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New approach to timelike Bertrand curves in 3-dimensional Minkowski space 三维闵科夫斯基空间中的贝特朗时间曲线新方法
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-12-05 DOI: 10.15330/cmp.15.2.482-494
H. A. Erdem, A. Uçum, K. Ilarslan, Ç. Camcı
{"title":"New approach to timelike Bertrand curves in 3-dimensional Minkowski space","authors":"H. A. Erdem, A. Uçum, K. Ilarslan, Ç. Camcı","doi":"10.15330/cmp.15.2.482-494","DOIUrl":"https://doi.org/10.15330/cmp.15.2.482-494","url":null,"abstract":"In the theory of curves in Euclidean $3$-space, it is well known that a curve $beta $ is said to be a Bertrand curve if for another curve $beta^{star}$ there exists a one-to-one correspondence between $beta $ and $beta^{star}$ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Minkowski $3$-space. Related examples that meet these conditions are given. Moreover, thanks to this new approach, timelike, spacelike and Cartan null Bertrand mates of a timelike general helix have been obtained.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138600392","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 truncation error bound for branched continued fractions of the special form on subsets of angular domains 角域子集上特殊形式分枝续分数的截断误差约束
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-11-21 DOI: 10.15330/cmp.15.2.437-448
D. Bodnar, O.S. Bodnar, I. Bilanyk
{"title":"A truncation error bound for branched continued fractions of the special form on subsets of angular domains","authors":"D. Bodnar, O.S. Bodnar, I. Bilanyk","doi":"10.15330/cmp.15.2.437-448","DOIUrl":"https://doi.org/10.15330/cmp.15.2.437-448","url":null,"abstract":"Truncation error bounds for branched continued fractions of the special form are established. These fractions can be obtained by fixing the values of variables in branched continued fractions with independent variables, which is an effective tool for approximating complex functions of two variables. The main result is a two-dimensional analog of the theorem considered in [SCIAM J. Numer. Anal. 1983, 20 (3), 1187$-$1197] for van Vleck's continued fractions. For its proving, the $mathcal{C}$-figure convergence and estimates of the difference between approximants of fractions in an angular domain are significantly used. In comparison with the previously established results, the elements of a branched continued fraction of the special form can tend to zero at a certain rate. An example of the effectiveness of using a two-dimensional analog of van Vleck's theorem is considered.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139252894","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
New $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomials and their matrices 新的 U$ 伯努利、U$ 欧拉和 U$ 日诺奇多项式及其矩阵
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-11-21 DOI: 10.15330/cmp.15.2.449-467
W. Ramirez, D. Bedoya, A. Urieles, C. Cesarano, M. Ortega
{"title":"New $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomials and their matrices","authors":"W. Ramirez, D. Bedoya, A. Urieles, C. Cesarano, M. Ortega","doi":"10.15330/cmp.15.2.449-467","DOIUrl":"https://doi.org/10.15330/cmp.15.2.449-467","url":null,"abstract":"In this paper, we introduce the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomials, their numbers, and their relationship with the Riemann zeta function. We also derive the Apostol-type generalizations to obtain some of their algebraic and differential properties. We introduce generalized $U$-Bernoulli, $U$-Euler and $U$-Genocchi polynomial Pascal-type matrix. We deduce some product formulas related to this matrix. Furthermore, we establish some explicit expressions for the $U$-Bernoulli, $U$-Euler, and $U$-Genocchi polynomial matrices, which involves the generalized Pascal matrix.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139253502","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 positive Cohen weakly nuclear multilinear operators 关于正Cohen弱核多线性算子
Carpathian Mathematical Publications Pub Date : 2023-11-14 DOI: 10.15330/cmp.15.2.396-410
A. Bougoutaia, A. Belacel, R. Macedo, H. Hamdi
{"title":"On positive Cohen weakly nuclear multilinear operators","authors":"A. Bougoutaia, A. Belacel, R. Macedo, H. Hamdi","doi":"10.15330/cmp.15.2.396-410","DOIUrl":"https://doi.org/10.15330/cmp.15.2.396-410","url":null,"abstract":"In this article, we establish new relationships involving the class of Cohen positive strongly $p$-summing multilinear operators. Furthermore, we introduce a new class of multilinear operators on Banach lattices, called positive Cohen weakly nuclear multilinear operators. We establish a Pietsch domination-type theorem for this new class of multilinear operators. As an application, we show that every positive Cohen weakly $p$-nuclear multilinear operator is positive Dimant strongly $p$-summing and Cohen positive strongly $p$-summing. We conclude with a tensor representation of our class.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901898","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
Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions 勒贝格可测函数空间上弱对称函数的代数
Carpathian Mathematical Publications Pub Date : 2023-11-14 DOI: 10.15330/cmp.15.2.411-419
I.V. Burtnyak, Yu.Yu. Chopyuk, S.I. Vasylyshyn, T.V. Vasylyshyn
{"title":"Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions","authors":"I.V. Burtnyak, Yu.Yu. Chopyuk, S.I. Vasylyshyn, T.V. Vasylyshyn","doi":"10.15330/cmp.15.2.411-419","DOIUrl":"https://doi.org/10.15330/cmp.15.2.411-419","url":null,"abstract":"In this work, we investigate algebras of block-symmetric and weakly symmetric polynomials and analytic functions on complex Banach spaces of Lebesgue measurable functions, for which the $p$th power of the absolute value is Lebesgue integrable, where $pin[1,+infty),$ and Lebesgue measurable essentially bounded functions on $[0,1].$ We construct generating systems of algebras of all weakly symmetric continuous complex-valued polynomials on these spaces. Also we establish conditions under which sets of weakly symmetric analytic functions are algebras.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134902994","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
Timelike spherical curves according to equiform Bishop frame in 3-dimensional Minkowski space 三维闵可夫斯基空间中等形Bishop框架的类时球曲线
Carpathian Mathematical Publications Pub Date : 2023-10-29 DOI: 10.15330/cmp.15.2.388-395
N. Elsharkawy, C. Cesarano, R. Dmytryshyn, A. Elsharkawy
{"title":"Timelike spherical curves according to equiform Bishop frame in 3-dimensional Minkowski space","authors":"N. Elsharkawy, C. Cesarano, R. Dmytryshyn, A. Elsharkawy","doi":"10.15330/cmp.15.2.388-395","DOIUrl":"https://doi.org/10.15330/cmp.15.2.388-395","url":null,"abstract":"In this paper, we study the equiform Bishop formulae for the equiform timelike curves in 3-dimensional Minkowski space where the equiform timelike spherical curves are defined according to the equiform Bishop frame. We establish a necessary and sufficient condition for an equiform timelike curve to be an equiform timelike spherical curve. Furthermore, we give certain characterizations of equiform spherical curves in 3-dimensional Minkowski space, which are timelike with an equiform spacelike principal normal vector.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136135287","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
Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $alpha$-stable stochastic process 各向同性$ α $稳定随机过程的转移概率密度的一些伪导数的双边估计
Carpathian Mathematical Publications Pub Date : 2023-10-19 DOI: 10.15330/cmp.15.2.381-387
M.M. Osypchuk
{"title":"Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $alpha$-stable stochastic process","authors":"M.M. Osypchuk","doi":"10.15330/cmp.15.2.381-387","DOIUrl":"https://doi.org/10.15330/cmp.15.2.381-387","url":null,"abstract":"In the paper, the transition probability density of an isotropic $alpha$-stable stochastic process in a finite dimensional Euclidean space is considered. The results of applying pseudo-differential operators with respect spatial variables to this function are estimated from the both side: above and below. Operators in the consideration are defined by the symbols $|lambda|^varkappa$ and $lambda|lambda|^{varkappa-1}$, where $varkappa$ is some constant. The first operator with negative sign is fractional Laplacian and the second one multiplied by imaginary unit is fractional gradient.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135779533","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
Characterizing Riesz bases via biorthogonal Bessel sequences 利用双正交贝塞尔序列表征Riesz碱基
Carpathian Mathematical Publications Pub Date : 2023-09-10 DOI: 10.15330/cmp.15.2.377-380
E. Zikkos
{"title":"Characterizing Riesz bases via biorthogonal Bessel sequences","authors":"E. Zikkos","doi":"10.15330/cmp.15.2.377-380","DOIUrl":"https://doi.org/10.15330/cmp.15.2.377-380","url":null,"abstract":"Recently D.T. Stoeva proved that if two Bessel sequences in a separable Hilbert space $mathcal H$ are biorthogonal and one of them is complete in $mathcal H$, then both sequences are Riesz bases for $mathcal H$. This improves a well known result where completeness is assumed on both sequences.
 In this note we present an alternative proof of Stoeva's result which is quite short and elementary, based on the notion of Riesz-Fischer sequences.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136071673","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
Some remarks on spectrum of nonlinear continuous operators 关于非线性连续算子谱的若干注记
Carpathian Mathematical Publications Pub Date : 2023-09-07 DOI: 10.15330/cmp.15.2.356-376
K.N. Soltanov
{"title":"Some remarks on spectrum of nonlinear continuous operators","authors":"K.N. Soltanov","doi":"10.15330/cmp.15.2.356-376","DOIUrl":"https://doi.org/10.15330/cmp.15.2.356-376","url":null,"abstract":"In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study this question it is used a different approach that allows the studying of all eigenvalues of a nonlinear operator relative to another nonlinear operator. Here we show that in nonlinear operators case it is necessary to seek the spectrum of the given nonlinear operator relative to another nonlinear operator satisfying certain conditions. The different examples, for which eigenvalues can be found, are provided. Moreover, the nonlinear problems including parameters are studied.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135096980","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
Metric and topology on the poset of compact pseudoultrametrics 紧致伪度量偏置集上的度量和拓扑
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-08-03 DOI: 10.15330/cmp.15.2.321-330
S. Nykorovych, O. Nykyforchyn
{"title":"Metric and topology on the poset of compact pseudoultrametrics","authors":"S. Nykorovych, O. Nykyforchyn","doi":"10.15330/cmp.15.2.321-330","DOIUrl":"https://doi.org/10.15330/cmp.15.2.321-330","url":null,"abstract":"In two ways we introduce metrics on the set of all pseudoultrametrics, not exceeding a given compact pseudoultrametric on a fixed set, and prove that the obtained metrics are compact and topologically equivalent. To achieve this, we give a characterization of the sets being the hypographs of the mentioned pseudoultrametrics, and apply Hausdorff metric to their family. It is proved that the uniform convergence metric is a limit case of metrics defined via hypographs. It is shown that the set of all pseudoultrametrics, not exceeding a given compact pseudoultrametric, with the induced topology is a Lawson compact Hausdorff upper semilattice.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88867723","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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