Mathematical Sciences and Applications ENotes
,
Volume 12
Issue 4
https://dergipark.org.tr/en/pub/mathenot
From 2021 onwards, Mathematical Sciences and Applications ENotes (MSAEN), will be published four times a year, at intervals of three months, and only in online version. Refreshing the Aim and Scope of the Journal...The editors have reviewed and adjusted the aims and scope of Mathematical Sciences and Applications ENotes (MSAEN). The journal’s central mission is to publish research of outstanding significance and timeliness. We are now providing more detailed guidance on the most important topics and areas that will be emphasized in the future in order to achieve this goal.The Journal welcomes papers on:Approximation theory, iteration methods and their applicationsApplied functional analysis and operator theoryReal and harmonic analysisComplex analysisNumerical analysisInterpolation theoryOptimization theoryFunctional, ordinary and partial differential equationsLinear and nonlinear integral equationsNumerical solution of differential and integral equationsFourier approximationNumerical linear algebraApplied mathematics
en
Journal Article
DergiPark
ULAKBİM Journal Systems
© 2024 All Rights Reserved.
dergipark.org.tr
Cover Image
dergipark.org.tr/media/cache/journal_croped/ce1d/009c/9530/5fbf968c94a9c.png"
dergiparkdestek@tubitak.gov.tr

Characterizations of Some New Classes of FourDimensional Matrices on the Double Series Spaces of First Order Cesaro Means
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1471156
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1471156
Okan Bodur, Canan Hazar Gulec
The main purpose in this study is to investigate some topological and algebraic properties of the absolutely double series spaces $\left\vert C_{1,1}\right\vert _{k}$ defined by combining the first order Cesaro means with the concept of absolute summability for $k\geq 1$. Beside this, we determine the $\alpha $dual of the space $\left\vert C_{1,1}\right\vert _{1}$ and the $\beta \left( bp\right) $ and $\gamma $duals of the spaces $% \left\vert C_{1,1}\right\vert _{k}$ for $k\geq 1.$ Finally, we characterize some new fourdimensional matrix classes $\left( \left\vert C_{1,1}\right\vert _{k},\upsilon \right) ,$ $\left( \left\vert C_{1,1}\right\vert _{1},\upsilon \right) $, $\left( \left\vert C_{1,1}\right\vert _{1},\mathcal{L}_{k}\right) ,$ $\left( \left\vert C_{1,1}\right\vert _{k},\mathcal{L}_{u}\right) ,$ $\left( \mathcal{L} _{u},\left\vert C_{1,1}\right\vert _{k}\right) $ and $\left( \mathcal{L} _{k},\left\vert C_{1,1}\right\vert _{1}\right) $, where $\upsilon \in \left\{ \mathcal{M}_{u},\mathcal{C}_{bp}\right\} $ for $1\leq k<\infty $. Hence, some important results concerned on Ces\`{a}ro matrix summation methods have been extended to double sequences.

Lacunary Statistically Convergence via Modulus Function Sequences
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1477450
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1477450
Erdal Bayram, Çiğdem Bektaş
Modifying the definition of density functions is one method used to generalise statistical convergence. In the present study, we use sequences of modulus functions and order $\alpha \in \left( 0,1\right] $ to introduce a new density. Based on this density framework, we define strong $(f_k)$lacunary summability of order $\alpha $ and $(f_k)$lacunary statistical convergence of order $\alpha $ for a sequence of modulus functions $(f_k)$. This concept holds an intermediate position between the usual convergence and the statistical convergence for lacunary sequences. We also establish inclusion theorems and relations between these two concepts in the study.

Taylor's Power Law and Packing Circles
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1448644
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1448644
Oğuzhan Kaya, Zeki Topçu
The famous Taylor Power Law is in general observed in ecology and relates the variance of the population of a certain species in a unit area while Circle Packing is an arrangement of circles in a given area. We show that the circle packing problem in $\mathbb{R}^2$ satisfies the Taylor power law formula for $b = 2$.

Inextensible Flow of Quaternionic Curves According to Type 2Quaternionic Frame in the Euclidean Space
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1481075
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1481075
Önder Gökmen Yıldız, Hazer Usta
In this paper, we investigate inextensible flows of quaternionic curve according to Type 2Quaternionic frame. We give necessary and sufficient conditions for inextensible flow of quaternionic curves. Moreover, we obtain evolution equations of the Frenet frame and curvatures according to Type 2Quaternionic frame.

On New Pell Spinor Sequences
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1451896
https://dergipark.org.tr/en/pub/mathenot/issue/86165/1451896
Tülay Erişir, Gökhan Mumcu, Mehmet Ali Güngör
Our motivation for this study is to define two new and particular sequences. The most essential feature of these sequences is that they are spinor sequences. In this study, these new spinor sequences obtained using spinor representations of Pell and PellLucas quaternions are expressed. Moreover, some formulas such that Binet formulas, Cassini formulas and generating functions of these spinor sequences, which are called as Pell and PellLucas spinor sequences, are given. Then, some relationships between Pell and PellLucas spinor sequences are obtained. Therefore, an easier and more interesting representations of Pell and PellLucas quaternions, which are a generalization of Pell and PellLucas number sequences, are obtained. We believe that these new spinor sequences will be useful and advantageable in many branches of science, such as geometry, algebra and physics.