Pub Date : 1900-01-01DOI: 10.3318/PRIA.2005.105.2.79
J. Bès, Kit C. Chan, Rebecca Sanders
Such a vector x is called a weakly sequentially hypercyclic vector for T. If there is an orbit orb(T, x) that is dense in X in the weak (respectively, norm) topology of X. we say that T is weakly hypercyclic (respectively, norm hypercyclic), and that x is a weakly (respectively, norm) hypercyclic vector for T. Clearly if T is norm hypercyclic, then T is weakly sequentially hypercyclic, which in turn implies T is weakly hypercyclic. Similarly, an operator T on a Banach space X is (a) norm supercyclic (b) weakly supercyclic (c) weakly sequentially supercyclic, provided there exists a vector x so that Orb(span(x),T) = {XTkx : X e C, k > 0} is (a) norm dense, (b) weakly dense, (c) weakly sequentially dense in X, respectively. It is not known whether an operator can be weakly sequentially hypercyclic
这样的向量x称为T的弱序超循环向量。如果在x的弱(分别，范数)拓扑中存在一个密集于x的轨道球(T, x)，我们说T是弱超循环(分别，范数超循环)，并且x是T的弱(分别，范数)超循环向量。显然，如果T是范数超循环，那么T是弱序超循环，这反过来意味着T是弱超循环。同样，在Banach空间X上的算子T是(a)范数超环(b)弱超环(c)弱序超环，只要存在一个向量X使得Orb(span(X)，T) = {XTkx: X ec, k > 0}分别在X上是(a)范数密集，(b)弱密集，(c)弱序密集。目前还不知道一个算子是否可以是弱序超循环的
{"title":"EVERY WEAKLY SEQUENTIALLY HYPERCYCLIC SHIFT IS NORM HYPERCYCLIC","authors":"J. Bès, Kit C. Chan, Rebecca Sanders","doi":"10.3318/PRIA.2005.105.2.79","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.2.79","url":null,"abstract":"Such a vector x is called a weakly sequentially hypercyclic vector for T. If there is an orbit orb(T, x) that is dense in X in the weak (respectively, norm) topology of X. we say that T is weakly hypercyclic (respectively, norm hypercyclic), and that x is a weakly (respectively, norm) hypercyclic vector for T. Clearly if T is norm hypercyclic, then T is weakly sequentially hypercyclic, which in turn implies T is weakly hypercyclic. Similarly, an operator T on a Banach space X is (a) norm supercyclic (b) weakly supercyclic (c) weakly sequentially supercyclic, provided there exists a vector x so that Orb(span(x),T) = {XTkx : X e C, k > 0} is (a) norm dense, (b) weakly dense, (c) weakly sequentially dense in X, respectively. It is not known whether an operator can be weakly sequentially hypercyclic","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128746151","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}
{"title":"The imp's staircase step response for an arbitrarily underdamped\u0000 second order system with setpoint filter","authors":"A. D. de Paor","doi":"10.1353/mpr.2020.0001","DOIUrl":"https://doi.org/10.1353/mpr.2020.0001","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128601892","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}
{"title":"IRREDUCIBLE REPRESENTATIONS OF HILBERT C-MODULES","authors":"Ljiljana Arambašić","doi":"10.1353/mpr.2005.0008","DOIUrl":"https://doi.org/10.1353/mpr.2005.0008","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131078022","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}
{"title":"From trivial spectrum subspaces to spaces of diagonalisable real matrices","authors":"Clément de Seguins Pazzis","doi":"10.1353/mpr.2018.0001","DOIUrl":"https://doi.org/10.1353/mpr.2018.0001","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126863407","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}
{"title":"On α-simply presented abelian p-groups","authors":"P. Danchev","doi":"10.1353/mpr.2014.0003","DOIUrl":"https://doi.org/10.1353/mpr.2014.0003","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123069244","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 : 1900-01-01DOI: 10.3318/PRIA.2014.114.12
F. J. Bertoloto
{"title":"Weak versions of Banach spaces of vector-valued functions","authors":"F. J. Bertoloto","doi":"10.3318/PRIA.2014.114.12","DOIUrl":"https://doi.org/10.3318/PRIA.2014.114.12","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122283651","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 : 1900-01-01DOI: 10.3318/PRIA.2002.102.1.49
J. King, M. Meere
In this paper we propose a new model for impurity diffusion in compound semiconductors. The model incorporates both the kick-out and the dissociative mechanism, as well as charge effects; the resulting system includes as limit cases many models that have previously appeared in the literature. An initial–boundary value problem that models surface source in-diffusion conditions is then considered. The model is studied using a combination of asymptotic and numerical techniques. In particular, the transition from dissociative to kick-out behaviour is analysed, with some noteworthy features of the solutions being highlighted in a number of regimes, including a novel class of moving boundary problems.
{"title":"A Combined Dissociative and Kick-out Diffusion Model with Charge Effects, Part I: In-Diffusion","authors":"J. King, M. Meere","doi":"10.3318/PRIA.2002.102.1.49","DOIUrl":"https://doi.org/10.3318/PRIA.2002.102.1.49","url":null,"abstract":"In this paper we propose a new model for impurity diffusion in compound semiconductors. The model incorporates both the kick-out and the dissociative mechanism, as well as charge effects; the resulting system includes as limit cases many models that have previously appeared in the literature. An initial–boundary value problem that models surface source in-diffusion conditions is then considered. The model is studied using a combination of asymptotic and numerical techniques. In particular, the transition from dissociative to kick-out behaviour is analysed, with some noteworthy features of the solutions being highlighted in a number of regimes, including a novel class of moving boundary problems.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121483739","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}
{"title":"Cauchy Integral and Pluriharmonic Conjugate Functions on Banach Function Spaces","authors":"K. Ho","doi":"10.1353/mpr.2023.0001","DOIUrl":"https://doi.org/10.1353/mpr.2023.0001","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122390102","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 : 1900-01-01DOI: 10.3318/PRIA.2003.103.2.143
T. T. West
The spectral theory of compact monothetic semigroups of linear operators examined by Kaashoek and West in [1], [2] together with two block matrix theorems where the blocks are either strictly positive or zero are used to give an exposition of Perron-Frobenius theory of positive matrices. The approach in this paper is based on ideas of Smyth and West developed in [4], [5]. We consider a linear operator T in finite dimensions which has a matrix representation [T] relative to a given basis. Where there is no ambiguity we often write the matrix as T. T ≥ 0 if [T] ij ≥ 0 (∀ i,j) while T > 0 if [T] ij > 0 (∀ i,j). The spectrum and spectral radius of T will be denoted by σ(T) and r(T) respectively. The trace of T (the sum of its eigenvalues) will be written as tr(T), and the peripheral spectrum will be denoted by π(T) = {λ ∈ σ(T); |λ| = r(T)}. The i th row and j th column of T relative to the given basis will be written row i (T) and col j (T) and the diagonal of T will be denoted diag(T). The spectral projection of T relative to π(T) will be written P π. Smyth [5] has introduced a hierarchy of subsets of matrices T ≥ 0. Definitions. (i) T is positive if T > 0; (ii) T is primitive if T k > 0 for some positive integer k; (iii) T is connected if ∀ i,j ∃ a positive integer k such that [T k ] ij > 0; (iv) T is potent if diag(T k) > 0 for some positive integer k; (v) T is zero-free if no row or column is zero; (vi) T has positive spectral radius.
利用Kaashoek和West在[1]，[2]中检验的线性算子紧一元半群的谱理论，以及两个块为严格正或为零的块矩阵定理，给出了Perron-Frobenius正矩阵理论。本文的方法是基于Smyth和West在[4]、[5]中发展起来的思想。我们考虑一个有限维的线性算子T，它相对于给定的基有一个矩阵表示[T]。在没有歧义的情况下，我们通常将矩阵写成T，如果[T] ij≥0(∀i,j)，则T≥0，而如果[T] ij > 0(∀i,j)，则T > 0。T的谱和谱半径分别用σ(T)和r(T)表示。T的迹(其特征值之和)记为tr(T)，外围频谱记为π(T) = {λ∈σ(T);|λ| = r(T)}。T相对于给定基的第i行和第j列写成row i (T)和col j (T)， T的对角线记作diag(T)。T相对于π(T)的光谱投影写成P π。Smyth[5]引入了矩阵T≥0的子集层次。定义。(i) T > 0时T为正;(ii)对于某正整数k，当T k > 0时，T为原元;(iii)∀i,j∃是一个正整数k，使得[T k] ij > 0;(iv)对于某正整数k，当diag(tk) > 0时，T是有效的;(v)如果没有行或列为零，则T为零;(vi) T具有正的谱半径。
{"title":"Compact Semigroups of Positive Matrices","authors":"T. T. West","doi":"10.3318/PRIA.2003.103.2.143","DOIUrl":"https://doi.org/10.3318/PRIA.2003.103.2.143","url":null,"abstract":"The spectral theory of compact monothetic semigroups of linear operators examined by Kaashoek and West in [1], [2] together with two block matrix theorems where the blocks are either strictly positive or zero are used to give an exposition of Perron-Frobenius theory of positive matrices. The approach in this paper is based on ideas of Smyth and West developed in [4], [5]. We consider a linear operator T in finite dimensions which has a matrix representation [T] relative to a given basis. Where there is no ambiguity we often write the matrix as T. T ≥ 0 if [T] ij ≥ 0 (∀ i,j) while T > 0 if [T] ij > 0 (∀ i,j). The spectrum and spectral radius of T will be denoted by σ(T) and r(T) respectively. The trace of T (the sum of its eigenvalues) will be written as tr(T), and the peripheral spectrum will be denoted by π(T) = {λ ∈ σ(T); |λ| = r(T)}. The i th row and j th column of T relative to the given basis will be written row i (T) and col j (T) and the diagonal of T will be denoted diag(T). The spectral projection of T relative to π(T) will be written P π. Smyth [5] has introduced a hierarchy of subsets of matrices T ≥ 0. Definitions. (i) T is positive if T > 0; (ii) T is primitive if T k > 0 for some positive integer k; (iii) T is connected if ∀ i,j ∃ a positive integer k such that [T k ] ij > 0; (iv) T is potent if diag(T k) > 0 for some positive integer k; (v) T is zero-free if no row or column is zero; (vi) T has positive spectral radius.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132562976","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 : 1900-01-01DOI: 10.3318/PRIA.2007.107.1.43
U. Saravanan, K. Rajagopal
We study several simple boundary value problems for a special class of inhomogeneous, isotropie, compressible elastic solids: inflation of a spherical shell; bending, stretching and shearing of a rectangular block; and straightening, stretching and shearing of a sector of a hollow cylinder. The purpose of the study is twofold: to establish new exact solutions to boundary value problems concerning inhomogeneous, isotropie, compressible elastic solids that have technological relevance (to the deformation of layered composites); and to reaffirm a thesis concerning an inherent difficulty with regard to the homogenization techniques that are in vogue that appeal to the stored energy in the homogenized body being the same as that for the inhomogeneous body. In addition to establishing new exact solutions for a class of inhomogeneous elastic solids, the study reinforces the thesis of Saravanan and Rajagopal that great care ought to be exercised in approximating even a very mildly inhomogeneous body by an equivalent homogeneous body when large deformations are involved.
{"title":"ON SOME FINITE DEFORMATIONS OF INHOMOGENEOUS COMPRESSIBLE ELASTIC SOLIDS","authors":"U. Saravanan, K. Rajagopal","doi":"10.3318/PRIA.2007.107.1.43","DOIUrl":"https://doi.org/10.3318/PRIA.2007.107.1.43","url":null,"abstract":"We study several simple boundary value problems for a special class of inhomogeneous, isotropie, compressible elastic solids: inflation of a spherical shell; bending, stretching and shearing of a rectangular block; and straightening, stretching and shearing of a sector of a hollow cylinder. The purpose of the study is twofold: to establish new exact solutions to boundary value problems concerning inhomogeneous, isotropie, compressible elastic solids that have technological relevance (to the deformation of layered composites); and to reaffirm a thesis concerning an inherent difficulty with regard to the homogenization techniques that are in vogue that appeal to the stored energy in the homogenized body being the same as that for the inhomogeneous body. In addition to establishing new exact solutions for a class of inhomogeneous elastic solids, the study reinforces the thesis of Saravanan and Rajagopal that great care ought to be exercised in approximating even a very mildly inhomogeneous body by an equivalent homogeneous body when large deformations are involved.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133280656","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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