In this work, we prove the uniform regularity of smooth solutions to the full compressible MHD system in (mathbb{T}^3). Here our result is obtained by using the bilinear commutator and product estimates.
{"title":"Uniform regularity for the nonisentropic MHD system","authors":"Kunlong Shi, T. Tang","doi":"10.3336/gm.57.2.08","DOIUrl":"https://doi.org/10.3336/gm.57.2.08","url":null,"abstract":"In this work, we prove the uniform regularity of smooth solutions to the full compressible MHD system in (mathbb{T}^3). Here our result is obtained by using the\u0000bilinear commutator and product estimates.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87107330","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 [28], for any real non associative algebra of dimension (mgeq2), having (k) linearly independent nilpotent elements (n_{1}), (n_{2}), …, (n_{k},) (1leq kleq m-1), Mencinger and Zalar defined near idempotents and near nilpotents associated to (n_{1}), (n_{2}), …, (n_{k}). Assuming (mathcal{N}_{k}mathcal{N}_{k}=left{ 0right}), where (mathcal{N} _{k}=operatorname*{span}left{ n_{1},n_{2},ldots,n_{k}right} ), they showed that if there exists a near idempotent or a near nilpotent, called (u), associated to (n_{1},n_{2},ldots,n_{k}) verifying (n_{i}uinmathbb{R}n_{i},) for (1leq ileq k), then any nilpotent element in (mathcal{N}_{k}) is unstable. They also raised the question of extending their results to cases where (mathcal{N}_{k}mathcal{N}_{k}not =left{ 0right} ) with (mathcal{N}_{k}mathcal{N}_{k}subsetmathcal{N}_{k}mathcal{ })and to cases where (mathcal{N}_{k}mathcal{N}_{k} notsubset mathcal{N}_{k}.) In this paper, positive answers are emphasized and in some cases under the weaker conditions (n_{i}uinmathcal{N}_{k}). In addition, we characterize all such algebras in dimension 3.
{"title":"On a generalization of some instability results for Riccati equations via nonassociative algebras","authors":"Hamza Boujemaa, B. Ferčec","doi":"10.3336/gm.57.2.06","DOIUrl":"https://doi.org/10.3336/gm.57.2.06","url":null,"abstract":"In [28], for any real non associative algebra of dimension (mgeq2),\u0000having (k) linearly independent nilpotent elements (n_{1}), (n_{2}), …,\u0000(n_{k},) (1leq kleq m-1), Mencinger and Zalar defined near idempotents and\u0000near nilpotents associated to (n_{1}), (n_{2}), …, (n_{k}). Assuming\u0000(mathcal{N}_{k}mathcal{N}_{k}=left{ 0right}), where (mathcal{N}\u0000_{k}=operatorname*{span}left{ n_{1},n_{2},ldots,n_{k}right} ), they\u0000showed that if there exists a near idempotent or a near nilpotent, called (u),\u0000associated to (n_{1},n_{2},ldots,n_{k}) verifying (n_{i}uinmathbb{R}n_{i},)\u0000for (1leq ileq k), then any nilpotent element in (mathcal{N}_{k}) is\u0000unstable. They also raised the question of extending their results to cases\u0000where (mathcal{N}_{k}mathcal{N}_{k}not =left{ 0right} ) with\u0000(mathcal{N}_{k}mathcal{N}_{k}subsetmathcal{N}_{k}mathcal{ })and to cases\u0000where (mathcal{N}_{k}mathcal{N}_{k} notsubset mathcal{N}_{k}.)\u0000\u0000\u0000In this paper, positive answers are emphasized and in some cases under the\u0000weaker conditions (n_{i}uinmathcal{N}_{k}). In addition, we characterize all\u0000such algebras in dimension 3.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77535558","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}
Richard Andr'avsik, V'aclav M'acha, Rostislav Vod'ak
Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a derivation of the relative energy inequality for the weak solutions to these equations. We show that the standard energy inequality implies the relative energy inequality. Consequently, the relative energy inequality allows us to achieve a weak-strong uniqueness result. In other words, we present that the weak solution of the Navier-Stokes system coincides with the strong solution emanated from the same initial conditions as long as the strong solution exists. For this purpose, a new assumption on the coercivity of the viscous stress tensor was introduced along with two natural examples satisfying it.
{"title":"Relative energy inequality and weak-strong uniqueness for an isothermal non-Newtonian compressible fluid","authors":"Richard Andr'avsik, V'aclav M'acha, Rostislav Vod'ak","doi":"10.3336/gm.58.1.07","DOIUrl":"https://doi.org/10.3336/gm.58.1.07","url":null,"abstract":"Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a derivation of the relative energy inequality for the weak solutions to these equations. We show that the standard energy inequality implies the relative energy inequality. Consequently, the relative energy inequality allows us to achieve a weak-strong uniqueness result. In other words, we present that the weak solution of the Navier-Stokes system coincides with the strong solution emanated from the same initial conditions as long as the strong solution exists. For this purpose, a new assumption on the coercivity of the viscous stress tensor was introduced along with two natural examples satisfying it.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80853275","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}
Herbert Batte, Mahadi Ddamulira, Juma Kasozi, F. Luca
Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (c) we write (m_{F,p}(c)) for the number of distinct representations of (c) as (F_k-p^ell) with (kge 2) and (ellge 0). We prove that (m_{F,p}(c)le 4).
{"title":"On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime","authors":"Herbert Batte, Mahadi Ddamulira, Juma Kasozi, F. Luca","doi":"10.3336/gm.57.2.02","DOIUrl":"https://doi.org/10.3336/gm.57.2.02","url":null,"abstract":"Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (c) we write (m_{F,p}(c)) for the number of distinct representations of (c) as (F_k-p^ell) with (kge 2) and (ellge 0). We prove that (m_{F,p}(c)le 4).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74079792","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 note we make progress toward a conjecture of Durham–Fanoni–Vlamis, showing that every infinite-type surface with finite-invariance index (1) and no nondisplaceable compact subsurfaces fails to have a good graph of curves, that is, a connected graph where vertices represent homotopy classes of essential simple closed curves and with a natural mapping class group action having infinite diameter orbits. Our arguments use tools developed by Mann–Rafi in their study of the coarse geometry of big mapping class groups.
在这篇文章中，我们对Durham-Fanoni-Vlamis的一个猜想取得了进展，证明了每一个具有fi - ni -t -invariance指标(1)且没有不可置换紧致子曲面的无限型曲面都不可能有一个好的曲线图，即顶点表示本质简单闭曲线的同伦类且具有具有无限直径轨道的自然映射类群作用的连通图。我们的论证使用了Mann-Rafi在研究大映射类群的粗糙几何时开发的工具。
{"title":"Graphs of curves for surfaces with finite-invariance index (1)","authors":"Justin Lanier, Marissa Loving","doi":"10.3336/gm.57.1.08","DOIUrl":"https://doi.org/10.3336/gm.57.1.08","url":null,"abstract":"In this note we make progress toward a conjecture of Durham–Fanoni–Vlamis, showing that every infinite-type surface with finite-invariance index (1) and no nondisplaceable compact subsurfaces fails to have a good graph of curves, that is, a connected graph where vertices represent homotopy classes of essential simple closed curves and with a natural mapping class group action having infinite diameter orbits. Our arguments use tools developed by Mann–Rafi in their study of the coarse geometry of big mapping class groups.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73263424","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 extend Jacobson's lemma for Drazin inverses to the generalized (n)-strong Drazin inverses in a ring, and prove that (1-ac) is generalized (n)-strong Drazin invertible if and only if (1-ba) is generalized (n)-strong Drazin invertible, provided that (a(ba)^{2}=abaca=acaba=(ac)^{2}a). In addition, Jacobson's lemma for the left and right Fredholm operators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.
{"title":"Jacobson's lemma for the generalized (n)-strong Drazin inverses in rings and in operator algebras","authors":"Yanxun Ren, Lining Jiang","doi":"10.3336/gm.57.1.01","DOIUrl":"https://doi.org/10.3336/gm.57.1.01","url":null,"abstract":"In this paper, we extend Jacobson's lemma for Drazin inverses to the generalized (n)-strong Drazin inverses in a ring, and prove that (1-ac) is generalized (n)-strong Drazin invertible if and only if (1-ba) is generalized (n)-strong Drazin invertible, provided that (a(ba)^{2}=abaca=acaba=(ac)^{2}a). In addition, Jacobson's lemma for the left and right Fredholm operators, and furthermore, for consistent in invertibility spectral property and consistent in Fredholm and index spectral property are investigated.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79685110","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}
M. Asadi, Zahra Hassanpour Yakhdani, Fatemeh Olyaninezhad, A. Sahleh
In this paper, we will use the categorical approach to Hilbert (C^{ast})-modules over a commutative (C^{ast})-algebra to investigate the approximately orthogonality preserving mappings on Hilbert (C^{ast})-modules over a commutative (C^{ast})-algebra. Indeed, we show that if (Psi:Gamma rightarrow Gamma^{prime} ) is a nonzero ( C_{0}(Z) )-linear (( delta , varepsilon))-orthogonality preserving mapping between the continuous fields of Hilbert spaces on a locally compact Hausdorff space (Z), then (Psi) is injective, continuous and also for every ( x, y in Gamma ) and (z in Z), [ vert langle Psi(x),Psi(y) rangle(z) - varphi^2(z) langle x,y rangle(z) vert leq frac{4(varepsilon - delta)}{(1-delta)(1+varepsilon)} Vert Psi(x) Vert Vert Psi(y) Vert, ] where (varphi(z) = sup { Vert Psi(u)(z) Vert : u ~ text{is a unit vector in} ~ Gamma }).
在本文中，我们将使用范畴方法对Hilbert (C^{ast}) -模在可交换(C^{ast}) -代数上研究Hilbert (C^{ast}) -模在可交换(C^{ast}) -代数上的近似正交保持映射。实际上，我们证明了如果(Psi:Gamma rightarrow Gamma^{prime})是局部紧化Hausdorff空间上Hilbert空间连续域之间的非零映射( C_{0}(Z) ) -线性映射(( delta , varepsilon)) -保正性映射(Z)，那么(Psi)是内射的，连续的，并且对于每一个( x, y in Gamma )和(z in Z), [vertlangle Psi(x),Psi(y) rangle(z) - varphi^2(z) langle x,yrangle(z) vert leq frac{4(varepsilon -delta)}{(1-delta)(1+varepsilon)} Vert Psi(x) Vert VertPsi(y) Vert,]其中(varphi(z) = sup { Vert Psi(u)(z)Vert : u ~ text{is a unit vector in} ~ Gamma })。
{"title":"Approximately orthogonality preserving mappings on Hilbert (C_{0}(Z))-modules","authors":"M. Asadi, Zahra Hassanpour Yakhdani, Fatemeh Olyaninezhad, A. Sahleh","doi":"10.3336/gm.57.1.05","DOIUrl":"https://doi.org/10.3336/gm.57.1.05","url":null,"abstract":"In this paper, we will use the categorical approach to\u0000Hilbert (C^{ast})-modules over a commutative (C^{ast})-algebra\u0000to investigate the approximately orthogonality preserving mappings\u0000on Hilbert (C^{ast})-modules over a commutative\u0000(C^{ast})-algebra.\u0000\u0000 Indeed, we show that if (Psi:Gamma rightarrow Gamma^{prime}\u0000) is a nonzero ( C_{0}(Z) )-linear\u0000 (( delta , varepsilon))-orthogonality preserving mapping\u0000 between the continuous fields of Hilbert spaces on a locally\u0000compact Hausdorff space (Z), then (Psi) is injective, continuous\u0000and also for every ( x, y in Gamma ) and (z in Z),\u0000[\u0000\u0000\u0000\u0000vert\u0000langle Psi(x),Psi(y) rangle(z) - varphi^2(z) langle x,y\u0000rangle(z) vert leq frac{4(varepsilon -\u0000delta)}{(1-delta)(1+varepsilon)} Vert Psi(x) Vert Vert\u0000Psi(y) Vert,\u0000\u0000\u0000]\u0000where (varphi(z) = sup { Vert Psi(u)(z)\u0000Vert : u ~ text{is a unit vector in} ~ Gamma }).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77295519","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}
Given an arbitrary category (mathcal{C}), a category (pro^{*^f})-(mathcal{C}) is constructed such that the known (pro)-(mathcal{C}) category may be considered as a subcategory of (pro^{*^f})-(mathcal{C}) and that (pro^{*^f})-(mathcal{C}) may be considered as a subcategory of (pro^*)-(mathcal{C}). Analogously to the construction of the shape category (Sh_{(mathcal{C},mathcal{D})}) and the coarse category (Sh^*_{(mathcal{C},mathcal{D})}), an (abstract) finite coarse shape category (Sh^{*^f}_{(mathcal{C},mathcal{D})}) is obtained. Between these three categories appropriate faithful functors are defined. The finite coarse shape is also defined by an intrinsic approach using the notion of the (epsilon)-continuity. The isomorphism of the finite coarse shape categories obtained by these two approaches is constructed. Besides, an overview of some basic properties related to the notion of the (epsilon)-continuity is given.
{"title":"The finite coarse shape - inverse systems approach and intrinsic approach","authors":"I. Jelić, Nikola Koceić Bilan","doi":"10.3336/gm.57.1.07","DOIUrl":"https://doi.org/10.3336/gm.57.1.07","url":null,"abstract":"Given an arbitrary category (mathcal{C}), a category (pro^{*^f})-(mathcal{C}) is constructed such that the known (pro)-(mathcal{C}) category may be considered as a subcategory of (pro^{*^f})-(mathcal{C}) and that (pro^{*^f})-(mathcal{C}) may be considered as a subcategory of (pro^*)-(mathcal{C}). Analogously to the construction of the shape category (Sh_{(mathcal{C},mathcal{D})}) and the coarse category (Sh^*_{(mathcal{C},mathcal{D})}), an (abstract) finite coarse shape category (Sh^{*^f}_{(mathcal{C},mathcal{D})}) is obtained. Between these three categories appropriate faithful functors are defined. The finite coarse shape is also defined by an intrinsic approach using the notion of the (epsilon)-continuity. The isomorphism of the finite coarse shape categories obtained by these two approaches is constructed. Besides, an overview of some basic properties related to the notion of the (epsilon)-continuity is given.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81040806","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}
Selective Rips complexes associated to two parameters are certain subcomplexes of Rips complexes consisting of thin simplices. They are designed to detect more closed geodesics than their Rips counterparts. In this paper we introduce a general definition of selective Rips complexes with countably many parameters and prove basic reconstruction properties associated with them. In particular, we prove that selective Rips complexes of a closed Riemannian manifold (X) attain the homotopy type of (X) at small scales. We also completely classify the resulting persistent fundamental group and (1)-dimensional persistent homology.
{"title":"Reconstruction properties of selective Rips complexes","authors":"Boštjan Lemež, Žiga Virk","doi":"10.3336/gm.57.1.06","DOIUrl":"https://doi.org/10.3336/gm.57.1.06","url":null,"abstract":"Selective Rips complexes associated to two parameters are certain subcomplexes of Rips complexes consisting of thin simplices. They are designed to detect more closed geodesics than their Rips counterparts. In this paper we introduce a general definition of selective Rips complexes with countably many parameters and prove basic reconstruction properties associated with them. In particular, we prove that selective Rips complexes of a closed Riemannian manifold (X) attain the homotopy type of (X) at small scales.\u0000We also completely classify the resulting persistent fundamental group and (1)-dimensional persistent homology.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79631741","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, based on the shift splitting of the coefficient matrix, a generalized two-sweep shift splitting (GTSS) method is introduced to solve the non-Hermitian positive definite linear systems. Theoretical analysis shows that the GTSS method is convergent to the unique solution of the linear systems under a loose restriction on the iteration parameter. Numerical experiments are reported to the efficiency of the GTSS method.
{"title":"A generalized two-sweep shift splitting method\u0000for non-Hermitian positive definite linear systems","authors":"Shiliang Wu, Cuixia Li","doi":"10.3336/gm.57.1.10","DOIUrl":"https://doi.org/10.3336/gm.57.1.10","url":null,"abstract":"In this paper, based on the shift splitting of the\u0000coefficient matrix, a generalized two-sweep shift splitting (GTSS)\u0000method is introduced to solve the non-Hermitian positive definite\u0000linear systems. Theoretical analysis shows that the GTSS method is\u0000convergent to the unique solution of the linear systems under a\u0000loose restriction on the iteration parameter. Numerical experiments\u0000are reported to the efficiency of the GTSS method.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79386358","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：