{"title":"On the solvability of some multi-point boundary value problems","authors":"C. P. Gupta, S. Ntouyas, P. Tsamatos","doi":"10.21136/am.1996.134310","DOIUrl":"https://doi.org/10.21136/am.1996.134310","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"2 1","pages":"1-17"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87619310","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}
Summary. The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the "locking" effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.
{"title":"Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements","authors":"I. Hlavácek","doi":"10.21136/am.1996.134316","DOIUrl":"https://doi.org/10.21136/am.1996.134316","url":null,"abstract":"Summary. The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the \"locking\" effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"18 1","pages":"107-121"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90696262","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}
Summary. We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.
{"title":"Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls","authors":"J. Daňková, J. Haslinger","doi":"10.21136/am.1996.134317","DOIUrl":"https://doi.org/10.21136/am.1996.134317","url":null,"abstract":"Summary. We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"16 1","pages":"123-147"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90139588","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 some of the cointegration tests applied to a single equation are compared. Many of the existent cointegration tests are simply extensions of the unit root tests applied to the residuals of the cointegrating regression and the habitual $H_{0}$ is no cointegration. However, some non residual-based tests and some tests of the opposite null hypothesis have recently appeared in literature. Monte Carlo simulations have been used for the power comparison of the nine selected tests ($ADF$, $hat{Z}_{alpha }$, $hat{Z}_{t}$, $DHS$, $J1$, $H1$, $H2$, $C$, $LBI$) using several types of data generating processes.
{"title":"A comparison of cointegration tests","authors":"Petr Mariel","doi":"10.21136/am.1996.134335","DOIUrl":"https://doi.org/10.21136/am.1996.134335","url":null,"abstract":"In this paper some of the cointegration tests applied to a single equation are compared. Many of the existent cointegration tests are simply extensions of the unit root tests applied to the residuals of the cointegrating regression and the habitual $H_{0}$ is no cointegration. However, some non residual-based tests and some tests of the opposite null hypothesis have recently appeared in literature. Monte Carlo simulations have been used for the power comparison of the nine selected tests ($ADF$, $hat{Z}_{alpha }$, $hat{Z}_{t}$, $DHS$, $J1$, $H1$, $H2$, $C$, $LBI$) using several types of data generating processes.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"13 1","pages":"411-431"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82976123","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}
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.
{"title":"Regularity and optimal control of quasicoupled and coupled heating processes","authors":"J. Jarusek","doi":"10.21136/am.1996.134315","DOIUrl":"https://doi.org/10.21136/am.1996.134315","url":null,"abstract":"Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"35 1","pages":"81-106"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74699101","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}
The error propagation law is investigated in the case of a nonlinear function of measured data with non-negligible uncertainty.
研究了测量数据具有不可忽略不确定性的非线性函数的误差传播规律。
{"title":"Nonlinear error propagation law","authors":"L. Kubácek","doi":"10.21136/am.1996.134330","DOIUrl":"https://doi.org/10.21136/am.1996.134330","url":null,"abstract":"The error propagation law is investigated in the case of a nonlinear function of measured data with non-negligible uncertainty.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"1 1","pages":"329-345"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79165637","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":"Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function","authors":"I. Hlavácek","doi":"10.21136/AM.1996.134337","DOIUrl":"https://doi.org/10.21136/AM.1996.134337","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"127 1","pages":"447-466"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73949250","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":"Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type","authors":"Liping Liu, M. Křížek, P. Neittaanmäki","doi":"10.21136/am.1996.134338","DOIUrl":"https://doi.org/10.21136/am.1996.134338","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"73 1","pages":"467-478"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80371681","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}
Summary. We deal with an optimal control prob l em with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequa l ity. The existence and uniqueness theorem for the state prob l em and the existence of an optima l thickness function are proved.
{"title":"Optimal design problems for a dynamic viscoelastic plate. I. Short memory material","authors":"I. Bock","doi":"10.21136/am.1995.134295","DOIUrl":"https://doi.org/10.21136/am.1995.134295","url":null,"abstract":"Summary. We deal with an optimal control prob l em with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequa l ity. The existence and uniqueness theorem for the state prob l em and the existence of an optima l thickness function are proved.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"23 1","pages":"285-304"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84649669","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}
Summary. We discuss the formulation o f a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been devel oped for parallel, distributed memory, message passing machines. The numerical proce dures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions of dissolved chemical species in groundwater. Domain decomposition, symmetric and nonsymmetric solvers have been developed for solving the systems of equations resulting from the discretization of the model. Results from applying this simu l ator to a bioremediation field problem with several injection and production wells each having multiple screens are presented.
{"title":"A parallel algorithm for two phase multicomponent contaminant transport","authors":"T. Arbogast, C. Dawson, M. Wheeler","doi":"10.21136/am.1995.134289","DOIUrl":"https://doi.org/10.21136/am.1995.134289","url":null,"abstract":"Summary. We discuss the formulation o f a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been devel oped for parallel, distributed memory, message passing machines. The numerical proce dures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions of dissolved chemical species in groundwater. Domain decomposition, symmetric and nonsymmetric solvers have been developed for solving the systems of equations resulting from the discretization of the model. Results from applying this simu l ator to a bioremediation field problem with several injection and production wells each having multiple screens are presented.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"6 1","pages":"163-174"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76000869","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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