We introduce logarithmic summability in intuitionistic fuzzy normed spaces($IFNS$) and give some Tauberian conditions for which logarithmic summability yields convergence in $IFNS$. Besides, we define the concept of slow oscillation with respect to logarithmic summability in $IFNS$, investigate its relation with the concept of q-boundedness and give Tauberian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between Ces`{a}ro summability method and logarithmic summability method in $IFNS$ is also proved in the paper.
{"title":"On the Logarithmic Summability of Sequences in Intuitionistic Fuzzy Normed Spaces","authors":"E. Yavuz","doi":"10.33401/fujma.792994","DOIUrl":"https://doi.org/10.33401/fujma.792994","url":null,"abstract":"We introduce logarithmic summability in intuitionistic fuzzy normed spaces($IFNS$) and give some Tauberian conditions for which logarithmic summability yields convergence in $IFNS$. Besides, we define the concept of slow oscillation with respect to logarithmic summability in $IFNS$, investigate its relation with the concept of q-boundedness and give Tauberian theorems by means of q-boundedness and slow oscillation with respect to logarithmic summability. A comparison theorem between Ces`{a}ro summability method and logarithmic summability method in $IFNS$ is also proved in the paper.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132572139","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}
In this paper, we investigate covariant and contravariant symbols of operators generated by a representation of the integer group $mathbb{Z}$. Then we describe some properties (Existence, Uniquenes s, Boundedness, Compactnessi and Finite rank) of these operators and reformulated some know results in terms of wavelet transform (covariant and contravariant symbols).
{"title":"Covariant and Contravariant Symbols of Operators on $l^{2}left(mathbb{Z}right)$","authors":"A. S. Elmabrok","doi":"10.33401/fujma.718157","DOIUrl":"https://doi.org/10.33401/fujma.718157","url":null,"abstract":"In this paper, we investigate covariant and contravariant symbols of operators generated by a representation of the integer group $mathbb{Z}$. Then we describe some properties (Existence, Uniquenes s, Boundedness, Compactnessi and Finite rank) of these operators and reformulated some know results in terms of wavelet transform (covariant and contravariant symbols). ","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115420556","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}
The object of the present paper is to classify $N(kappa)$-contact metric manifolds admitting the semi-symmetric non-metric connection with certain curvature conditions the projectively curvature tensor. We studied projective flat, $xi- $projectively flat, $phi- $projectively flat $N(kappa )$-contact metric manifolds admitting the semi-symmetric non-metric connection. Also, we examine such manifolds under some local symmetry conditions related to projective curvature tensor.
{"title":"Projective Curvature Tensor on $N(kappa)-$Contact Metric Manifold Admitting Semi-Symmetric Non-Metric Connection","authors":"Mustafa Altın","doi":"10.33401/fujma.733415","DOIUrl":"https://doi.org/10.33401/fujma.733415","url":null,"abstract":"The object of the present paper is to classify $N(kappa)$-contact metric manifolds admitting the semi-symmetric non-metric connection with certain curvature conditions the projectively curvature tensor. We studied projective flat, $xi- $projectively flat, $phi- $projectively flat $N(kappa )$-contact metric manifolds admitting the semi-symmetric non-metric connection. Also, we examine such manifolds under some local symmetry conditions related to projective curvature tensor. ","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125138525","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}
This paper investigates the effects of the YHP roughness model on the mean flow solutions of some flows belong to the family of the rotating BEK system flows. The governing mean flow equations are formulated in the rotating frame of reference, therefore, they include terms arising from the centrifugal force. These mean flow equations are solved using the method of lines and the backward difference method. Then, obtained results are compared for specifically selected value of roughness parameters with the results of a fundamentally different roughness model, the MW model. The results of the YHP model reveal that applying surface roughness changes the characteristics of the mean flow components. Moreover, the comparison of the YHP and MW models points that these changes are notably different for each model. Therefore, possible future researches can be conducted to investigate the stability characteristics of the flows due to the selection of the roughness model.
{"title":"On the Mean Flow Solutions of Related Rotating Disk Flows of the BEK System","authors":"B. Alveroğlu","doi":"10.33401/fujma.796886","DOIUrl":"https://doi.org/10.33401/fujma.796886","url":null,"abstract":"This paper investigates the effects of the YHP roughness model on the mean flow solutions of some flows belong to the family of the rotating BEK system flows. The governing mean flow equations are formulated in the rotating frame of reference, therefore, they include terms arising from the centrifugal force. These mean flow equations are solved using the method of lines and the backward difference method. Then, obtained results are compared for specifically selected value of roughness parameters with the results of a fundamentally different roughness model, the MW model. The results of the YHP model reveal that applying surface roughness changes the characteristics of the mean flow components. Moreover, the comparison of the YHP and MW models points that these changes are notably different for each model. Therefore, possible future researches can be conducted to investigate the stability characteristics of the flows due to the selection of the roughness model.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126013587","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}
In 1730 James Stirling, building on the work of Abraham de Moivre, published what is known as Stirling's approximation of $n!$. He gave a good formula which is asymptotic to $n!$. Since then hundreds of papers have given alternative proofs of his result and improved upon it, including notably by Burside, Gosper, and Mortici. However Srinivasa Ramanujan gave a remarkably better asymptotic formula. Hirschhorn and Villarino gave a nice proof of Ramanujan's result and an error estimate for the approximation. In recent years there have been several improvements of Stirling's formula including by Nemes, Windschitl, and Chen. Here it is shown (i) how all these asymptotic results can be easily verified; (ii) how Hirschhorn and Villarino's argument allows a tweaking of Ramanujan's result to give a better approximation; (iii) that a new asymptotic formula can be obtained by further tweaking of Ramanujan's result; (iv) that Chen's asymptotic formula is better than the others mentioned here, and the new asymptotic formula is comparable with Chen's.
{"title":"Tweaking Ramanujan's Approximation of n!","authors":"S. Morris","doi":"10.33401/fujma.995150","DOIUrl":"https://doi.org/10.33401/fujma.995150","url":null,"abstract":"In 1730 James Stirling, building on the work of Abraham de Moivre, published what is known as Stirling's approximation of $n!$. He gave a good formula which is asymptotic to $n!$. Since then hundreds of papers have given alternative proofs of his result and improved upon it, including notably by Burside, Gosper, and Mortici. However Srinivasa Ramanujan gave a remarkably better asymptotic formula. Hirschhorn and Villarino gave a nice proof of Ramanujan's result and an error estimate for the approximation. In recent years there have been several improvements of Stirling's formula including by Nemes, Windschitl, and Chen. Here it is shown (i) how all these asymptotic results can be easily verified; (ii) how Hirschhorn and Villarino's argument allows a tweaking of Ramanujan's result to give a better approximation; (iii) that a new asymptotic formula can be obtained by further tweaking of Ramanujan's result; (iv) that Chen's asymptotic formula is better than the others mentioned here, and the new asymptotic formula is comparable with Chen's.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113959499","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}
This paper addresses optimal control problems governed by semilinear parabolic partial differential equations, subject to control constraints and state constraints of integral type. Since such problems may not have classical solutions, a relaxed optimal control problem is considered. The relaxed control problem is discretized by using a finite element method and the behavior in the limit of discrete optimality, admissibility and extremality properties is studied. A conditional descent method with penalties applied to the discrete problems is proposed. It is shown that the accumulation points of sequences produced by this method are admissible and extremal for the discrete problem. Finally, numerical examples are given.
{"title":"An Optimization Method for Semilinear Parabolic Relaxed Constrained Optimal Control Problems","authors":"B. Kokkinis","doi":"10.33401/fujma.645321","DOIUrl":"https://doi.org/10.33401/fujma.645321","url":null,"abstract":"This paper addresses optimal control problems governed by semilinear parabolic partial differential equations, subject to control constraints and state constraints of integral type. Since such problems may not have classical solutions, a relaxed optimal control problem is considered. The relaxed control problem is discretized by using a finite element method and the behavior in the limit of discrete optimality, admissibility and extremality properties is studied. A conditional descent method with penalties applied to the discrete problems is proposed. It is shown that the accumulation points of sequences produced by this method are admissible and extremal for the discrete problem. Finally, numerical examples are given.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"544 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123102884","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}
We have given a simple contact Hamiltonian description of a system with exponentially vanishing (or zero) potential under a friction term that is quadratic in velocity. We have given two applications: to cavity solitons and to a free body under air friction.
{"title":"Contact Hamiltonian Description of Systems with Exponentially Decreasing Force and Friction that is Quadratic in Velocity","authors":"Furkan Semih Dündar","doi":"10.33401/fujma.716406","DOIUrl":"https://doi.org/10.33401/fujma.716406","url":null,"abstract":"We have given a simple contact Hamiltonian description of a system with exponentially vanishing (or zero) potential under a friction term that is quadratic in velocity. We have given two applications: to cavity solitons and to a free body under air friction.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131013260","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}
In the paper, we have considered the real and dual bicomplex numbers separately. Firstly, we examine the dual numbers and investigate the characteristic properties of them. Then, we give the definition, feature and related concepts about bicomplex numbers. And we define the number of dual $k-$ Pell bicomplex numbers that are not found for the first time in the literature and we examine the norm and conjugate properties of these numbers. We give equations about conjugates and give also some important characteristic of these newly defined numbers, and we write the recursive correlations of these numbers. Using these relations we give some important identities such as Vajda's, Honsberger's and d'Ocagne identities.
{"title":"On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them","authors":"S. Halici, Şule Çürük","doi":"10.33401/fujma.718298","DOIUrl":"https://doi.org/10.33401/fujma.718298","url":null,"abstract":"In the paper, we have considered the real and dual bicomplex numbers separately. Firstly, we examine the dual numbers and investigate the characteristic properties of them. Then, we give the definition, feature and related concepts about bicomplex numbers. And we define the number of dual $k-$ Pell bicomplex numbers that are not found for the first time in the literature and we examine the norm and conjugate properties of these numbers. We give equations about conjugates and give also some important characteristic of these newly defined numbers, and we write the recursive correlations of these numbers. Using these relations we give some important identities such as Vajda's, Honsberger's and d'Ocagne identities.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116152457","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}
The main purpose of this study is to characterize some matrix classes from classical sequence spaces into a newly introduced space and find the norm of some special matrix operators. Also, we give certain geometric properties of this space.
{"title":"Certain Geometric Properties and Matrix Transformations on a Newly Introduced Banach Space","authors":"M. İlkhan","doi":"10.33401/fujma.721287","DOIUrl":"https://doi.org/10.33401/fujma.721287","url":null,"abstract":"The main purpose of this study is to characterize some matrix classes from classical sequence spaces into a newly introduced space and find the norm of some special matrix operators. Also, we give certain geometric properties of this space.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121772138","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}
We establish after some technical results a characterization of maximal null hypersurfaces in terms of a constant mean curvature screen foliation (in the slices) induced by the Chen's vector field. Thereafter, bounds are provided for both the squared norm of the (screen) shape operator for non totally geodesic maximal null hypersurfaces and the scalar curvature of the fiber. In terms of the scalar curvature of the fiber and the warping function, we establish necessary and sufficient conditions for Null Convergence Condition (NCC) to be satisfied in which case we prove that there are no non totally geodesic maximal null hypersurfaces. A generic example consisting of graphs of functions defined on the fiber is given to support our results. Finally, we provide lower bounds for the extrinsic scalar curvature and give a characterization result for Willmore null hypersurfaces in generalized Robertson-Walker spacetimes.
{"title":"Maximal and Willmore Null Hypersurfaces in Generalized Robertson-Walker Spacetimes","authors":"C. Atindogbe, H. Hounnon","doi":"10.33401/fujma.670266","DOIUrl":"https://doi.org/10.33401/fujma.670266","url":null,"abstract":"We establish after some technical results a characterization of maximal null hypersurfaces in terms of a constant mean curvature screen foliation (in the slices) induced by the Chen's vector field. Thereafter, bounds are provided for both the squared norm of the (screen) shape operator for non totally geodesic maximal null hypersurfaces and the scalar curvature of the fiber. In terms of the scalar curvature of the fiber and the warping function, we establish necessary and sufficient conditions for Null Convergence Condition (NCC) to be satisfied in which case we prove that there are no non totally geodesic maximal null hypersurfaces. A generic example consisting of graphs of functions defined on the fiber is given to support our results. Finally, we provide lower bounds for the extrinsic scalar curvature and give a characterization result for Willmore null hypersurfaces in generalized Robertson-Walker spacetimes.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129403588","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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