Pub Date : 2023-08-03DOI: 10.15673/pigc.v16i2.2451
Mykola Kozlovskyi
Даються необхідні та достатні умови існування нарізно неперервної функції на добутку n компактних просторів із одноточковою множиною точок розриву.
{"title":"Одноточкові розриви нарізно неперервних функцій багатьох змінних на добутку компактних просторів","authors":"Mykola Kozlovskyi","doi":"10.15673/pigc.v16i2.2451","DOIUrl":"https://doi.org/10.15673/pigc.v16i2.2451","url":null,"abstract":"Даються необхідні та достатні умови існування нарізно неперервної функції на добутку n компактних просторів із одноточковою множиною точок розриву.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81440694","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 : 2023-08-03DOI: 10.15673/pigc.v16i2.2439
J. Hernández
It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups with open shifts are topological groups and to give a sufficient condition under which a locally compact monothetic topological semigroup is a compact topological group.
{"title":"Pseudocompact and precompact topological subsemigroups of topological groups","authors":"J. Hernández","doi":"10.15673/pigc.v16i2.2439","DOIUrl":"https://doi.org/10.15673/pigc.v16i2.2439","url":null,"abstract":"It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups with open shifts are topological groups and to give a sufficient condition under which a locally compact monothetic topological semigroup is a compact topological group.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90247921","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 : 2023-06-16DOI: 10.15673/tmgc.v16i1.2400
S. Gryshchuk
New representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra are found.
利用双调和代数中的单基因函数，给出了实系数lam系统解的新表示。
{"title":"Representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra","authors":"S. Gryshchuk","doi":"10.15673/tmgc.v16i1.2400","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2400","url":null,"abstract":"New representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra are found.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74563210","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 : 2023-06-16DOI: 10.15673/tmgc.v16i1.2450
Andriy Leonidovych Targonskiy
In the geometric theory of functions of a complex variable, the well-known direction is relatedIn the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work
{"title":"Extreme problem for a mosaic system of points on the open sets and nonoverlapping domains","authors":"Andriy Leonidovych Targonskiy","doi":"10.15673/tmgc.v16i1.2450","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2450","url":null,"abstract":"In the geometric theory of functions of a complex variable, the well-known direction is relatedIn the geometric theory of functions of a complex variable, the well-known direction is related to the estimates of the products of the inner radii of pairwise nonoverlapping domains. This direction is called extreme problems in classes of pairwise nonoverlapping domains. One of the problems of this type is considered in the present work","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86651789","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 : 2023-05-04DOI: 10.15673/tmgc.v16i1.2387
I. Denega, Yaroslav V. Zabolotnyi
In the paper we give a brief overview of the O. Bakhtin' scientific results
本文简要概述了巴赫金的科学成果
{"title":"A.K. Bakhtin. Scientific legacy","authors":"I. Denega, Yaroslav V. Zabolotnyi","doi":"10.15673/tmgc.v16i1.2387","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2387","url":null,"abstract":"In the paper we give a brief overview of the O. Bakhtin' scientific results","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74594937","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 : 2023-05-04DOI: 10.15673/tmgc.v16i1.2440
Тетяна Осіпчук, Максим Володимирович Ткачук
The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not intersecting the given set. A closed set is called weakly 1-convex if it is approximated from the outside by a family of open weakly 1-convex sets. A point of the complement of a set to the whole plane is called a 1-nonconvexity point of the set if any straight passing through the point intersects the set. It is proved that if an open, weakly 1-convex set has a non-empty set of 1-nonconvexity points, then the latter set is also open. It is also shown that the non-empty interior of a closed, weakly 1-convex set in the plane is weakly 1-convex.
{"title":"On weakly 1-convex sets in the plane","authors":"Тетяна Осіпчук, Максим Володимирович Ткачук","doi":"10.15673/tmgc.v16i1.2440","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2440","url":null,"abstract":"The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not intersecting the given set. A closed set is called weakly 1-convex if it is approximated from the outside by a family of open weakly 1-convex sets. A point of the complement of a set to the whole plane is called a 1-nonconvexity point of the set if any straight passing through the point intersects the set. It is proved that if an open, weakly 1-convex set has a non-empty set of 1-nonconvexity points, then the latter set is also open. It is also shown that the non-empty interior of a closed, weakly 1-convex set in the plane is weakly 1-convex.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81652860","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 : 2023-05-04DOI: 10.15673/tmgc.v16i1.2385
S. Plaksa
We consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces.Monogenic functions are understood as continuous and differentiable in the sense of G^ateaux functions.We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.
{"title":"Monogenic functions and harmonic vectors","authors":"S. Plaksa","doi":"10.15673/tmgc.v16i1.2385","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2385","url":null,"abstract":"We consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces.Monogenic functions are understood as continuous and differentiable in the sense of G^ateaux functions.We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91170256","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 : 2023-05-04DOI: 10.15673/tmgc.v16i1.2394
B. Klishchuk, R. Salimov, M. Stefanchuk
We study the asymptotic behavior at infinity of ring Q-homeomorphisms with respect to p-modulus for p>n
研究了p>n时环q模在无穷远处的渐近性
{"title":"On the asymptotic behavior at infinity of one mapping class","authors":"B. Klishchuk, R. Salimov, M. Stefanchuk","doi":"10.15673/tmgc.v16i1.2394","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2394","url":null,"abstract":"We study the asymptotic behavior at infinity of ring Q-homeomorphisms with respect to p-modulus for p>n","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80723082","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 : 2023-05-04DOI: 10.15673/tmgc.v16i1.2421
Vitalii Shpakivskyi
In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.
{"title":"σ-monogenic functions in commutative algebras","authors":"Vitalii Shpakivskyi","doi":"10.15673/tmgc.v16i1.2421","DOIUrl":"https://doi.org/10.15673/tmgc.v16i1.2421","url":null,"abstract":"In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136375650","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 : 2023-03-04DOI: 10.15673/tmgc.v15i3-4.2430
V. Kiosak, Olexandr Lesechko, O. Latysh
The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.
{"title":"On geodesic mappings of symmetric pairs","authors":"V. Kiosak, Olexandr Lesechko, O. Latysh","doi":"10.15673/tmgc.v15i3-4.2430","DOIUrl":"https://doi.org/10.15673/tmgc.v15i3-4.2430","url":null,"abstract":"The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86000110","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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