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Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures 与monge - ampantere结构相关的伪黎曼和黑森几何
IF 0.6
Archivum Mathematicum Pub Date : 2023-05-05 DOI: 10.5817/AM2022-5-329
Radek Such'anek, Stanislav Hronek
{"title":"Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures","authors":"Radek Such'anek, Stanislav Hronek","doi":"10.5817/AM2022-5-329","DOIUrl":"https://doi.org/10.5817/AM2022-5-329","url":null,"abstract":"We study properties of pseudo-Riemannian metrics corresponding to Monge-Amp`ere structures on four-dimensional $T^*M$. We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Pl\"ucker embedding equation. We also focus on pullbacks of the pseudo-metrics on two-dimensional $M$ and describe the corresponding Hessian structures.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"131 5 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81147534","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}
引用次数: 1
Some properties of algebras of real-valued measurable functions 实值可测函数代数的一些性质
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-5-383
A. Estaji, Ahmad Mahmoudi Darghadam
{"title":"Some properties of algebras of real-valued measurable functions","authors":"A. Estaji, Ahmad Mahmoudi Darghadam","doi":"10.5817/am2023-5-383","DOIUrl":"https://doi.org/10.5817/am2023-5-383","url":null,"abstract":". Let M ( X, A ) ( M ∗ ( X, A )) be the f -ring of all (bounded) real-mea-surable functions on a T -measurable space ( X, A ), let M K ( X, A ) be the family of all f ∈ M ( X, A ) such that coz( f ) is compact, and let M ∞ ( X, A ) be all f ∈ M ( X, A ) that { x ∈ X : | f ( x ) | ≥ 1 n } is compact for any n ∈ N . We introduce realcompact subrings of M ( X, A ), we show that M ∗ ( X, A ) is a realcompact subring of M ( X, A ), and also M ( X, A ) is a realcompact if and only if ( X, A ) is a compact measurable space. For every nonzero real Riesz map ϕ : M ( X, A ) → R , we prove that there is an element x 0 ∈ X such that ϕ ( f ) = f ( x 0 ) for every f ∈ M ( X, A ) if ( X, A ) is a compact measurable space. We confirm that M ∞ ( X, A ) is equal to the intersection of all free maximal ideals of M ∗ ( X, A ), and also M K ( X, A ) is equal to the intersection of all free ideals of M ( X, A ) (or M ∗ ( X, A )). We show that M ∞ ( X, A ) and M K ( X, A ) do not have free ideal.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"66 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88780151","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}
引用次数: 0
Equivalence of ill-posed dynamical systems 不适定动力系统的等价性
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-1-133
T. Suda
{"title":"Equivalence of ill-posed dynamical systems","authors":"T. Suda","doi":"10.5817/am2023-1-133","DOIUrl":"https://doi.org/10.5817/am2023-1-133","url":null,"abstract":". The problem of topological classification is fundamental in the study of dynamical systems. However, when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence. For example, when a system has trajectories distinguished only by parametrization, we cannot apply the usual definition of equivalence based on the phase space, which presupposes the uniqueness of trajectories. In this study, we formulate a notion of “topological equivalence” using the axiomatic theory of topological dynamics proposed by Yorke [7], where dynamical systems are considered to be shift-invariant subsets of a space of partial maps. In particular, we study how the type of problems can be regarded as invariants under the morphisms between systems and how the usual definition of topological equivalence can be generalized. This article is intended to also serve as a brief introduction to the axiomatic theory of ordinary differential equations (or topological dynamics) based on the formalism presented in [6].","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80885356","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}
引用次数: 1
A Frankel type theorem for CR submanifolds of Sasakian manifolds sasaki流形CR子流形的Frankel型定理
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-5-369
D. Di Pinto, A. Lotta
{"title":"A Frankel type theorem for CR submanifolds of Sasakian manifolds","authors":"D. Di Pinto, A. Lotta","doi":"10.5817/am2023-5-369","DOIUrl":"https://doi.org/10.5817/am2023-5-369","url":null,"abstract":". We prove a Frankel type theorem for CR submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about CR submanifolds of Sasakian space forms.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"54 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84732770","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}
引用次数: 0
Numerical approaches to the modelling of quasi-brittle crack propagation 准脆性裂纹扩展模拟的数值方法
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-3-295
J. Vala
{"title":"Numerical approaches to the modelling of quasi-brittle crack propagation","authors":"J. Vala","doi":"10.5817/am2023-3-295","DOIUrl":"https://doi.org/10.5817/am2023-3-295","url":null,"abstract":". Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus, due to significance of such materials in the design and construction of buildings, semi-heuristic computational models must be taken into consideration. These models generate mathematical problems, whose solvability is not transparent frequently, which limits the credibility of all results of ad hoc designed numerical simulations. In this short paper such phenomena are demonstrated on a simple model problem, covering both micro-and macro-cracking, with references to needful generalizations and more realistic computational settings.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89822327","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}
引用次数: 0
On the diophantine equation $x^2+2^a3^b73^c=y^n $ 在丢番图方程上，x^2+2^a3^b73^c=y^n
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-5-411
M. Alan, Mustafa Aydin
{"title":"On the diophantine equation $x^2+2^a3^b73^c=y^n $","authors":"M. Alan, Mustafa Aydin","doi":"10.5817/am2023-5-411","DOIUrl":"https://doi.org/10.5817/am2023-5-411","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"76 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72684716","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}
引用次数: 0
Delay-dependent stability conditions for fundamental characteristic functions 基本特征函数的时滞相关稳定性条件
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-1-77
H. Matsunaga
{"title":"Delay-dependent stability conditions for fundamental characteristic functions","authors":"H. Matsunaga","doi":"10.5817/am2023-1-77","DOIUrl":"https://doi.org/10.5817/am2023-1-77","url":null,"abstract":". This paper is devoted to the investigation on the stability for two characteristic functions f 1 ( z ) = z 2 + pe − zτ + q and f 2 ( z ) = z 2 + pze − zτ + q , where p and q are real numbers and τ > 0. The obtained theorems describe the explicit stability dependence on the changing delay τ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84410249","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}
引用次数: 0
A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type 拟线性Lane-Emden型方程径向正解的先验界
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-2-155
Soohyun Bae
{"title":"A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type","authors":"Soohyun Bae","doi":"10.5817/am2023-2-155","DOIUrl":"https://doi.org/10.5817/am2023-2-155","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83116944","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}
引用次数: 0
Finite-time blow-up in a two-species chemotaxis-competition model with single production 单产两物种趋化竞争模型的有限时间爆炸
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-2-215
M. Mizukami, Yuya Tanaka
{"title":"Finite-time blow-up in a two-species chemotaxis-competition model with single production","authors":"M. Mizukami, Yuya Tanaka","doi":"10.5817/am2023-2-215","DOIUrl":"https://doi.org/10.5817/am2023-2-215","url":null,"abstract":". This paper is concerned with blow-up of solutions to a two-species chemotaxis-competition model with production from only one species. In previous papers there are a lot of studies on boundedness for a two-species chemotaxis-competition model with productions from both two species. On the other hand, finite-time blow-up was recently obtained under smallness conditions for competitive effects. Now, in the biological view, the production term seems to promote blow-up phenomena; this implies that the lack of the production term makes the solution likely to be bounded. Thus, it is expected that there exists a solution of the system with single production such that the species which does not produce the chemical substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that this conjecture is true.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"159 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81727322","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}
引用次数: 1
Riccati matrix differential equation and the discrete order preserving property Riccati矩阵微分方程及其离散阶保持性质
IF 0.6
Archivum Mathematicum Pub Date : 2023-01-01 DOI: 10.5817/am2023-1-125
Viera Štoudková Růžičková
{"title":"Riccati matrix differential equation and the discrete order preserving property","authors":"Viera Štoudková Růžičková","doi":"10.5817/am2023-1-125","DOIUrl":"https://doi.org/10.5817/am2023-1-125","url":null,"abstract":"","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"PP 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84299192","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}
引用次数: 0
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