Pub Date : 2021-01-01DOI: 10.2478/aupcsm-2021-0006
M. Ślosarski
Abstract In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.
{"title":"Metrizable space of multivalued maps","authors":"M. Ślosarski","doi":"10.2478/aupcsm-2021-0006","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0006","url":null,"abstract":"Abstract In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"15 1","pages":"77 - 93"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89691752","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 : 2021-01-01DOI: 10.2478/aupcsm-2021-0002
Z. Malki, Farida Berhoun, A. Ouahab
Abstract We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.
{"title":"System of boundary random fractional differential equations via Hadamard derivative","authors":"Z. Malki, Farida Berhoun, A. Ouahab","doi":"10.2478/aupcsm-2021-0002","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0002","url":null,"abstract":"Abstract We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"3 1","pages":"17 - 41"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88794767","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 : 2021-01-01DOI: 10.2478/aupcsm-2021-0005
Slawomir Przybylo
Abstract We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.
{"title":"Equivalential algebras with conjunction on the regular elements","authors":"Slawomir Przybylo","doi":"10.2478/aupcsm-2021-0005","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0005","url":null,"abstract":"Abstract We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"7 1","pages":"63 - 75"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87298083","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 : 2021-01-01DOI: 10.2478/aupcsm-2021-0007
Nathan Grieve
Abstract We study the property of continuous Castelnuovo-Mumford regularity, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the Abelian variety’s endo-morphism algebra. This result builds on earlier work of Mumford and Kempf and applies the form of the Riemann-Roch Theorem that was established in N. Grieve [New York J. Math. 23 (2017), 1087-1110]. In a complementary direction, we explain how these topics pertain to the Index and Generic Vanishing Theory conditions for simple semihomogeneous vector bundles. In doing so, we refine results from M. Gulbrandsen [Matematiche (Catania) 63 (2008), no. 1, 123–137], N. Grieve [Internat. J. Math. 25 (2014), no. 4, 1450036, 31] and D. Mumford [Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969), Edizioni Cremonese, Rome, 1970, pp. 29-100].
本文研究了给定Abelian变量上的半齐次向量束的连续Castelnuovo-Mumford正则性，该正则性由a . k ronya和Y. Mustopa [Adv. Geom. 20 (2020)， no. 1]表述。3, 401 - 412]。我们的主要结果给出了一个新颖的描述。通过对阿贝尔变体的内模代数的Wedderburn分解得到若干归一化多项式函数。该结果建立在Mumford和Kempf早期工作的基础上，并应用了N. Grieve建立的Riemann-Roch定理的形式[New York J. Math. 23(2017)， 1087-1110]。在补充的方向上，我们解释了这些主题如何与简单半齐次向量束的索引和一般消失理论条件相关联。在此过程中，我们改进了M. Gulbrandsen [Matematiche (Catania) 63 (2008)， no。[j] .中国科学:国际科学。数学学报，25(2014)，第1期。D. Mumford[关于代数变量的问题(c.m.e, III Ciclo, Varenna, 1969)，罗马，1970,pp. 29-100]。
{"title":"Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles","authors":"Nathan Grieve","doi":"10.2478/aupcsm-2021-0007","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0007","url":null,"abstract":"Abstract We study the property of continuous Castelnuovo-Mumford regularity, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the Abelian variety’s endo-morphism algebra. This result builds on earlier work of Mumford and Kempf and applies the form of the Riemann-Roch Theorem that was established in N. Grieve [New York J. Math. 23 (2017), 1087-1110]. In a complementary direction, we explain how these topics pertain to the Index and Generic Vanishing Theory conditions for simple semihomogeneous vector bundles. In doing so, we refine results from M. Gulbrandsen [Matematiche (Catania) 63 (2008), no. 1, 123–137], N. Grieve [Internat. J. Math. 25 (2014), no. 4, 1450036, 31] and D. Mumford [Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969), Edizioni Cremonese, Rome, 1970, pp. 29-100].","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"2 1","pages":"95 - 119"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88945034","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 : 2021-01-01DOI: 10.2478/AUPCSM-2021-0001
B. Selmi
Abstract In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.
摘要本文利用辅助测度的互多重分形Hausdorff维数的表征，研究了小支撑测度的投影。
{"title":"Projections of measures with small supports","authors":"B. Selmi","doi":"10.2478/AUPCSM-2021-0001","DOIUrl":"https://doi.org/10.2478/AUPCSM-2021-0001","url":null,"abstract":"Abstract In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"111 1","pages":"5 - 15"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80650251","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 : 2021-01-01DOI: 10.2478/aupcsm-2021-0003
Farid Nouioua, Bilal Basti
Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
{"title":"Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions","authors":"Farid Nouioua, Bilal Basti","doi":"10.2478/aupcsm-2021-0003","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0003","url":null,"abstract":"Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"12 1","pages":"43 - 56"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82087276","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 : 2021-01-01DOI: 10.2478/aupcsm-2021-0008
Hossein Sabzrou
Abstract Let L be a not necessarily saturated lattice in ℤn with a defining matrix B. We explicitly compute the set of circuits of L in terms of maximal minors of B. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals.
{"title":"A determinantal formula for circuits of integer lattices","authors":"Hossein Sabzrou","doi":"10.2478/aupcsm-2021-0008","DOIUrl":"https://doi.org/10.2478/aupcsm-2021-0008","url":null,"abstract":"Abstract Let L be a not necessarily saturated lattice in ℤn with a defining matrix B. We explicitly compute the set of circuits of L in terms of maximal minors of B. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"140 1","pages":"121 - 127"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80412152","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 : 2020-04-25DOI: 10.2478/aupcsm-2020-0004
R. Laterveer
We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.
证明了由fatighti - mongardi构造的一类K3型Fano四重矩阵具有乘法的chow - k n次分解。我们提出了这四倍的周氏环的一些结果。
{"title":"On the Chow ring of certain Fano fourfolds","authors":"R. Laterveer","doi":"10.2478/aupcsm-2020-0004","DOIUrl":"https://doi.org/10.2478/aupcsm-2020-0004","url":null,"abstract":"\u0000 We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"33 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77767193","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 : 2020-04-01DOI: 10.2478/aupcsm-2020-0010
Zbigniew Burdak, W. Grygierzec
The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.
{"title":"On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions","authors":"Zbigniew Burdak, W. Grygierzec","doi":"10.2478/aupcsm-2020-0010","DOIUrl":"https://doi.org/10.2478/aupcsm-2020-0010","url":null,"abstract":"\u0000 The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"25 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86295058","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 : 2020-02-27DOI: 10.2478/aupcsm-2020-0008
H. Özarslan
This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.
本文给出了一个关于无穷级数的绝对矩阵可和性的定理。用拟β幂递增序列代替几乎递增序列证明了这一定理。
{"title":"A new result on the quasi power increasing sequences","authors":"H. Özarslan","doi":"10.2478/aupcsm-2020-0008","DOIUrl":"https://doi.org/10.2478/aupcsm-2020-0008","url":null,"abstract":"\u0000 This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"18 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83356684","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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