Pub Date : 2021-12-31DOI: 10.2478/9788366675360-008
G. Filipuk, T. Kecker, F. Zullo
. In this paper we study a nonlinear di ↵ erential equation related to a non-homogeneous Airy equation. The linear equation has two families of solutions. We apply a procedure of resolution of points of indeterminacy to a system of first order di ↵ erential equations equivalent to the nonlinear equation and study how the corresponding families of solutions are transformed
{"title":"ON A REGULARISATION OF A NONLINEAR DIFFERENTIAL EQUATION RELATED TO THE NON-HOMOGENEOUS AIRY EQUATION","authors":"G. Filipuk, T. Kecker, F. Zullo","doi":"10.2478/9788366675360-008","DOIUrl":"https://doi.org/10.2478/9788366675360-008","url":null,"abstract":". In this paper we study a nonlinear di ↵ erential equation related to a non-homogeneous Airy equation. The linear equation has two families of solutions. We apply a procedure of resolution of points of indeterminacy to a system of first order di ↵ erential equations equivalent to the nonlinear equation and study how the corresponding families of solutions are transformed","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"214 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122379654","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 : 2021-12-31DOI: 10.2478/9788366675360-014
A. Lind, E. Porten
{"title":"DIRECTIONAL DENSITY OF POLYNOMIAL HULLS AT SINGULARITIES","authors":"A. Lind, E. Porten","doi":"10.2478/9788366675360-014","DOIUrl":"https://doi.org/10.2478/9788366675360-014","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115786723","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 : 2021-12-31DOI: 10.2478/9788366675360-017
A. Pietiurenko
{"title":"SOLVING MATH PROBLEMS USING THE AREA METHOD","authors":"A. Pietiurenko","doi":"10.2478/9788366675360-017","DOIUrl":"https://doi.org/10.2478/9788366675360-017","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128077727","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 : 2021-12-31DOI: 10.2478/9788366675360-021
P. Walczak
{"title":"CANAL SURFACES AND FOLIATIONS – A SURVEY","authors":"P. Walczak","doi":"10.2478/9788366675360-021","DOIUrl":"https://doi.org/10.2478/9788366675360-021","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131798986","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 : 2021-12-31DOI: 10.2478/9788366675360-019
V. Rovenský
{"title":"ON A RIEMANNIAN MANIFOLD WITH TWO ORTHOGONAL DISTRIBUTIONS","authors":"V. Rovenský","doi":"10.2478/9788366675360-019","DOIUrl":"https://doi.org/10.2478/9788366675360-019","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130485316","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 : 2021-12-31DOI: 10.2478/9788366675360-013
K. Leśniak, N. Snigireva, F. Strobin
{"title":"A FRACTAL TRIANGLE ARISING IN THE AIMD DYNAMICS","authors":"K. Leśniak, N. Snigireva, F. Strobin","doi":"10.2478/9788366675360-013","DOIUrl":"https://doi.org/10.2478/9788366675360-013","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117161906","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 : 2021-12-31DOI: 10.2478/9788366675360-020
C. Schiebold
{"title":"ON THE 2-SOLITON ASYMPTOTICS FOR THE d x d-MATRIX KORTEWEG-DE VRIES EQUATION","authors":"C. Schiebold","doi":"10.2478/9788366675360-020","DOIUrl":"https://doi.org/10.2478/9788366675360-020","url":null,"abstract":"","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121548168","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 : 2021-11-15DOI: 10.2478/9788366675360-004
L. Barnsley, M. Barnsley
We introduce a method for constructing collections of subsets of $mathbb{R}^{n}$, using an iterated function system, a set $T,$ and a cost function. We refer to these collections as tilings. The special case where $T$ is the central open set of an iterated function system that obeys the open set condition is emphasized. The notion of the central open set associated with an iterated function system of similitudes, introduced in 2005 by Bandt, Hung, and Rao, is reviewed. A practical method for calculating pictures of central open sets is described. Some general properties and examples of the tilings are presented.
{"title":"CENTRAL OPEN SETS TILINGS","authors":"L. Barnsley, M. Barnsley","doi":"10.2478/9788366675360-004","DOIUrl":"https://doi.org/10.2478/9788366675360-004","url":null,"abstract":"We introduce a method for constructing collections of subsets of $mathbb{R}^{n}$, using an iterated function system, a set $T,$ and a cost function. We refer to these collections as tilings. The special case where $T$ is the central open set of an iterated function system that obeys the open set condition is emphasized. The notion of the central open set associated with an iterated function system of similitudes, introduced in 2005 by Bandt, Hung, and Rao, is reviewed. A practical method for calculating pictures of central open sets is described. Some general properties and examples of the tilings are presented.","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116734234","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 : 2021-05-14DOI: 10.2478/9788366675360-012
Daniel Luckhardt, Matt Insall
We generalize the concept of a norm on a vector space to one of a norm on a category. This provides a unified perspective on many specific matters in many different areas of mathematics like set theory, functional analysis, measure theory, topology, and metric space theory. We will especially address the two last areas in which the monotone-light factorization and, respectively, the Gromov-Hausdorff distance will naturally appear. In our formalization a Schr"oder-Bernstein property becomes an axiom of a norm which constitutes interesting properties of the categories in question. The proposed concept provides a convenient framework for metrizations.
{"title":"NORMS ON CATEGORIES AND ANALOGS OF THE SCHRÖDER-BERNSTEIN THEOREM","authors":"Daniel Luckhardt, Matt Insall","doi":"10.2478/9788366675360-012","DOIUrl":"https://doi.org/10.2478/9788366675360-012","url":null,"abstract":"We generalize the concept of a norm on a vector space to one of a norm on a category. This provides a unified perspective on many specific matters in many different areas of mathematics like set theory, functional analysis, measure theory, topology, and metric space theory. We will especially address the two last areas in which the monotone-light factorization and, respectively, the Gromov-Hausdorff distance will naturally appear. In our formalization a Schr\"oder-Bernstein property becomes an axiom of a norm which constitutes interesting properties of the categories in question. The proposed concept provides a convenient framework for metrizations.","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131674918","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 : 2021-04-29DOI: 10.2478/9788366675360-010
O. Gutik, Pavlo Khylynskyi
In the paper we study algebraic properties of the monoid IN ∞ of cofinite partial isometries of the set of positive integers N with the bounded finite noise j. For the monoids IN ∞ we prove counterparts of some classical results of Eberhart and Selden describing the closure of the bicyclic semigroup in a locally compact topological inverse semigroup. In particular we show that for any positive integer j every Hausdorff shift-continuous topology τ on IN ∞ is discrete and if IN g[j] ∞ is a proper dense subsemigroup of a Hausdorff semitopological semigroup S, then S IN ∞ is a closed ideal of S, and moreover if S is a topological inverse semigroup then S IN ∞ is a topological group. Also we describe the algebraic and topological structure of the closure of the monoid IN ∞ in a locally compact topological inverse semigroup.
{"title":"ON THE MONOID OF COFINITE PARTIAL ISOMETRIES OF N WITH A BOUNDED FINITE NOISE","authors":"O. Gutik, Pavlo Khylynskyi","doi":"10.2478/9788366675360-010","DOIUrl":"https://doi.org/10.2478/9788366675360-010","url":null,"abstract":"In the paper we study algebraic properties of the monoid IN ∞ of cofinite partial isometries of the set of positive integers N with the bounded finite noise j. For the monoids IN ∞ we prove counterparts of some classical results of Eberhart and Selden describing the closure of the bicyclic semigroup in a locally compact topological inverse semigroup. In particular we show that for any positive integer j every Hausdorff shift-continuous topology τ on IN ∞ is discrete and if IN g[j] ∞ is a proper dense subsemigroup of a Hausdorff semitopological semigroup S, then S IN ∞ is a closed ideal of S, and moreover if S is a topological inverse semigroup then S IN ∞ is a topological group. Also we describe the algebraic and topological structure of the closure of the monoid IN ∞ in a locally compact topological inverse semigroup.","PeriodicalId":265359,"journal":{"name":"Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121206848","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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