Y.L. Tenkeu Jeufack, E.R. Alomo Temgoua, O. Heubo-Kwegna
In this paper, we introduce the notions of radical filters and extended filters of Intuitionistic Linear algebras (IL-algebras for short) and give some of their properties. The notion of closure operation on an IL-algebra is also introduced as well as the study of some of their main properties. The radical of filters and extended filters are examples of closure operations among several others provided. The class of stable closure operations on an IL-algebra L is used to study the unifying properties of some subclasses of the lattice of filters of L. In particular, we obtain that for a stable closure operation c on an IL-algebra, the collection of c-closed elements of its lattice of filters forms a complete Heyting algebra. Hyperarchimedean IL-algebras are also characterized using closure operations. It is shown that the image of a semi-prime closure operation on an IL-algebra is isomorphic to a quotient IL-algebra. Some properties of the quotients induced by closure operations on an IL-algebra are explored.
本文介绍了直觉线性代数（简称 IL-代数）的基滤波器和扩展滤波器的概念，并给出了它们的一些性质。我们还介绍了 IL-algebra 上的闭包运算概念，以及对它们的一些主要性质的研究。滤波器的基和扩展滤波器是闭包运算的例子，还提供了其他一些例子。特别是，我们得到，对于 IL 代数上的稳定闭包运算 c，其滤波器晶格的 c 闭元素集合构成一个完整的海廷代数。我们还利用闭包运算描述了超拱IL代数的特征。研究表明，IL-代数上半prime闭包运算的映像与商IL-代数同构。还探讨了闭包运算在 IL 代数上引起的商的一些性质。
{"title":"Closure Operations on Intuitionistic Linear Algebras","authors":"Y.L. Tenkeu Jeufack, E.R. Alomo Temgoua, O. Heubo-Kwegna","doi":"10.2478/amsil-2024-0007","DOIUrl":"https://doi.org/10.2478/amsil-2024-0007","url":null,"abstract":"\u0000 In this paper, we introduce the notions of radical filters and extended filters of Intuitionistic Linear algebras (IL-algebras for short) and give some of their properties. The notion of closure operation on an IL-algebra is also introduced as well as the study of some of their main properties. The radical of filters and extended filters are examples of closure operations among several others provided. The class of stable closure operations on an IL-algebra L is used to study the unifying properties of some subclasses of the lattice of filters of L. In particular, we obtain that for a stable closure operation c on an IL-algebra, the collection of c-closed elements of its lattice of filters forms a complete Heyting algebra. Hyperarchimedean IL-algebras are also characterized using closure operations. It is shown that the image of a semi-prime closure operation on an IL-algebra is isomorphic to a quotient IL-algebra. Some properties of the quotients induced by closure operations on an IL-algebra are explored.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"9 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140225401","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}
Motivated by the Szostok problem on functions with monotonic differences (2005, 2007), we consider a-Wright convex functions as a generalization of Wright convex functions. An application of these results to obtain new proofs of known results as well as new results is presented.
{"title":"On Functions with Monotonic Differences","authors":"T. Rajba","doi":"10.2478/amsil-2024-0009","DOIUrl":"https://doi.org/10.2478/amsil-2024-0009","url":null,"abstract":"\u0000 Motivated by the Szostok problem on functions with monotonic differences (2005, 2007), we consider a-Wright convex functions as a generalization of Wright convex functions. An application of these results to obtain new proofs of known results as well as new results is presented.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"45 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140224767","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}
{"title":"On a Certain Polish Mathematician: A Brief Summary of Scientific Research and Achievements of Kazimierz Nikodem, Professor of Mathematics","authors":"Mirosław Adamek","doi":"10.2478/amsil-2024-0005","DOIUrl":"https://doi.org/10.2478/amsil-2024-0005","url":null,"abstract":"","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"5 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140225650","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 analyze in our paper questions of the theory of relativity. We approach this theory from the point of view of velocities and their composition. This is where the functional equations appear. Solving them leads to a world where velocities are bounded from above, the upper bound being exactly the “speed of light”.
{"title":"Speed of Light or Composition of Velocities","authors":"Maciej Sablik","doi":"10.2478/amsil-2024-0008","DOIUrl":"https://doi.org/10.2478/amsil-2024-0008","url":null,"abstract":"\u0000 We analyze in our paper questions of the theory of relativity. We approach this theory from the point of view of velocities and their composition. This is where the functional equations appear. Solving them leads to a world where velocities are bounded from above, the upper bound being exactly the “speed of light”.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"19 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140226133","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 consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.
我们考虑斯特克洛夫型算子序列和相关函数方程。对于合适的序列，我们建立了渐近公式。
{"title":"Steklov Type Operators and Functional Equations","authors":"Gabriela Motronea, D. Popa, I. Raşa","doi":"10.2478/amsil-2024-0006","DOIUrl":"https://doi.org/10.2478/amsil-2024-0006","url":null,"abstract":"\u0000 We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"17 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139776362","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 consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.
我们考虑斯特克洛夫型算子序列和相关函数方程。对于合适的序列，我们建立了渐近公式。
{"title":"Steklov Type Operators and Functional Equations","authors":"Gabriela Motronea, D. Popa, I. Raşa","doi":"10.2478/amsil-2024-0006","DOIUrl":"https://doi.org/10.2478/amsil-2024-0006","url":null,"abstract":"\u0000 We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"217 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835841","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 study, the resolvent of the impulsive singular Hahn–Sturm– Liouville operator is considered. An integral representation for the resolvent of this operator is obtained.
{"title":"The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators","authors":"B. Allahverdiev, H. Tuna, Hamlet A. Isayev","doi":"10.2478/amsil-2024-0001","DOIUrl":"https://doi.org/10.2478/amsil-2024-0001","url":null,"abstract":"\u0000 In this study, the resolvent of the impulsive singular Hahn–Sturm– Liouville operator is considered. An integral representation for the resolvent of this operator is obtained.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"119 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139615206","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}
J. Chimpanzo, M.V. Otero-Espinar, A. Borges, P. Vasco, P. Catarino
Abstract A new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
摘要 介绍了一种新的二维共轭数和卢卡斯共轭数。研究了这些新的二维序列所满足的一些性质和同一性。
{"title":"Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers","authors":"J. Chimpanzo, M.V. Otero-Espinar, A. Borges, P. Vasco, P. Catarino","doi":"10.2478/amsil-2023-0022","DOIUrl":"https://doi.org/10.2478/amsil-2023-0022","url":null,"abstract":"Abstract A new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139211948","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}
Abstract In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [12], [13]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.
{"title":"On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order","authors":"Abhijit Banerjee, Jhuma Sarkar","doi":"10.2478/amsil-2023-0018","DOIUrl":"https://doi.org/10.2478/amsil-2023-0018","url":null,"abstract":"Abstract In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [12], [13]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139250434","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}
Abstract We present Hermite–Hadamard–Fejér type inequalities for strongly MφMψ -convex functions. Some refinements of them and bounds for the integral mean of the product of two functions are also obtained.
{"title":"Strongly MφMψ -Convex Functions, The Hermite–Hadamard–Fejér Inequality and Related Results","authors":"M. Bombardelli, S. Varošanec","doi":"10.2478/amsil-2023-0019","DOIUrl":"https://doi.org/10.2478/amsil-2023-0019","url":null,"abstract":"Abstract We present Hermite–Hadamard–Fejér type inequalities for strongly MφMψ -convex functions. Some refinements of them and bounds for the integral mean of the product of two functions are also obtained.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248722","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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