We introduce Markov-like functions on intervals as a generalization of generalized Markov interval functions and define the notation of the same pattern between Markov-like functions. Then we show that two generalized inverse limits with Markov-like bonding functions having the same pattern are homeomorphic. This result gives a generalization of the results of S. Holte ([9]) and I. Banič and T. Lunder ([5]).
作为广义马尔可夫区间函数的推广，我们引入了区间上的类马尔可夫函数，并定义了类马尔可夫函数之间相同模式的符号。然后证明了具有相同模式的类马尔可夫键函数的两个广义逆极限是同胚的。该结果推广了S. Holte([9])和I. baninik and T. Lunder([5])的结果。
{"title":"Markov-like set-valued functions on intervals and their inverse limits","authors":"Hayato Imamura","doi":"10.3336/GM.53.2.10","DOIUrl":"https://doi.org/10.3336/GM.53.2.10","url":null,"abstract":"We introduce Markov-like functions on intervals as a generalization of generalized Markov interval functions and define the notation of the same pattern between Markov-like functions. Then we show that two generalized inverse limits with Markov-like bonding functions having the same pattern are homeomorphic. This result gives a generalization of the results of S. Holte ([9]) and I. Banič and T. Lunder ([5]).","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81368243","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":"Trinomials ax8+bx+c with Galois groups of order 1344","authors":"Szabolcs Tengely","doi":"10.3336/GM.53.2.04","DOIUrl":"https://doi.org/10.3336/GM.53.2.04","url":null,"abstract":"","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84860388","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}
F. Capulín, L. Juárez-Villa, Fernando Orozco-Zitli
In this paper we discuss the notions of pseudo-contractibility and weak contractibility on hyperspaces of (Hausdorff) continua. Also we prove that if a continuum X contains an R-set then it is not pseudocontractible. As a consequence we have that the existence of an R-set in a continuum X implies non(pseudo)-contractibility of some hyperspaces.
{"title":"Ri-sets, pseudo-contractibility and weak contractibility on hyperspaces of continua","authors":"F. Capulín, L. Juárez-Villa, Fernando Orozco-Zitli","doi":"10.3336/GM.53.2.08","DOIUrl":"https://doi.org/10.3336/GM.53.2.08","url":null,"abstract":"In this paper we discuss the notions of pseudo-contractibility and weak contractibility on hyperspaces of (Hausdorff) continua. Also we prove that if a continuum X contains an R-set then it is not pseudocontractible. As a consequence we have that the existence of an R-set in a continuum X implies non(pseudo)-contractibility of some hyperspaces.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86765883","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 consider a class of parabolic free boundary problems with heterogeneous coefficients including, from a physical point of view, the evolutionary dam problem. We establish existence of a solution for this problem. We use a regularized problem for which we prove existence of a solution by applying the Tychonoff fixed point theorem. Then we pass to the limit to get a solution of our problem. We also give a regularity result of the solutions.
{"title":"On the existence of a solution of a class of non-stationary free boundary problems","authors":"M. Bousselsal, A. Lyaghfouri, E. Zaouche","doi":"10.3336/GM.53.2.13","DOIUrl":"https://doi.org/10.3336/GM.53.2.13","url":null,"abstract":"We consider a class of parabolic free boundary problems with heterogeneous coefficients including, from a physical point of view, the evolutionary dam problem. We establish existence of a solution for this problem. We use a regularized problem for which we prove existence of a solution by applying the Tychonoff fixed point theorem. Then we pass to the limit to get a solution of our problem. We also give a regularity result of the solutions.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72643680","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, M. Mencinger, Jadranska Ljubljana Slovenia mechanics
The paper introduces two algebraic concepts, near-idempotents and near-nilpotents associated to subspaces N of critical points, which can be used to re-phrase a theorem due to Boujemaa, El Qotbi and Rouiouih on stability for the Ricatti equation, ẋ = x(t)2, associated to algebra A ≈ R. Using this concepts their result corresponds to the case dim N = 1. Our main results are a generalization of the above mentioned theorem to N of arbitrary dimension and a counter-example which shows, even in the general setting, that the essential condition that critical points must be eigenvectors of a suitable multiplication operator cannot be omitted from the formulation due to Boujemaa et al.
{"title":"Near-idempotents, near-nilpotents and stability of critical points for Riccati equations","authors":"B. Zalar, M. Mencinger, Jadranska Ljubljana Slovenia mechanics","doi":"10.3336/GM.53.2.06","DOIUrl":"https://doi.org/10.3336/GM.53.2.06","url":null,"abstract":"The paper introduces two algebraic concepts, near-idempotents and near-nilpotents associated to subspaces N of critical points, which can be used to re-phrase a theorem due to Boujemaa, El Qotbi and Rouiouih on stability for the Ricatti equation, ẋ = x(t)2, associated to algebra A ≈ R. Using this concepts their result corresponds to the case dim N = 1. Our main results are a generalization of the above mentioned theorem to N of arbitrary dimension and a counter-example which shows, even in the general setting, that the essential condition that critical points must be eigenvectors of a suitable multiplication operator cannot be omitted from the formulation due to Boujemaa et al.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78593167","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 a characterization of inverse sequences with upper semicontinuous bonding functions fi : [0, 1] ⊸ [0, 1] for which the inverse limit of the inverse sequence with f i as bonding functions is connected. As a byproduct, we obtain another characterization of connected inverse limits of inverse sequences with a single bonding function.
{"title":"Inverse component cropping sequences and connected inverse limits over intervals","authors":"I. Banič, Matevz Crepnjak","doi":"10.3336/GM.53.2.09","DOIUrl":"https://doi.org/10.3336/GM.53.2.09","url":null,"abstract":"We give a characterization of inverse sequences with upper semicontinuous bonding functions fi : [0, 1] ⊸ [0, 1] for which the inverse limit of the inverse sequence with f i as bonding functions is connected. As a byproduct, we obtain another characterization of connected inverse limits of inverse sequences with a single bonding function.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83360799","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 study the generalized minimal residual (GMRES) method for solving tridiagonal block Toeplitz linear system Ax = b with m × m diagonal blocks. For m = 1, these systems becomes tridiagonal Toeplitz linear systems, and for m > 1, A becomes an m-tridiagonal Toeplitz matrix. Our first main goal is to find the exact expressions for the GMRES residuals for b = (B1, 0, . . . , 0) , b = (0, . . . , 0, BN ) T , where B1 and BN are m-vectors. The upper and lower bounds for the GMRES residuals were established to explain numerical behavior. The upper bounds for the GMRES residuals on tridiagonal block Toeplitz linear systems has been studied previously in [1]. Also, in this paper, we consider the normal tridiagonal block Toeplitz linear systems. The second main goal is to find the lower bounds for the GMRES residuals for these systems.
{"title":"GMRES on tridiagonal block Toeplitz linear systems","authors":"R. Doostaki, Young Researchers","doi":"10.3336/GM.53.2.12","DOIUrl":"https://doi.org/10.3336/GM.53.2.12","url":null,"abstract":"We study the generalized minimal residual (GMRES) method for solving tridiagonal block Toeplitz linear system Ax = b with m × m diagonal blocks. For m = 1, these systems becomes tridiagonal Toeplitz linear systems, and for m > 1, A becomes an m-tridiagonal Toeplitz matrix. Our first main goal is to find the exact expressions for the GMRES residuals for b = (B1, 0, . . . , 0) , b = (0, . . . , 0, BN ) T , where B1 and BN are m-vectors. The upper and lower bounds for the GMRES residuals were established to explain numerical behavior. The upper bounds for the GMRES residuals on tridiagonal block Toeplitz linear systems has been studied previously in [1]. Also, in this paper, we consider the normal tridiagonal block Toeplitz linear systems. The second main goal is to find the lower bounds for the GMRES residuals for these systems.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74885705","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}
Suppose given a polynomial dynamical system of degree m. It is known that if the algebra associated to the corresponding homogeneous dynamical system of degree m has an idempotent element then the original dynamical system is unbounded. In this work, we give a sufficient condition ensuring the unboundedness even when there is no idempotent. Some applications are also given.
{"title":"On unbounded polynomial dynamical systems","authors":"Hamza Boujemaa, Said El Qotbi","doi":"10.3336/gm.53.2.07","DOIUrl":"https://doi.org/10.3336/gm.53.2.07","url":null,"abstract":"Suppose given a polynomial dynamical system of degree m. It is known that if the algebra associated to the corresponding homogeneous dynamical system of degree m has an idempotent element then the original dynamical system is unbounded. In this work, we give a sufficient condition ensuring the unboundedness even when there is no idempotent. Some applications are also given.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76597494","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 study a nonlinear anisotropic elliptic problem under Robin type boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(.)-capacity. We prove an existence and uniqueness result of entropy or renormalized solution.
{"title":"Multivalued anisotropic problem with Fourier boundary condition involving diffuse Radon measure data and variable exponents","authors":"Ibrahime Konaté, S. Ouaro","doi":"10.7151/DMDICO.1205","DOIUrl":"https://doi.org/10.7151/DMDICO.1205","url":null,"abstract":"In this paper we study a nonlinear anisotropic elliptic problem under Robin type boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(.)-capacity. We prove an existence and uniqueness result of entropy or renormalized solution.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76031050","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}
This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+chi)_{x_2}-(u+chi)_t=0. Our technique is based on the idea that we transform the weak form of this equation into a similar situation to the proof of the uniqueness in the incompressible case (see [12]). It is also difficult to adapt the proof obtained in [12] by using some properties of the solutions as in [12, Sect. 2].
{"title":"Uniqueness of solution of a heterogeneous evolution dam problem associated with a compressible fluid flow through a rectangular porous medium","authors":"E. Zaouche","doi":"10.3336/gm.55.1.08","DOIUrl":"https://doi.org/10.3336/gm.55.1.08","url":null,"abstract":"This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+chi)_{x_2}-(u+chi)_t=0. Our technique is based on the idea that we transform the weak form of this equation into a similar situation to the proof of the uniqueness in the incompressible case (see [12]). It is also difficult to adapt the proof obtained in [12] by using some properties of the solutions as in [12, Sect. 2].","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79502514","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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