The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian.
{"title":"Limit theorems for numbers satisfying a class of triangular arrays","authors":"I. Belovas","doi":"10.3336/gm.56.2.01","DOIUrl":"https://doi.org/10.3336/gm.56.2.01","url":null,"abstract":"The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84720757","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}
In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.
{"title":"Regularity of a weak solution to a linear fluid-composite structure interaction problem","authors":"M. Galić","doi":"10.3336/gm.56.2.11","DOIUrl":"https://doi.org/10.3336/gm.56.2.11","url":null,"abstract":"In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84085653","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}
In this paper, we observe the possibility that the group (S_{n}times S_{m}) acts as a flag-transitive automorphism group of a block design with point set ({1,ldots ,n}times {1,ldots ,m},4leq nleq mleq 70). We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with (nm) points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.
{"title":"Groups (S_n times S_m) in construction of flag-transitive block designs","authors":"Snježana Braić, Josko Mandic, Aljoša Šubašić, Tanja Vojkovic, Tanja Vucicic","doi":"10.3336/gm.56.2.02","DOIUrl":"https://doi.org/10.3336/gm.56.2.02","url":null,"abstract":"In this paper, we observe the possibility that the group (S_{n}times S_{m}) acts as a flag-transitive automorphism group of a block design with point set ({1,ldots ,n}times {1,ldots ,m},4leq nleq mleq 70). We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with (nm) points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84771204","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}
Let (Phi_n(x)) be the (n)-th cyclotomic polynomial. In this paper, for odd primes (plt q lt r) with (qequiv pm1pmod p) and (8requiv pm1pmod {pq}), we prove that the coefficients of (Phi_{pqr}(x)) do not exceed (1) in modulus if and only if (i) (p=3), (qgeq 19) and (qequiv 1pmod 3) or (ii) (p=7), (qgeq83) and (qequiv -1pmod 7).
{"title":"A remark on flat ternary cyclotomic polynomials","authors":"Bin Zhang","doi":"10.3336/gm.56.2.03","DOIUrl":"https://doi.org/10.3336/gm.56.2.03","url":null,"abstract":"Let (Phi_n(x)) be the (n)-th cyclotomic polynomial. In this paper, for odd primes (plt q lt r) with (qequiv pm1pmod p) and (8requiv pm1pmod {pq}), we prove that the coefficients of (Phi_{pqr}(x)) do not exceed (1) in modulus if and only if (i) (p=3), (qgeq 19) and (qequiv 1pmod 3) or (ii) (p=7), (qgeq83) and (qequiv -1pmod 7).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80352665","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}
In this paper we apply the intrinsic approach to shape to study attractors in topological spaces.
本文应用形状的本征方法来研究拓扑空间中的吸引子。
{"title":"Semiflows and intrinsic shape in topological spaces","authors":"M. Shoptrajanov, N. Shekutkovski","doi":"10.3336/gm.56.2.09","DOIUrl":"https://doi.org/10.3336/gm.56.2.09","url":null,"abstract":"In this paper we apply the intrinsic approach to shape to study attractors in topological spaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88234649","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}
In this paper we consider pentadiagonal ((n+1)times(n+1)) matrices with two subdiagonals and two superdiagonals at distances (k) and (2k) from the main diagonal where (1le k lt 2kle n). We give an explicit formula for their determinants and also consider the Toeplitz and “imperfect” Toeplitz versions of such matrices. Imperfectness means that the first and last (k) elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerváry and Szász we also show how these determinants can be factorized.
本文考虑五对角线((n+1)times(n+1))矩阵，在距离主对角线(k)和(2k)处有两个次对角线和两个超对角线，其中(1le k lt 2kle n)。我们给出了它们的行列式的显式公式，并考虑了这种矩阵的Toeplitz和“不完全”Toeplitz版本。不完美意味着主对角线的第一个和最后一个(k)元素与中间的元素不同。利用Egerváry和Szász的重排，我们还展示了这些决定因素是如何被分解的。
{"title":"Determinants of some pentadiagonal matrices","authors":"L. Losonczi","doi":"10.3336/gm.56.2.05","DOIUrl":"https://doi.org/10.3336/gm.56.2.05","url":null,"abstract":"In this paper we consider pentadiagonal ((n+1)times(n+1)) matrices with two subdiagonals and two superdiagonals at distances (k) and (2k) from the main diagonal where (1le k lt 2kle n). We give an explicit formula for their determinants and also consider the Toeplitz and “imperfect” Toeplitz versions of such matrices. Imperfectness means that the first and last (k) elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerváry and Szász we also show how these determinants can be factorized.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87070287","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}
We give the characterization and description of all full Hilbert modules and associated algebras having the property that each relatively strictly closed submodule is orthogonally complemented. A strict topology is determined by an essential closed two-sided ideal in the associated algebra and a related ideal submodule. It is shown that these are some modules over hereditary algebras containing the essential ideal isomorphic to the algebra of (not necessarily all) compact operators on a Hilbert space. The characterization and description of that broader class of Hilbert modules and their associated algebras is given. As auxiliary results we give properties of strict and relatively strict submodule closures, the characterization of orthogonal closedness and orthogonal complementing property for single submodules, relation of relative strict topology and projections, properties of outer direct sums with respect to the ideals in (ell_infty) and isomorphisms of Hilbert modules, and we prove some properties of hereditary algebras and associated hereditary modules with respect to the multiplier algebras, multiplier Hilbert modules, corona algebras and corona modules.
{"title":"Hilbert (C^{*})-modules in which all relatively strictly closed submodules are complemented","authors":"B. Guljaš","doi":"10.3336/gm.56.2.08","DOIUrl":"https://doi.org/10.3336/gm.56.2.08","url":null,"abstract":"We give the characterization and description of all full Hilbert modules and associated algebras having the property that each relatively strictly closed submodule is orthogonally complemented. A strict topology is determined by an essential closed two-sided ideal in the associated algebra and a related ideal submodule. It is shown that these are some modules over hereditary algebras containing the essential ideal isomorphic to the algebra of (not necessarily all) compact operators on a Hilbert space. The characterization and description of that broader class of Hilbert modules and their associated algebras is given. As auxiliary results we give properties of strict and relatively strict submodule closures, the characterization of orthogonal closedness and orthogonal complementing property for single submodules, relation of relative strict topology and projections, properties of outer direct sums with respect to the ideals in (ell_infty) and isomorphisms of Hilbert modules, and we prove some properties of hereditary algebras and associated hereditary modules with respect to the multiplier algebras, multiplier Hilbert modules, corona algebras and corona modules.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84632653","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}
All non-trivial point and block-primitive 1-(v, k, k) designs 𝓓 that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.
{"title":"Symmetric 1-designs from PGL2(q), for q an odd prime power","authors":"Xavier Mbaale, B. Rodrigues","doi":"10.3336/gm.56.1.01","DOIUrl":"https://doi.org/10.3336/gm.56.1.01","url":null,"abstract":"All non-trivial point and block-primitive 1-(v, k, k) designs 𝓓 that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86405611","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}
In this paper, the unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup is determined. In explicit determination of the unitary dual the external approach is used, which represents the basic approach for finding the unitary dual, and consists of two main steps: a complete description of the non-unitary dual and the extraction of the classes of unitarizable representations among the obtained irreducible subquotients. We expect that our results will provide deeper insight into the structure of the unitary dual in the general case.
{"title":"Unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup","authors":"Darija Brajković Zorić","doi":"10.3336/gm.56.1.08","DOIUrl":"https://doi.org/10.3336/gm.56.1.08","url":null,"abstract":"In this paper, the unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup is determined. In explicit determination of the unitary dual the external approach is used, which represents the basic approach for finding the unitary dual, and consists of two main steps: a complete description of the non-unitary dual and the extraction of the classes of unitarizable representations among the obtained irreducible subquotients. We expect that our results will provide deeper insight into the structure of the unitary dual in the general case.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75992710","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}
I. Kosi-Ulbl, Nejc Širovnik, J. Vukman, Global Gaming Solutions Partner WinSystems
The purpose of this paper is to prove the following result. Let n≥3 be some fixed integer and let R be a (n+1)!2n-2-torsion free semiprime unital ring. Suppose there exists an additive mapping D: R→ R satisfying the relation for all x ∈ R. In this case D is a derivation. The history of this result goes back to a classical result of Herstein, which states that any Jordan derivation on a 2-torsion free prime ring is a derivation.
{"title":"A result related to derivations on unital semiprime rings","authors":"I. Kosi-Ulbl, Nejc Širovnik, J. Vukman, Global Gaming Solutions Partner WinSystems","doi":"10.3336/gm.56.1.07","DOIUrl":"https://doi.org/10.3336/gm.56.1.07","url":null,"abstract":"The purpose of this paper is to prove the following result. Let n≥3 be some fixed integer and let R be a (n+1)!2n-2-torsion free semiprime unital ring. Suppose there exists an additive mapping D: R→ R satisfying the relation for all x ∈ R. In this case D is a derivation. The history of this result goes back to a classical result of Herstein, which states that any Jordan derivation on a 2-torsion free prime ring is a derivation.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76349665","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}
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