Pub Date : 2023-01-01DOI: 10.7494/opmath.2023.43.6.759
Hamid El Bahja
We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard (p(x,t),q(x,t))-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time (L^{infty}) bounds for the weak solutions.
{"title":"Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions","authors":"Hamid El Bahja","doi":"10.7494/opmath.2023.43.6.759","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.6.759","url":null,"abstract":"We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard (p(x,t),q(x,t))-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time (L^{infty}) bounds for the weak solutions.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71343452","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.2.145
Yuji Hamana
This article deals with the first hitting times of a Bessel process to a square-root boundary. We obtain the explicit form of the distribution function of the hitting time by means of zeros of the confluent hypergeometric function with respect to the first parameter. In deducing the distribution function, the time that a radial Ornstein-Uhlenbeck process reaches a certain point is very useful and plays an important role. We also give its distribution function in the case that the starting point is closer to the origin than the arrival site.
{"title":"Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes","authors":"Yuji Hamana","doi":"10.7494/opmath.2023.43.2.145","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.2.145","url":null,"abstract":"This article deals with the first hitting times of a Bessel process to a square-root boundary. We obtain the explicit form of the distribution function of the hitting time by means of zeros of the confluent hypergeometric function with respect to the first parameter. In deducing the distribution function, the time that a radial Ornstein-Uhlenbeck process reaches a certain point is very useful and plays an important role. We also give its distribution function in the case that the starting point is closer to the origin than the arrival site.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342739","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.3.393
M. Changat, Lekshmi Kamal K. Sheela, Prasanth G. Narasimha-Shenoi
The interval function and the induced path function are two well studied class of set functions of a connected graph having interesting properties and applications to convexity, metric graph theory. Both these functions can be framed as special instances of a general set function termed as a transit function defined on the Cartesian product of a non-empty set (V) to the power set of (V) satisfying the expansive, symmetric and idempotent axioms. In this paper, we propose a set of independent first order betweenness axioms on an arbitrary transit function and provide characterization of the interval function of Ptolemaic graphs and the induced path function of chordal graphs in terms of an arbitrary transit function. This in turn gives new characterizations of the Ptolemaic and chordal graphs.
{"title":"Axiomatic characterizations of Ptolemaic and chordal graphs","authors":"M. Changat, Lekshmi Kamal K. Sheela, Prasanth G. Narasimha-Shenoi","doi":"10.7494/opmath.2023.43.3.393","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.3.393","url":null,"abstract":"The interval function and the induced path function are two well studied class of set functions of a connected graph having interesting properties and applications to convexity, metric graph theory. Both these functions can be framed as special instances of a general set function termed as a transit function defined on the Cartesian product of a non-empty set (V) to the power set of (V) satisfying the expansive, symmetric and idempotent axioms. In this paper, we propose a set of independent first order betweenness axioms on an arbitrary transit function and provide characterization of the interval function of Ptolemaic graphs and the induced path function of chordal graphs in terms of an arbitrary transit function. This in turn gives new characterizations of the Ptolemaic and chordal graphs.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342850","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.5.621
N. Charradi, S. Sajid
This paper deals with the existence of solutions to the following differential inclusion: (dot{x}(t)in F(t,x(t))) a.e. on ([0, T[) and (x(t)in K), for all (t in [0, T]), where (F: [0, T]times K rightarrow 2^E) is a Carath�odory multifunction and (K) is a closed subset of a separable Banach space (E).
本文讨论了以下微分包含的解的存在性:(dot{x}(t)in F(t,x(t))) a.e.在([0, T[)和(x(t)in K)上，对于所有(t in [0, T])，其中(F: [0, T]times K rightarrow 2^E)是Carath - odory多函数，(K)是可分Banach空间(E)的闭子集。
{"title":"A viability result for Carath�odory non-convex differential inclusion in Banach spaces","authors":"N. Charradi, S. Sajid","doi":"10.7494/opmath.2023.43.5.621","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.5.621","url":null,"abstract":"This paper deals with the existence of solutions to the following differential inclusion: (dot{x}(t)in F(t,x(t))) a.e. on ([0, T[) and (x(t)in K), for all (t in [0, T]), where (F: [0, T]times K rightarrow 2^E) is a Carath�odory multifunction and (K) is a closed subset of a separable Banach space (E).","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71343126","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.6.813
Anna Kosiorowska, Adrian Michalski, Iwona W�och
In this paper we consider secondary dominating sets, also named as ((1,k))-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the ((1,1))-dominating sets and proper ((1,2))-dominating sets. We introduce ((1,overline{2}))-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.
{"title":"On minimum intersections of certain secondary dominating sets in graphs","authors":"Anna Kosiorowska, Adrian Michalski, Iwona W�och","doi":"10.7494/opmath.2023.43.6.813","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.6.813","url":null,"abstract":"In this paper we consider secondary dominating sets, also named as ((1,k))-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the ((1,1))-dominating sets and proper ((1,2))-dominating sets. We introduce ((1,overline{2}))-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71343334","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.2.199
Fernando A. Morales
We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.
{"title":"Asymptotic analysis of the steady advection-diffusion problem in axial domains","authors":"Fernando A. Morales","doi":"10.7494/opmath.2023.43.2.199","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.2.199","url":null,"abstract":"We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342974","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 : 2023-01-01DOI: 10.7494/opmath.2023.43.5.651
Ay�e Kabata�
In this paper, asymptotic formulae for solutions and Green's function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.
本文研究了一类边值问题的解和格林函数在方程和边界条件包含谱参数时的渐近公式。
{"title":"One boundary value problem including a spectral parameter in all boundary conditions","authors":"Ay�e Kabata�","doi":"10.7494/opmath.2023.43.5.651","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.5.651","url":null,"abstract":"In this paper, asymptotic formulae for solutions and Green's function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71343177","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 : 2022-09-19DOI: 10.7494/opmath.2023.43.4.493
�ywilla Fechner, E. Gselmann, L�szl� Sz�kelyhidi
In one of our former papers "Endomorphisms of the measure algebra of commutative hypergroups" we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra.
{"title":"Generalized derivations and generalized exponential monomials on hypergroups","authors":"�ywilla Fechner, E. Gselmann, L�szl� Sz�kelyhidi","doi":"10.7494/opmath.2023.43.4.493","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.4.493","url":null,"abstract":"In one of our former papers \"Endomorphisms of the measure algebra of commutative hypergroups\" we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44720795","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 : 2022-06-10DOI: 10.7494/opmath.2023.43.1.101
M. Lindner, Dennis Schmeckpeper
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.
{"title":"A note on Hausdorff convergence of pseudospectra","authors":"M. Lindner, Dennis Schmeckpeper","doi":"10.7494/opmath.2023.43.1.101","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.1.101","url":null,"abstract":"For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47684028","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 : 2022-01-31DOI: 10.7494/opmath.2022.42.3.459
E. Zalot
The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.
{"title":"Spectral resolutions for non-self-adjoint block convolution operators","authors":"E. Zalot","doi":"10.7494/opmath.2022.42.3.459","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.3.459","url":null,"abstract":"The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49506745","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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