Pub Date : 2021-11-17DOI: 10.12697/acutm.2021.25.18
K. Ho
This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.
本文建立了混合范数空间的外推理论。利用这一外推理论，我们得到了Rubio de Francia Littlewood-Paley函数和几何极大函数在混合范数空间上的映射性质。作为这些结果的特例，我们得到了变指数混合范数Lebesgue空间和混合范数Lorentz空间上的映射性质。
{"title":"Extrapolation to mixed norm spaces and applications","authors":"K. Ho","doi":"10.12697/acutm.2021.25.18","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.18","url":null,"abstract":"This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"s1-15 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85971946","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.14
Santosh Kumar, B. Pal
We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.
{"title":"K-type slant helices on spacelike and timelike surfaces","authors":"Santosh Kumar, B. Pal","doi":"10.12697/acutm.2021.25.14","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.14","url":null,"abstract":"We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M ⊂ E13, so that the curve becomes a K-type spacelike slant helix with K ∈ {1,2,3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"2016 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86294265","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.17
M. Düldül, Merih Özçetin
The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.
{"title":"Intersection curve of two parametric surfaces in Euclidean n-space","authors":"M. Düldül, Merih Özçetin","doi":"10.12697/acutm.2021.25.17","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.17","url":null,"abstract":"The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"97 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85174498","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.13
S. Yildiz
In the present paper, an interesting type of convergence named ideal relative uniform convergence for double sequences of functions has been introduced for the first time. Then, the Korovkin type approximation theorem via this new type of convergence has been proved. An example to show that the new type of convergence is stronger than the convergence considered before has been given. Finally, the rate of I2-relative uniform convergence has been computed.
{"title":"I_2-Relative uniform convergence and Korovkin type approximation","authors":"S. Yildiz","doi":"10.12697/acutm.2021.25.13","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.13","url":null,"abstract":"In the present paper, an interesting type of convergence named ideal relative uniform convergence for double sequences of functions has been introduced for the first time. Then, the Korovkin type approximation theorem via this new type of convergence has been proved. An example to show that the new type of convergence is stronger than the convergence considered before has been given. Finally, the rate of I2-relative uniform convergence has been computed.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"34 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87410218","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.21
A. Sofo
An investigation into a family of definite integrals containing log-polylog functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals and may be represented as a BBP-type formula. In a special case we prove that the corresponding log integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function.
{"title":"Some BBP-type series for polylog integrals","authors":"A. Sofo","doi":"10.12697/acutm.2021.25.21","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.21","url":null,"abstract":"An investigation into a family of definite integrals containing log-polylog functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals and may be represented as a BBP-type formula. In a special case we prove that the corresponding log integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"7 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86521000","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.16
S. Haslett, J. Isotalo, S. Puntanen
In this article we consider the partitioned fixed linear model F : y = X1β1 + X2β2 + ε" and the corresponding mixed model M : y =X1β1+X2u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β1 in the fixed model F remains BLUE in the mixed model M . In this paper we extend the results concerning further equalities arising from models F and M.
本文考虑了分块固定线性模型F: y =X1β1+ X2β2 + ε”和相应的混合模型M: y =X1β1+X2u+ ε，其中ε为随机误差向量，u为随机效应向量。2006年，Isotalo, M¨ols和Puntanen发现了固定模型F中β1的可估计参数函数的最佳线性无偏估计量(BLUE)的任意表示在混合模型M中保持BLUE的条件。本文推广了由模型F和M导出的进一步等式的结果。
{"title":"Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model","authors":"S. Haslett, J. Isotalo, S. Puntanen","doi":"10.12697/acutm.2021.25.16","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.16","url":null,"abstract":"In this article we consider the partitioned fixed linear model F : y = X1β1 + X2β2 + ε\" and the corresponding mixed model M : y =X1β1+X2u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β1 in the fixed model F remains BLUE in the mixed model M . In this paper we extend the results concerning further equalities arising from models F and M.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"21 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87879955","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.15
H. Arif, J. Lellep
The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.
{"title":"Stability of nanobeams and nanoplates with defects","authors":"H. Arif, J. Lellep","doi":"10.12697/acutm.2021.25.15","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.15","url":null,"abstract":"The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"40 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89462980","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.20
B. Roy
In this paper, a new class called (µ, λ)θ -irresolute functions has been defined with the notion of generalized topology. We obtain some characterizations of such functions and some relations between similar types of functions are established. Some basic properties of such functions are also discussed. Such functions unify different types of weakly irresolute functions by T. Noiri.
{"title":"A unified theory for irresolute functions","authors":"B. Roy","doi":"10.12697/acutm.2021.25.20","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.20","url":null,"abstract":"In this paper, a new class called (µ, λ)θ -irresolute functions has been defined with the notion of generalized topology. We obtain some characterizations of such functions and some relations between similar types of functions are established. Some basic properties of such functions are also discussed. Such functions unify different types of weakly irresolute functions by T. Noiri.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"92 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79356644","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 study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation D : A ↦ ( A/J_A )∗ if D∗∗(A∗∗) ⊆ WAP (A/J_A ), then weak module amenability of A∗∗ implies that of A. Also we prove that under certain conditions for the module derivation D, if A∗∗ is weak module amenable then A is also weak module amenable.
{"title":"Weak module amenability for the second dual of a Banach algebra","authors":"Shabani Soltanmoradi, Davood Ebrahimi Bagha, Pourbahri Rahpeyma","doi":"10.12697/acutm.2021.25.19","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.19","url":null,"abstract":"In this paper we study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation D : A ↦ ( A/J_A )∗ if D∗∗(A∗∗) ⊆ WAP (A/J_A ), then weak module amenability of A∗∗ implies that of A. Also we prove that under certain conditions for the module derivation D, if A∗∗ is weak module amenable then A is also weak module amenable.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"23 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88393519","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 : 2021-08-20DOI: 10.12697/acutm.2022.26.05
J. Lellep, Shahid Mubasshar
The natural vibrations of curved nano-beams and nano-arches are studied. The nano-arches under consideration have piecewise constant thickness; these are weakened with stable cracks located at re-entrant corners of the steps. A method of determination of natural frequencies is developed making use of the method of weightless rotating spring. The aim of the paper is to assess the sensitivity of the eigenfrequencies on the geometrical and physical parameters of the nano-arch. The results of the calculations favourably compare with similar works of other researchers.
{"title":"Natural vibrations of curved nano-beams and nano-arches","authors":"J. Lellep, Shahid Mubasshar","doi":"10.12697/acutm.2022.26.05","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.05","url":null,"abstract":"The natural vibrations of curved nano-beams and nano-arches are studied. The nano-arches under consideration have piecewise constant thickness; these are weakened with stable cracks located at re-entrant corners of the steps. A method of determination of natural frequencies is developed making use of the method of weightless rotating spring. The aim of the paper is to assess the sensitivity of the eigenfrequencies on the geometrical and physical parameters of the nano-arch. The results of the calculations favourably compare with similar works of other researchers.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89891007","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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