Pub Date : 2024-01-12DOI: 10.36753/mathenot.1395051
Pakize Uygun, M. Atc̣eken, Tuğba Mert
In this paper we present invariant submanifolds of an almost $alpha $-cosymplectic $(k, mu, nu)$-space. Then, we gave some results for an invariant submanifold of an almost $alpha $-cosymplectic $(k,mu,nu)$-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic $(k, mu, nu)$-space.
{"title":"Certain Results for Invariant Submanifolds of an Almost $alpha$-Cosymplectic $(k,mu ,nu )$-Space","authors":"Pakize Uygun, M. Atc̣eken, Tuğba Mert","doi":"10.36753/mathenot.1395051","DOIUrl":"https://doi.org/10.36753/mathenot.1395051","url":null,"abstract":"In this paper we present invariant submanifolds of an almost $alpha $-cosymplectic $(k, mu, nu)$-space. Then, we gave some results for an invariant submanifold of an almost $alpha $-cosymplectic $(k,mu,nu)$-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic $(k, mu, nu)$-space.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"48 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509762","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}
Pub Date : 2023-10-25DOI: 10.36753/mathenot.1180832
Asit SAHA, Seydi Battal Gazi KARAKOÇ, Khalid K. ALİ
The aim of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher-order dispersion term. For this purpose, the first and second simplest methods are used to build soliton solutions of travelling wave solutions. Furthermore, the bifurcation behavior of traveling waves including new types of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and beneficial tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher-order dispersion will add some value to the literature of mathematical and plasma physics.
{"title":"New exact soliton solutions, bifurcation and multistability behaviors of traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov equation with higher order dispersion","authors":"Asit SAHA, Seydi Battal Gazi KARAKOÇ, Khalid K. ALİ","doi":"10.36753/mathenot.1180832","DOIUrl":"https://doi.org/10.36753/mathenot.1180832","url":null,"abstract":"The aim of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher-order dispersion term. For this purpose, the first and second simplest methods are used to build soliton solutions of travelling wave solutions. Furthermore, the bifurcation behavior of traveling waves including new types of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and beneficial tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher-order dispersion will add some value to the literature of mathematical and plasma physics.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"16 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972245","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}
Pub Date : 2023-09-13DOI: 10.36753/mathenot.1330281
Nimet PANCAROĞLU AKIN, Erdinç DÜNDAR
In this paper, we define the concepts of lacunary $mathcal{I}^{ast}$-convergence and strongly lacunary $mathcal{I}^{ast}$-convergence. We investigate the relations between strongly lacunary $mathcal{I}$-convergence and strongly lacunary $mathcal{I}^{ast}$-convergence. Also, we define the concept of strongly lacunary $mathcal{I}^{ast}$-Cauchy sequence and investigate the relations between strongly lacunary $mathcal{I}$-Cauchy sequence and strongly lacunary $mathcal{I}^{ast}$-Cauchy sequence.
{"title":"Strongly Lacunary $mathcal{I}^{ast }$-Convergence and Strongly Lacunary $mathcal{I}^{ast }$-Cauchy Sequence","authors":"Nimet PANCAROĞLU AKIN, Erdinç DÜNDAR","doi":"10.36753/mathenot.1330281","DOIUrl":"https://doi.org/10.36753/mathenot.1330281","url":null,"abstract":"In this paper, we define the concepts of lacunary $mathcal{I}^{ast}$-convergence and strongly lacunary $mathcal{I}^{ast}$-convergence. We investigate the relations between strongly lacunary $mathcal{I}$-convergence and strongly lacunary $mathcal{I}^{ast}$-convergence. Also, we define the concept of strongly lacunary $mathcal{I}^{ast}$-Cauchy sequence and investigate the relations between strongly lacunary $mathcal{I}$-Cauchy sequence and strongly lacunary $mathcal{I}^{ast}$-Cauchy sequence.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135786272","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}
Pub Date : 2023-08-14DOI: 10.36753/mathenot.1300609
Gonca DURMAZ GÜNGÖR, İshak ALTUN
By employing α-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.
{"title":"Some Fixed Point Results for α-Admissible mappings on Quasi Metric Space Via θ-Contractions","authors":"Gonca DURMAZ GÜNGÖR, İshak ALTUN","doi":"10.36753/mathenot.1300609","DOIUrl":"https://doi.org/10.36753/mathenot.1300609","url":null,"abstract":"By employing α-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135308456","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}
Pub Date : 2023-07-13DOI: 10.36753/mathenot.1308678
Mukaddes Arslan, Ramazan Sunar
In this study, we introduced the concepts of rough convergence, rough Cauchy double sequence and the set of rough limit points of a double sequence, as well as the rough convergence criteria associated with this set in n-normed spaces. Later, we proved that this set is both closed and convex. Finally, we presented the relationships between rough convergence and rough Cauchy double sequence in n -normed spaces.
在这项研究中，我们介绍了粗糙收敛、粗糙考奇双序列和双序列粗糙极限点集合的概念，以及在 n 规范空间中与该集合相关的粗糙收敛准则。随后，我们证明了这个集合既是封闭的又是凸的。最后，我们介绍了 n 规范空间中粗糙收敛与粗糙考奇双序列之间的关系。
{"title":"Rough Convergence of Double Sequence in n-Normed Spaces","authors":"Mukaddes Arslan, Ramazan Sunar","doi":"10.36753/mathenot.1308678","DOIUrl":"https://doi.org/10.36753/mathenot.1308678","url":null,"abstract":"In this study, we introduced the concepts of rough convergence, rough Cauchy double sequence and the set of rough limit points of a double sequence, as well as the rough convergence criteria associated with this set in n-normed spaces. Later, we proved that this set is both closed and convex. Finally, we presented the relationships between rough convergence and rough Cauchy double sequence in n -normed spaces.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139359921","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}
Pub Date : 2023-04-01DOI: 10.36753/mathenot.1212331
Sevcan Demi̇rkale, E. Tas
In the present paper, $P-$distributional convergence which is defined by power series method has been introduced. We give equivalent expressions for $P-$distributional convergence of spliced sequences. Moreover, convergence of a bounded $infty$-spliced sequence via power series method is represented in terms of Bochner integral in Banach spaces.
{"title":"Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces","authors":"Sevcan Demi̇rkale, E. Tas","doi":"10.36753/mathenot.1212331","DOIUrl":"https://doi.org/10.36753/mathenot.1212331","url":null,"abstract":"In the present paper, $P-$distributional convergence which is defined by power series method has been introduced. We give equivalent expressions for $P-$distributional convergence of spliced sequences. Moreover, convergence of a bounded $infty$-spliced sequence via power series method is represented in terms of Bochner integral in Banach spaces.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130156455","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}
Pub Date : 2023-04-01DOI: 10.36753/mathenot.1084371
C. Raposo, A. Cattai, O. Vera, Ganesh CH. GORAIN, D. Pereira
This manuscript deals with global solution, polynomial stability and blow-up behavior at a finite time for the nonlinear system begin{align*} left{ begin{array}{rcl} & u'' - Delta_{p} u + theta + alpha u' = leftvert urightvert ^{p-2}uln leftvert urightvert &theta' - Delta theta = u' end{array}% right. end{align*} where $Delta_{p}$ is the nonlinear $p$-Laplacian operator, $ 2 leq p < infty$. Taking into account that the initial data is in a suitable stability set created from the Nehari manifold, the global solution is constructed by means of the Faedo-Galerkin approximations. Polynomial decay is proven for a subcritical level of initial energy. The blow-up behavior is shown on an instability set with negative energy values.
本文研究非线性系统begin{align*} left begin{array}{rcl} & u " - Delta_{p} u + theta + alpha u' = leftvert urightvert ^{p-2}uln leftvert urightvert &theta' - Delta theta = u' end{array}% right的全局解、多项式稳定性和有限时间爆破行为。end{align*}其中$Delta_{p}$是非线性的$p$-拉普拉斯算子，$ 2 leq p < infty$。考虑到初始数据处于由Nehari流形创建的合适的稳定集中，通过Faedo-Galerkin近似构造了全局解。在亚临界能级上证明了多项式衰减。在具有负能值的不稳定集上显示了爆炸行为。
{"title":"Global Solution and Blow-up for a Thermoelastic System of $p$-Laplacian Type with Logarithmic Source","authors":"C. Raposo, A. Cattai, O. Vera, Ganesh CH. GORAIN, D. Pereira","doi":"10.36753/mathenot.1084371","DOIUrl":"https://doi.org/10.36753/mathenot.1084371","url":null,"abstract":"This manuscript deals with global solution, polynomial stability and blow-up behavior at a finite time for the nonlinear system begin{align*} left{ begin{array}{rcl} & u'' - Delta_{p} u + theta + alpha u' = leftvert urightvert ^{p-2}uln leftvert urightvert &theta' - Delta theta = u' end{array}% right. end{align*} where $Delta_{p}$ is the nonlinear $p$-Laplacian operator, $ 2 leq p < infty$. Taking into account that the initial data is in a suitable stability set created from the Nehari manifold, the global solution is constructed by means of the Faedo-Galerkin approximations. Polynomial decay is proven for a subcritical level of initial energy. The blow-up behavior is shown on an instability set with negative energy values.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132751744","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}
Pub Date : 2023-04-01DOI: 10.36753/mathenot.1117985
Y. Yılmaz, H. Levent, Hacer Bozkurt
In this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining the concept of dimensions in these spaces, we show that the set of $n$-dimensional interval vectors is actually a $(n_{r},n_{s})$-dimensional quasilinear space and any quasilinear space is $left( n_{r},0_{s}right) $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $(2_{r},0_{s})$ and $(0_{r},2_{s})$-dimensional subspaces. We define the concept of dimension in a quasilinear space with natural number pairs. Further, we define an inner product on some spaces and talk about them as inner product quasilinear spaces. Further, we show that some of them have Hilbert quasilinear space structure.
{"title":"On the Algebra of Interval Vectors","authors":"Y. Yılmaz, H. Levent, Hacer Bozkurt","doi":"10.36753/mathenot.1117985","DOIUrl":"https://doi.org/10.36753/mathenot.1117985","url":null,"abstract":"In this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining the concept of dimensions in these spaces, we show that the set of $n$-dimensional interval vectors is actually a $(n_{r},n_{s})$-dimensional quasilinear space and any quasilinear space is $left( n_{r},0_{s}right) $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $(2_{r},0_{s})$ and $(0_{r},2_{s})$-dimensional subspaces. We define the concept of dimension in a quasilinear space with natural number pairs. Further, we define an inner product on some spaces and talk about them as inner product quasilinear spaces. Further, we show that some of them have Hilbert quasilinear space structure.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134100961","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}
Pub Date : 2023-04-01DOI: 10.36753/mathenot.1057344
Harikrishnan Sugumaran, D. Vi̇vek, E. Elsayed
This manuscript is devoted to investigate the existence, uniqueness and stability of pantograph equations with Hilfer generalized proportional fractional derivative. The concerned results are obtained using standard theorems.
{"title":"On the Study of Pantograph Differential Equations with Proportional Fractional Derivative","authors":"Harikrishnan Sugumaran, D. Vi̇vek, E. Elsayed","doi":"10.36753/mathenot.1057344","DOIUrl":"https://doi.org/10.36753/mathenot.1057344","url":null,"abstract":"This manuscript is devoted to investigate the existence, uniqueness and stability of pantograph equations with Hilfer generalized proportional fractional derivative. The concerned results are obtained using standard theorems.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127981919","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}
Pub Date : 2023-03-28DOI: 10.36753/mathenot.1056913
M. Kirişci, Musa Bardak, N. Topaç
The purpose of this paper is to measure the effect of Coronavirus quarantine on the cognition and behavior of children in the early childhood period using the Fuzzy Set Theory. In this study, after the Coronavirus quarantine, the thoughts of the children and their parents' observations and thoughts about the cognition and behavior of their children were questioned. This investigation was used to measure the change in children's cognition and behavior of the Coronavirus quarantine, both in questions asked to children and in questions asked to parents. The fuzzy Conjoint Method was used to analyze the data obtained. The measurements of the effect of the Corona-virus quarantine have been recorded in the form of degrees of similarity and its level of agreement.
{"title":"The Effect of Corona-Virus Disease (COVID-19) Outbreak Quarantine on the Belief and Behavior of Children in Early Childhood with a Fuzzy Conjoint Method","authors":"M. Kirişci, Musa Bardak, N. Topaç","doi":"10.36753/mathenot.1056913","DOIUrl":"https://doi.org/10.36753/mathenot.1056913","url":null,"abstract":"The purpose of this paper is to measure the effect of Coronavirus quarantine on the cognition and behavior of children in the early childhood period using the Fuzzy Set Theory. In this study, after the Coronavirus quarantine, the thoughts of the children and their parents' observations and thoughts about the cognition and behavior of their children were questioned. This investigation was used to measure the change in children's cognition and behavior of the Coronavirus quarantine, both in questions asked to children and in questions asked to parents. The fuzzy Conjoint Method was used to analyze the data obtained. The measurements of the effect of the Corona-virus quarantine have been recorded in the form of degrees of similarity and its level of agreement.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129809113","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}
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