Pub Date : 2024-06-03DOI: 10.12697/acutm.2024.28.02
A. Mürk, J. Lellep
The dynamic plastic response of circular plates to asymmetric loading is studied. An approximate theoretical procedure is developed for the evaluation of asymmetrical residual de ections. The solution technique is based on the equality of the internal dissipation and the external work, respectively. Maximal residual de ections are defined for plates of piece-wise constant thickness.
{"title":"Asymmetric dynamic plastic response of stepped plates","authors":"A. Mürk, J. Lellep","doi":"10.12697/acutm.2024.28.02","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.02","url":null,"abstract":"The dynamic plastic response of circular plates to asymmetric loading is studied. An approximate theoretical procedure is developed for the evaluation of asymmetrical residual de ections. The solution technique is based on the equality of the internal dissipation and the external work, respectively. Maximal residual de ections are defined for plates of piece-wise constant thickness.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141271970","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.03
K. Eftekharinasab, Ruslana Horidko
We generalize the Nagumo–Brezis theorem to the category of MCk-Fréchet manifolds. Then we will apply the obtained result to locate a critical value of a real-valued mapping over these manifolds.
{"title":"On a generalization of the Nagumo–Brezis theorem","authors":"K. Eftekharinasab, Ruslana Horidko","doi":"10.12697/acutm.2024.28.03","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.03","url":null,"abstract":"We generalize the Nagumo–Brezis theorem to the category of MCk-Fréchet manifolds. Then we will apply the obtained result to locate a critical value of a real-valued mapping over these manifolds.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141271245","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.01
M. Berberler
Graph energy is a measurement of determining the structural information content of graphs. The first Zagreb index can be handled with its connection to graph energy. In this paper, a novel and significant application of the first Zagreb index to composite graphs based on fractal graphs is revealed, and by the relation between quasi-Laplacian energy and the vertex degrees of a graph, we derive closed-form formulas for the quasi-Laplacian energy of fractal graphs or namely R-graphs, R-vertex and edge join, R-vertex and edge corona, R-vertex and edge neighborhood graphs in terms of the corresponding energy, the first Zagreb indices, number of vertices and edges of the underlying graphs.
图能量是确定图的结构信息含量的一种测量方法。第一萨格勒布指数可以通过与图能的联系来处理。本文揭示了第一萨格勒布指数在基于分形图的复合图中的新颖而重要的应用，以及准拉普拉奇能量与图的顶点度之间的关系、我们推导出了分形图（即 R 图、R 顶点和边连接图、R 顶点和边日冕图、R 顶点和边邻接图）的准拉普拉斯能量的闭式公式，这些公式与底层图的相应能量、第一萨格勒布指数、顶点数和边数有关。
{"title":"Quasi-Laplacian energy of fractal graphs","authors":"M. Berberler","doi":"10.12697/acutm.2024.28.01","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.01","url":null,"abstract":"Graph energy is a measurement of determining the structural information content of graphs. The first Zagreb index can be handled with its connection to graph energy. In this paper, a novel and significant application of the first Zagreb index to composite graphs based on fractal graphs is revealed, and by the relation between quasi-Laplacian energy and the vertex degrees of a graph, we derive closed-form formulas for the quasi-Laplacian energy of fractal graphs or namely R-graphs, R-vertex and edge join, R-vertex and edge corona, R-vertex and edge neighborhood graphs in terms of the corresponding energy, the first Zagreb indices, number of vertices and edges of the underlying graphs.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141272236","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.09
N. Vaysfeld, Z. Zhuravlova
The exact solution of the poroelastic axisymmetric problem for a layer with a cylinderical hole is constructed under assumptions of Biot's model. The calculations provided by derived explicit formulas for full stress and pore pressure allow to state some important dependencies between the poroelastic stress state of the layer and type of poroelastic materials, loading types and height of the layer.
{"title":"The poroelastic layer with an axisymmetric cylindrical hole under different types of loading","authors":"N. Vaysfeld, Z. Zhuravlova","doi":"10.12697/acutm.2024.28.09","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.09","url":null,"abstract":"The exact solution of the poroelastic axisymmetric problem for a layer with a cylinderical hole is constructed under assumptions of Biot's model. The calculations provided by derived explicit formulas for full stress and pore pressure allow to state some important dependencies between the poroelastic stress state of the layer and type of poroelastic materials, loading types and height of the layer.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141271183","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.08
Ljubov Jaanuska, Helle Hein
The present research focuses on establishing the stiffness parameter of elastic springs placed at the ends of non-uniform rods. The governing equation for the longitudinal vibrations of the rod was solved using the Haar wavelet integration method. The calculated natural frequency parameters closely aligned with those available in the literature. The normalised values of the first ten natural frequency parameters were used in the feature vector to predict the stiffness parameter of the springs. A feedforward neural network with two hidden layers made accurate predictions when the range of each natural frequency parameterwithin its domain exceeded one. The insights garnered from this study contribute to the design, optimisation and assessment of diverse engineering applications.
{"title":"Stiffness parameter prediction for elastic supports of non-uniform rods","authors":"Ljubov Jaanuska, Helle Hein","doi":"10.12697/acutm.2024.28.08","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.08","url":null,"abstract":"\u0000\u0000\u0000The present research focuses on establishing the stiffness parameter of elastic springs placed at the ends of non-uniform rods. The governing equation for the longitudinal vibrations of the rod was solved using the Haar wavelet integration method. The calculated natural frequency parameters closely aligned with those available in the literature. The normalised values of the first ten natural frequency parameters were used in the feature vector to predict the stiffness parameter of the springs. A feedforward neural network with two hidden layers made accurate predictions when the range of each natural frequency parameterwithin its domain exceeded one. The insights garnered from this study contribute to the design, optimisation and assessment of diverse engineering applications.\u0000\u0000\u0000","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141272118","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.10
Jaagup Kirme
We prove a refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators. Refinements of a Bishop–Phelps–Bollobás type theorem for Asplund operators with values in spaces C0(L) by the same authors, and an extension of this theorem for Asplund operators with values in uniform algebras by Cascales, Guirao, and Kadets, follow.
{"title":"refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators","authors":"Jaagup Kirme","doi":"10.12697/acutm.2024.28.10","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.10","url":null,"abstract":"We prove a refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators. Refinements of a Bishop–Phelps–Bollobás type theorem for Asplund operators with values in spaces C0(L) by the same authors, and an extension of this theorem for Asplund operators with values in uniform algebras by Cascales, Guirao, and Kadets, follow.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141271339","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.07
Elmostafa Azizi
In this article, we introduce a notion of compatibility between two Endo-Lie algebras defined on the same linear space. Compatibility means that any linear combination of the two structures always induces a new Endo-Lie algebras structure. In this case of compatibility, we show that the notions of bialgebras, standard Manin triples and matched pairs are equivalent. We find this equivalence for the case of compatible Lie algebras since this is a particular case of compatible Endo-Lie algebras.
{"title":"Equivalent Notions in the context of compatible Endo-Lie Algebras","authors":"Elmostafa Azizi","doi":"10.12697/acutm.2024.28.07","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.07","url":null,"abstract":"In this article, we introduce a notion of compatibility between two Endo-Lie algebras defined on the same linear space. Compatibility means that any linear combination of the two structures always induces a new Endo-Lie algebras structure. In this case of compatibility, we show that the notions of bialgebras, standard Manin triples and matched pairs are equivalent. We find this equivalence for the case of compatible Lie algebras since this is a particular case of compatible Endo-Lie algebras.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141269846","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}
Statistical Killing vector field is introduced and Hopf hypersurfaces of complex space forms with the condition of being structural statistical Killing vector field are studied. It is shown that these hypersurfaces have at most three distinct constant principal curvatures.
{"title":"Statistical Killing vector fields on the Hopf hypersurfaces in the complex space forms","authors":"Esmaiel Abedi, Nasibeh Moghanian, Mohamad Ilmakchi, Najma Mosadegh Kordmahaleh","doi":"10.12697/acutm.2024.28.05","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.05","url":null,"abstract":"Statistical Killing vector field is introduced and Hopf hypersurfaces of complex space forms with the condition of being structural statistical Killing vector field are studied. It is shown that these hypersurfaces have at most three distinct constant principal curvatures.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141272630","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 : 2024-06-03DOI: 10.12697/acutm.2024.28.06
S. Pahan
The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton.
本文的主要目的是研究在几乎伪对称洛伦兹凯勒时空流形中，当一些不同的曲率张量完全消失时，h-几乎共形η-里奇-布尔基尼孤子。我们还探索了在不同的完美流体（如硬物质、尘埃流体、暗流体和辐射流体）中，h-几乎共形的里奇-布尔吉尼孤子是稳定、收缩还是膨胀的条件。我们观察到，在某些特定条件下，具有 h 几乎保角 η-里奇-布尔吉尼孤子的完美流体时空是一个具有恒定黎曼曲率的流形。我们还进一步完善了在具有环形矢量场ξ的完美uid时空中与梯度为h的近保角η-Ricci-Bourguignon孤子有关的势函数的分类。最后，我们建立了一个 h-almost conformal η-Ricci-Bourguignon 孤子的例子。
{"title":"On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime","authors":"S. Pahan","doi":"10.12697/acutm.2024.28.06","DOIUrl":"https://doi.org/10.12697/acutm.2024.28.06","url":null,"abstract":"The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141272949","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 : 2023-12-01DOI: 10.12697/acutm.2023.27.11
Tülay Yagmur
In this paper, we introduce and study a new hybrid number sequence with Horadam numbers and a finite operator, called Horadam finite operator hybrid numbers. We derive recurrence relation, Binet-like formula, ordinary generating function, exponential generating function, Poisson generating function, and summation formula for Horadam finite operator hybrid numbers. Moreover, we give matrix representation and Cassini's identities for these numbers.
{"title":"On Horadam finite operator hybrid numbers","authors":"Tülay Yagmur","doi":"10.12697/acutm.2023.27.11","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.11","url":null,"abstract":"In this paper, we introduce and study a new hybrid number sequence with Horadam numbers and a finite operator, called Horadam finite operator hybrid numbers. We derive recurrence relation, Binet-like formula, ordinary generating function, exponential generating function, Poisson generating function, and summation formula for Horadam finite operator hybrid numbers. Moreover, we give matrix representation and Cassini's identities for these numbers.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138611440","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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