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Robust interpolation of sequences with periodically stationary multiplicative seasonal increments 周期平稳乘性季节增量序列的鲁棒插值
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-13 DOI: 10.15330/cmp.14.1.105-126
M. Luz, M. Moklyachuk
{"title":"Robust interpolation of sequences with periodically stationary multiplicative seasonal increments","authors":"M. Luz, M. Moklyachuk","doi":"10.15330/cmp.14.1.105-126","DOIUrl":"https://doi.org/10.15330/cmp.14.1.105-126","url":null,"abstract":"We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the interpolation problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal interpolation of the functionals. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear interpolation of the functionals are proposed in the case where spectral densities of the sequences are not exactly known while some sets of admissible spectral densities are given.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74130610","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: 1
Composition of entire and analytic functions in the unit ball 单位球内整体函数和解析函数的组成
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-09 DOI: 10.15330/cmp.14.1.95-104
Andriy Ivanovych Bandura, O. Skaskiv, I. Tymkiv
{"title":"Composition of entire and analytic functions in the unit ball","authors":"Andriy Ivanovych Bandura, O. Skaskiv, I. Tymkiv","doi":"10.15330/cmp.14.1.95-104","DOIUrl":"https://doi.org/10.15330/cmp.14.1.95-104","url":null,"abstract":"In this paper, we investigate a composition of entire function of several complex variables and analytic function in the unit ball. We modified early known results with conditions providing equivalence of boundedness of $L$-index in a direction for such a composition and boundedness of $l$-index of initial function of one variable, where the continuous function $L:mathbb{B}^nto mathbb{R}_+$ is constructed by the continuous function $l: mathbb{C}^mto mathbb{R}_+.$ Taking into account new ideas from recent results on composition of entire functions, we remove a condition that a directional derivative of the inner function $Phi$ in the composition does not equal to zero. Instead of the condition we construct a greater function $L(z)$ for which $F(z)=f(underbrace{Phi(z),ldots,Phi(z)}_{mtext{ times}})$ has bounded $L$-index in a direction, where $fcolon mathbb{C}^mto mathbb{C}$ is an entire function of bounded $l$-index in the direction $(1,ldots,1)$, $Phicolon mathbb{B}^nto mathbb{C}$ is an analytic function in the unit ball. \u0000We weaken the condition $|partial_{mathbf{b}}^kPhi(z)|le K|partial_{mathbf{b}}Phi(z)|^k$ for all $zinmathbb{B}^n$, where $Kgeq 1$ is a constant, $mathbf{b}inmathbb{C}^nsetminus{0}$ is a given direction and $${partial_{mathbf{b}} F(z)}:=sumlimits_{j=1}^{n}!frac{partial F(z)}{partial z_{j}}{b_{j}}, partial_{mathbf{b}}^k F(z):=partial_{mathbf{b}}big(partial_{mathbf{b}}^{k-1} F(z)big).$$ It is replaced by the condition $|partial_{mathbf{b}}^kPhi(z)|le K(l(Phi(z)))^{1/(N_{mathbf{1}}(f,l)+1)}|partial_{mathbf{b}}Phi(z)|^k$, where $N_{mathbf{1}}(f,l)$ is the $l$-index of the function $f$ in the direction $mathbf{1}=(1,ldots,1).$ The described result is an improvement of previous one. It is also a new result for the one-dimensional case $n=1,$ $m=1$, i.e. for an analytic function $Phi$ in the unit disc and for an entire function $f: mathbb{C}tomathbb{C}$ of bounded $l$-index.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86058721","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: 1
Krasnoselskii iteration process for approximating fixed points of enriched generalized nonexpansive mappings in Banach spaces Banach空间中富广义非扩张映射不动点逼近的Krasnoselskii迭代过程
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-07 DOI: 10.15330/cmp.14.1.86-94
E. Şimşek, I. Yildirim
{"title":"Krasnoselskii iteration process for approximating fixed points of enriched generalized nonexpansive mappings in Banach spaces","authors":"E. Şimşek, I. Yildirim","doi":"10.15330/cmp.14.1.86-94","DOIUrl":"https://doi.org/10.15330/cmp.14.1.86-94","url":null,"abstract":"We consider the class of enriched generalized nonexpansive mappings which includes enriched Kannan mappings, nonexpansive enriched Chatterjea mappings and enriched mappings. We prove some fixed point theorems for enriched generalized nonexpansive mappings using Krasnoselskii iteration process in Banach spaces. We also give stability result for such mappings under some appropriate conditions. The results presented in this paper improve and extend some works in literature.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86748117","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
Fixed sets and fixed points for mappings in generalized $rm Lim$-spaces of Fréchet 广义$rm Lim$-空间中映射的不动集和不动点
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-06-02 DOI: 10.15330/cmp.15.1.260-269
V. Babenko, V. Babenko, O. Kovalenko
{"title":"Fixed sets and fixed points for mappings in generalized $rm Lim$-spaces of Fréchet","authors":"V. Babenko, V. Babenko, O. Kovalenko","doi":"10.15330/cmp.15.1.260-269","DOIUrl":"https://doi.org/10.15330/cmp.15.1.260-269","url":null,"abstract":"In the article, we axiomatically define generalized $rm Lim$-spaces $(X,{rm Lim})$, Cauchy structures, contractive mappings and prove an abstract version of the contraction mapping principle. We also consider ways to specify families of Cauchy sequences and contraction conditions using a base in $X^2$, distance-like or sum-like functions with values in some partially ordered set $Y$. We establish fixed set and fixed point theorems for generalized contractions of the Meir-Keeler and Taylor, Ćirić and Caristi types. The obtained results generalize many known fixed point theorems and are new even in many classical situations.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72953889","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
Elements of high order in finite fields specified by binomials 用二项式表示的有限域中的高阶元
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-04-29 DOI: 10.15330/cmp.14.1.238-246
V. Bovdi, A. Diene, R. Popovych
{"title":"Elements of high order in finite fields specified by binomials","authors":"V. Bovdi, A. Diene, R. Popovych","doi":"10.15330/cmp.14.1.238-246","DOIUrl":"https://doi.org/10.15330/cmp.14.1.238-246","url":null,"abstract":"Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $pgeq 5$. For any integer $mgeq 2$ and $ain F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to explicitly construct elements of high order in the field $F_q[x]/langle x^m-arangle$. Namely, we find elements with multiplicative order of at least $5^{sqrt[3]{m/2}}$, which is better than previously obtained bound for such family of extension fields.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87528924","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
A Bezout ring with nonzero principal Jacobson radical 具有非零主Jacobson根的Bezout环
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-04-27 DOI: 10.15330/cmp.14.1.72-75
A. Gatalevych, A. Dmytruk
{"title":"A Bezout ring with nonzero principal Jacobson radical","authors":"A. Gatalevych, A. Dmytruk","doi":"10.15330/cmp.14.1.72-75","DOIUrl":"https://doi.org/10.15330/cmp.14.1.72-75","url":null,"abstract":"In this paper, we study a commutative Bezout domain with nonzero Jacobson radical being a principal ideal. It has been proved that such a Bezout domain is a ring of the stable range 1. As a result, we have obtained that such a Bezout domain is a ring over which any matrix can be reduced to a canonical diagonal form by means of elementary transformations of its rows and columns.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76336789","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
Essentially iso-retractable modules and rings 本质上是等伸缩模块和环
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-04-27 DOI: 10.15330/cmp.14.1.76-85
A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar
{"title":"Essentially iso-retractable modules and rings","authors":"A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar","doi":"10.15330/cmp.14.1.76-85","DOIUrl":"https://doi.org/10.15330/cmp.14.1.76-85","url":null,"abstract":"A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : Mrightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V$-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73001086","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
$m$-quasi-$*$-Einstein contact metric manifolds $m$-准-$*$-爱因斯坦接触度量流形
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-04-25 DOI: 10.15330/cmp.14.1.61-71
H. Kumara, V. Venkatesha, D. Naik
{"title":"$m$-quasi-$*$-Einstein contact metric manifolds","authors":"H. Kumara, V. Venkatesha, D. Naik","doi":"10.15330/cmp.14.1.61-71","DOIUrl":"https://doi.org/10.15330/cmp.14.1.61-71","url":null,"abstract":"The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $eta$-Einstein and $f$ is constant. Next, we show that in a Sasakian manifold if $g$ represents an $m$-quasi-$*$-Einstein metric with a conformal vector field $V$, then $V$ is Killing and $M$ is $eta$-Einstein. Finally, we prove that if a non-Sasakian $(kappa,mu)$-contact manifold admits a gradient $m$-quasi-$*$-Einstein metric, then it is $N(kappa)$-contact metric manifold or a $*$-Einstein.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77864139","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
Identities relating six members of the Fibonacci family of sequences 关于斐波那契数列族的六个成员的恒等式
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-02-27 DOI: 10.15330/cmp.14.1.6-19
R. Frontczak, T. Goy, M. Shattuck
{"title":"Identities relating six members of the Fibonacci family of sequences","authors":"R. Frontczak, T. Goy, M. Shattuck","doi":"10.15330/cmp.14.1.6-19","DOIUrl":"https://doi.org/10.15330/cmp.14.1.6-19","url":null,"abstract":"In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences. These identities are obtained as special cases of formulas relating two linear combinations of products of three generalized Fibonacci or Lucas sequences. The latter formulas are in turn obtained from a more general generating function result for the product of three terms coming from second-order linearly recurrent sequences with arbitrary initial values. We employ algebraic arguments to establish our results, making use of the Binet-like formulas of the underlying sequences. Among the sequences for which the aforementioned identities are found include the Fibonacci, Pell, Jacobsthal and Mersenne numbers, along with their associated Lucas companion sequences.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86329870","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: 1
A corrigendum to "A note on compact-like semitopological groups" [Carpathian Math. Publ. 2019, 11 (2), 442-452] “关于类紧半拓扑群的注解”的更正[喀尔巴阡数学]。科学通报，2019,11 (2)，442-452 [j]
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-01-08 DOI: 10.15330/cmp.14.1.5
L. Peng
{"title":"A corrigendum to \"A note on compact-like semitopological groups\" [Carpathian Math. Publ. 2019, 11 (2), 442-452]","authors":"L. Peng","doi":"10.15330/cmp.14.1.5","DOIUrl":"https://doi.org/10.15330/cmp.14.1.5","url":null,"abstract":"A corrigendum to \"A note on compact-like semitopological groups\" [Carpathian Math. Publ. 2019, 11 (2), 442-452]","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84112569","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
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