{"title":"Tangentials in cubic structures","authors":"V. Volenec, Z. Kolar-Begović, R. Kolar-Šuper","doi":"10.3336/gm.55.2.10","DOIUrl":"https://doi.org/10.3336/gm.55.2.10","url":null,"abstract":"In this paper we study geometric concepts in a general cubic structure. The well-known relationships on the cubic curve motivate us to introduce new concepts into a general cubic structure. We will define the concept of the tangential of a point in a general cubic structure and we will study tangentials of higher-order. The characterization of this concept will be also given by means of the associated totally symmetric quasigroup. We will introduce the concept of associated and corresponding points in a cubic structure, and discuss the number of mutually different corresponding points. The properties of the introduced geometric concepts will be investigated in a general cubic structure.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78317232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Further results on common properties of the products ac and bd","authors":"Qingping Zeng, Kai Yan, Zhenying Wu","doi":"10.3336/gm.55.2.07","DOIUrl":"https://doi.org/10.3336/gm.55.2.07","url":null,"abstract":"In this paper, we continue to investigate common properties of the products ac and bd in various categories under the assumption acd=dbd and dba=aca. These properties include generalized strongly Drazin invertibility and generalized Hirano invertibility in rings, abstract index of Fredholm elements and B-Fredholm elements in the Banach algebra context, complementability of kernels and ranges for bounded linear operators on Banach spaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79066070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Permutation orbifolds of 𝔰𝔩2 vertex operator algebras","authors":"A. Milas, M. Penn","doi":"10.3336/gm.55.2.08","DOIUrl":"https://doi.org/10.3336/gm.55.2.08","url":null,"abstract":"We analyze two types of permutation orbifolds: (i) S2-orbifolds of the universal level k vertex operator algebra Vk(𝔰𝔩2) and of its simple quotient Lk(𝔰𝔩2), and (ii) the S3-orbifold of the level one simple vertex operator algebra L1(𝔰𝔩2). We determine their structures and discuss related W-algebras.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75457403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Zalar, Smetanova Maribor Slovenia architecture, B. Ferčec, Yilei Tang, M. Mencinger, Jadranska Ljubljana Slovenia mechanics
{"title":"Partial qualitative analysis of planar 𝓐Q-Riccati equations","authors":"B. Zalar, Smetanova Maribor Slovenia architecture, B. Ferčec, Yilei Tang, M. Mencinger, Jadranska Ljubljana Slovenia mechanics","doi":"10.3336/gm.55.2.11","DOIUrl":"https://doi.org/10.3336/gm.55.2.11","url":null,"abstract":"If we view the field of complex numbers as a 2-dimensional commutative real algebra, we can consider the differential equation z'=az2+bz+c as a particular case of 𝓐- Riccati equations z'=a · (z · z)+b · z+c where 𝓐=( ℝn,·) is a commutative, possibly nonassociative algebra, a,b,c∈𝓐 and z:I → 𝓐 is defined on some nontrivial real interval. In the case 𝓐=ℂ, the nature of (at most two) critical points can be described using purely algebraic conditions involving involution * of ℂ. In the present paper we study the critical points of 𝓛(π)- Riccati equations, where 𝓛(π) is the limit case of the so-called family of planar Lyapunov algebras, which characterize 2-dimensional homogeneous systems of quadratic ODEs with stable origin. The number of possible critical points is 1, 3 or ∞, depending on coefficients. The nature of critical points is also completely described. Finally, simultaneous stability of the origin is considered for homogeneous quadratic part corresponding to algebras 𝓛(θ).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80158386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hölder continuity for the solutions of the p(x)-Laplace equation\u0000with general right-hand side","authors":"A. Lyaghfouri","doi":"10.3336/gm.57.1.03","DOIUrl":"https://doi.org/10.3336/gm.57.1.03","url":null,"abstract":"We show that bounded solutions of the quasilinear elliptic equation\u0000(Delta_{p(x)} u=g+div(textbf{F})) are locally Hölder continuous\u0000provided that the functions (g) and (textbf{F}) are in suitable\u0000Lebesgue spaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76702888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}