Pub Date : 1900-01-01DOI: 10.3318/PRIA.2006.106.1.19
J. N. Flavin
A Dirichlet boundary value problem for a nonlinear elliptic p.d.e. is considered in a right cylinder, the boundary value on the lateral surface being independent of the axial coordinate. An inequality estimate, in terms of data, is obtained for the spatial rate of convergence as one recedes from the plane ends of the solution of the problem, to the solution of the corresponding two-dimensional solution (induced by the lateral boundary condition). The estimate is for a suitably defined, cross-sectional measure, which is positive-definite in the perturbation (i.e. the difference between the solution and that of the two-dimensional state). The estimate is obtained by establishing a differential inequality for the cross-sectional measure. The cross-sectional measure is analogous to a Liapunov functional that has been used in time-dependent, initial boundary value problems. The paper concludes with a discussion of the estimate obtained.
{"title":"A SPATIAL DECAY ESTIMATE FOR A NONLINEAR ELLIPTIC PROBLEM","authors":"J. N. Flavin","doi":"10.3318/PRIA.2006.106.1.19","DOIUrl":"https://doi.org/10.3318/PRIA.2006.106.1.19","url":null,"abstract":"A Dirichlet boundary value problem for a nonlinear elliptic p.d.e. is considered in a right cylinder, the boundary value on the lateral surface being independent of the axial coordinate. An inequality estimate, in terms of data, is obtained for the spatial rate of convergence as one recedes from the plane ends of the solution of the problem, to the solution of the corresponding two-dimensional solution (induced by the lateral boundary condition). The estimate is for a suitably defined, cross-sectional measure, which is positive-definite in the perturbation (i.e. the difference between the solution and that of the two-dimensional state). The estimate is obtained by establishing a differential inequality for the cross-sectional measure. The cross-sectional measure is analogous to a Liapunov functional that has been used in time-dependent, initial boundary value problems. The paper concludes with a discussion of the estimate obtained.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"50 2 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":"133750120","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.2006.106.2.115
K. Rajagopal, G. Saccomandi
There are many applications, elasto-hydrodynamics being one, where the fluid can be modelled as an incompressible fluid with a viscosity that depends on the pressure (see [15]). The justification for such an assumption stems from the fact that while the density changes by merely a few percent, the pressure can change significantly and the viscosity can change by several orders of magnitude. Of course, there is the possibility that the dependence of viscosity on density is such that even a small change in density causes this change. Experiments clearly suggest that viscosity varies exponentially with pressure and that it is the relationship between the viscosity and the pressure that causes the tremendous change that occurs in the viscosity. That the viscosity of liquids could depend upon the pressure was known to the pioneers of the field. Stokes [14] is in fact very careful to delineate the special class of flows, those in channels and pipes at moderate pressures, when viscosity could be assumed a constant. There is also a considerable amount of literature even prior to 1930 concerning the variation of viscosity with pressure (see Bridgman [4] on the physics of high pressures for a detailed discussion of the same). Bridgman [4] makes it abundantly clear that he devoted a great deal of attention to determining the variation
{"title":"UNSTEADY EXACT SOLUTION FOR FLOWS OF FLUIDS WITH PRESSURE-DEPENDENT VISCOSITIES","authors":"K. Rajagopal, G. Saccomandi","doi":"10.3318/PRIA.2006.106.2.115","DOIUrl":"https://doi.org/10.3318/PRIA.2006.106.2.115","url":null,"abstract":"There are many applications, elasto-hydrodynamics being one, where the fluid can be modelled as an incompressible fluid with a viscosity that depends on the pressure (see [15]). The justification for such an assumption stems from the fact that while the density changes by merely a few percent, the pressure can change significantly and the viscosity can change by several orders of magnitude. Of course, there is the possibility that the dependence of viscosity on density is such that even a small change in density causes this change. Experiments clearly suggest that viscosity varies exponentially with pressure and that it is the relationship between the viscosity and the pressure that causes the tremendous change that occurs in the viscosity. That the viscosity of liquids could depend upon the pressure was known to the pioneers of the field. Stokes [14] is in fact very careful to delineate the special class of flows, those in channels and pipes at moderate pressures, when viscosity could be assumed a constant. There is also a considerable amount of literature even prior to 1930 concerning the variation of viscosity with pressure (see Bridgman [4] on the physics of high pressures for a detailed discussion of the same). Bridgman [4] makes it abundantly clear that he devoted a great deal of attention to determining the variation","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"64 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":"132349702","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.2016.116.07
B. Duggal, D. Djordjevic, R. Harte, S. Zivkovic-Zlatanovic
{"title":"Polynomially Meromorphic Operators","authors":"B. Duggal, D. Djordjevic, R. Harte, S. Zivkovic-Zlatanovic","doi":"10.3318/PRIA.2016.116.07","DOIUrl":"https://doi.org/10.3318/PRIA.2016.116.07","url":null,"abstract":"","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":"133060622","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.2007.107.2.183
N. Grenier-Boley
Let Κ be a field of arbitrary characteristic and let g be a prime number different from the characteristic of K. If A is a central simple algebra over Κ whose index is a power of q, we show the triviality of the Whitehead groups SKi(A) and USKi(A) when the cohomological ^-dimension of Κ is at most 2. We give a global version of this result and indicate what can be done in the case where the index of the algebra is a power of the characteristic of the field. Triviality results of the Whitehead group KiSpin(A) are easily derived.
{"title":"ON THE TRIVIALITY OF CERTAIN WHITEHEAD GROUPS","authors":"N. Grenier-Boley","doi":"10.3318/PRIA.2007.107.2.183","DOIUrl":"https://doi.org/10.3318/PRIA.2007.107.2.183","url":null,"abstract":"Let Κ be a field of arbitrary characteristic and let g be a prime number different from the characteristic of K. If A is a central simple algebra over Κ whose index is a power of q, we show the triviality of the Whitehead groups SKi(A) and USKi(A) when the cohomological ^-dimension of Κ is at most 2. We give a global version of this result and indicate what can be done in the case where the index of the algebra is a power of the characteristic of the field. Triviality results of the Whitehead group KiSpin(A) are easily derived.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"14 2 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":"133815237","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.2016.116.05
Elmiloud Chil, Mokaddem Mohamed
{"title":"A relationship between the order convergence and the relative uniform convergence in a Riesz space","authors":"Elmiloud Chil, Mokaddem Mohamed","doi":"10.3318/pria.2016.116.05","DOIUrl":"https://doi.org/10.3318/pria.2016.116.05","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":"115220897","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.2008.109.1.67
L. Theate, J. Wengenroth
We will show that many results related to invertibility in Frechet algebras can be proved by a general version of a classical method of R. Arens. In particular, we show (even improvements of) recent results of S. Dineen by arguments free of any technicalities.
{"title":"RIGHT-INVERTIBILITY FOR FRÉCHET ALGEBRAS","authors":"L. Theate, J. Wengenroth","doi":"10.3318/PRIA.2008.109.1.67","DOIUrl":"https://doi.org/10.3318/PRIA.2008.109.1.67","url":null,"abstract":"We will show that many results related to invertibility in Frechet algebras can be proved by a general version of a classical method of R. Arens. In particular, we show (even improvements of) recent results of S. Dineen by arguments free of any technicalities.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"4 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":"114347521","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.2004.104.2.211
M. Crabb, J. Duncan, C. McGregor
{"title":"SPECTRA IN SOME INVERSE SEMIGROUP ALGEBRAS","authors":"M. Crabb, J. Duncan, C. McGregor","doi":"10.3318/PRIA.2004.104.2.211","DOIUrl":"https://doi.org/10.3318/PRIA.2004.104.2.211","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"13 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":"115363061","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.2008.108.2.205
M. Curran
{"title":"AUTOMORPHISMS OF SEMIDIRECT PRODUCTS","authors":"M. Curran","doi":"10.3318/PRIA.2008.108.2.205","DOIUrl":"https://doi.org/10.3318/PRIA.2008.108.2.205","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"118 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":"115374488","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":"Some Classes of Banach Analytic Spaces","authors":"Le Mau Hai","doi":"10.1353/mpr.2016.0006","DOIUrl":"https://doi.org/10.1353/mpr.2016.0006","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"16 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":"124463312","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":"Path-Connected Components in Weighted Composition Operators on the Disk Algebra with the Essential Operator Norm","authors":"K. Izuchi, Y. Izuchi","doi":"10.3318/PRIA.2015.115.5","DOIUrl":"https://doi.org/10.3318/PRIA.2015.115.5","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"65 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":"124489389","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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