulas involving polygonal numbers and Horadam numbers 涉及多边形数和贺达姆数的特殊公式
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-06-30 DOI: 10.15330/cmp.13.1.207-216
K. Adegoke, R. Frontczak, T. Goy
{"title":"Special formulas involving polygonal numbers and Horadam numbers","authors":"K. Adegoke, R. Frontczak, T. Goy","doi":"10.15330/cmp.13.1.207-216","DOIUrl":"https://doi.org/10.15330/cmp.13.1.207-216","url":null,"abstract":"Some convolution-type identities involving polygonal numbers and Horadam numbers are derived. The method of proof is to properly relate the generating functions to each other. Additionally, we prove a general non-convolutional result involving these number families and discuss some of the consequences.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73686405","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}
引用次数: 5
On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers 关于$k$-斐波那契平衡和$k$-斐波那契卢卡斯平衡数
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-06-30 DOI: 10.15330/cmp.13.1.259-271
S. Rihane
{"title":"On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers","authors":"S. Rihane","doi":"10.15330/cmp.13.1.259-271","DOIUrl":"https://doi.org/10.15330/cmp.13.1.259-271","url":null,"abstract":"The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+cdots+(n-1) = (n+1)+(n+2)+cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is called a Lucas-balancing number. For an integer $kgeq 2$, let $(F_n^{(k)})_n$ be the $k$-generalized Fibonacci sequence which starts with $0,ldots,0,1,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. The purpose of this paper is to show that 1, 6930 are the only balancing numbers and 1, 3 are the only Lucas-balancing numbers which are a term of $k$-generalized Fibonacci sequence. This generalizes the result from [Fibonacci Quart. 2004, 42 (4), 330-340].","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88601573","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}
引用次数: 3
Bases in finite groups of small order 小阶有限群中的基
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-06-20 DOI: 10.15330/cmp.13.1.149-159
T. Banakh, V. Gavrylkiv
{"title":"Bases in finite groups of small order","authors":"T. Banakh, V. Gavrylkiv","doi":"10.15330/cmp.13.1.149-159","DOIUrl":"https://doi.org/10.15330/cmp.13.1.149-159","url":null,"abstract":"A subset $B$ of a group $G$ is called a basis of $G$ if each element $gin G$ can be written as $g=ab$ for some elements $a,bin B$. The smallest cardinality $|B|$ of a basis $Bsubseteq G$ is called the basis size of $G$ and is denoted by $r[G]$. We prove that each finite group $G$ has $r[G]>sqrt{|G|}$. If $G$ is Abelian, then $r[G]ge sqrt{2|G|-|G|/|G_2|}$, where $G_2={gin G:g^{-1} = g}$. Also we calculate the basis sizes of all Abelian groups of order $le 60$ and all non-Abelian groups of order $le 40$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"44 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75688338","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}
引用次数: 0
Про спадкову незвідність деяких мономіальних матриць над локальними кільцями
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-06-19 DOI: 10.15330/cmp.13.1.127-133
A.A. Tylyshchak, M. Demko
{"title":"Про спадкову незвідність деяких мономіальних матриць над локальними кільцями","authors":"A.A. Tylyshchak, M. Demko","doi":"10.15330/cmp.13.1.127-133","DOIUrl":"https://doi.org/10.15330/cmp.13.1.127-133","url":null,"abstract":"Розглядаються мономіальні матриці над локальним кільцем $R$ головних ідеалів вигляду $M(t,k,n)=Phileft(begin{smallmatrix}I_k&00,,&tI_{n-k}end{smallmatrix}right)$, $0<k<n$, де $t$ $-$ твірний елемент радикалу Джекобсона $J(R)$ кільця $R$, $Phi$ $-$ супровідна матриця многочлена $lambda^n-1$ і $I_k$ $-$ одинична $ktimes k$ матриця. В роботі встановлено критерій спадкової незвідності $M(t,k,n)$ у випадку, коли $t^{left[frac{kcdot(n-k)}{n}right]+1}not=0$.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"32 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72487521","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}
引用次数: 0
On Hadamard composition of Gelfond-Leont'ev derivatives of entire and analytic functions in the unit disk 单位圆盘上全函数和解析函数的gelfund - leont 'ev导数的Hadamard复合
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-06-05 DOI: 10.15330/CMP.13.1.98-109
O. Mulyava, M. Sheremeta
{"title":"On Hadamard composition of Gelfond-Leont'ev derivatives of entire and analytic functions in the unit disk","authors":"O. Mulyava, M. Sheremeta","doi":"10.15330/CMP.13.1.98-109","DOIUrl":"https://doi.org/10.15330/CMP.13.1.98-109","url":null,"abstract":"For an entire function and an analytic in the unit disk function the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders. A relationship between the behaviors of the maximal terms of Hadamard composition of Gelfond-Leont'ev derivatives and of the Gelfond-Leont'ev derivative of Hadamard composition is established.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75545815","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}
引用次数: 0
Remarks on continuously distributed sequences 关于连续分布序列的注释
IF 0.8
Carpathian Mathematical Publications Pub Date : 2021-05-23 DOI: 10.15330/CMP.13.1.89-97
M. Paštéka
{"title":"Remarks on continuously distributed sequences","authors":"M. Paštéka","doi":"10.15330/CMP.13.1.89-97","DOIUrl":"https://doi.org/10.15330/CMP.13.1.89-97","url":null,"abstract":"In the first part of the paper we define the notion of the density as certain type of finitely additive probability measure and the distribution function of sequences with respect to the density. Then we derive some simple criterions providing the continuity of the distribution function of given sequence. These criterions we apply to the van der Corput’s sequences. The Weyl’s type criterions of continuity of the distribution function are proven.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":"75 1","pages":"89-97"},"PeriodicalIF":0.8,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88533967","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}
引用次数: 2
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