Till now the finite element analysis for semiregular finite elements has been restricted to interpolation theorems (see [2], [3], [5] and references there). In this paper a complete finite element analysis is presented briefly.
{"title":"Finite element variational crimes in the case of semiregular elements","authors":"A. Ženíšek","doi":"10.21136/am.1996.134332","DOIUrl":"https://doi.org/10.21136/am.1996.134332","url":null,"abstract":"Till now the finite element analysis for semiregular finite elements has been restricted to interpolation theorems (see [2], [3], [5] and references there). In this paper a complete finite element analysis is presented briefly.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"44 1","pages":"367-398"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90126773","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 actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.
{"title":"Dynamic credibility with outliers and missing observations","authors":"T. Cipra","doi":"10.21136/AM.1996.134318","DOIUrl":"https://doi.org/10.21136/AM.1996.134318","url":null,"abstract":"In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"12 1","pages":"149-159"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81783660","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":"Seasonal time series with missing observations","authors":"T. Ratinger","doi":"10.21136/AM.1996.134312","DOIUrl":"https://doi.org/10.21136/AM.1996.134312","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"47 1","pages":"41-55"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80603772","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":"Linear model with inaccurate variance components","authors":"L. Kubácek","doi":"10.21136/am.1996.134336","DOIUrl":"https://doi.org/10.21136/am.1996.134336","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"46 1","pages":"433-445"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86518118","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 find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.
{"title":"LFS functions in multi-objective programming","authors":"L. Neralić, S. Zlobec","doi":"10.21136/AM.1996.134331","DOIUrl":"https://doi.org/10.21136/AM.1996.134331","url":null,"abstract":"We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"77 1","pages":"347-366"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81178948","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}
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
将一种适用于非均匀三角剖分的新型后处理技术应用于模型最优形状设计问题的灵敏度分析。
{"title":"A recovered gradient method applied to smooth optimal shape problems","authors":"I. Hlavácek, J. Chleboun","doi":"10.21136/am.1996.134327","DOIUrl":"https://doi.org/10.21136/am.1996.134327","url":null,"abstract":"A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"9 1","pages":"281-297"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88808084","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 propose and examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $mathcal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.
{"title":"How to recover the gradient of linear elements on nonuniform triangulations","authors":"I. Hlavácek, M. Křížek, Vladislav Pištora","doi":"10.21136/am.1996.134325","DOIUrl":"https://doi.org/10.21136/am.1996.134325","url":null,"abstract":"We propose and examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $mathcal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"61 1","pages":"241-267"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88372655","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 Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $tau ^V(mathbb{e}) = tau (mathbb{e}) - 2mu _1 Delta mathbb{e}$, where the nonlinear function $tau (mathbb{e})$ satisfies $tau _{ij}(mathbb{e})e_{ij} ge c|mathbb{e}|^p$ or $tau _{ij}(mathbb{e})e_{ij} ge c(|mathbb{e}|^2+|mathbb{e}|^p)$. First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for $p > 1$ for both models. Then, under vanishing higher viscosity $mu _1$, the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for $p > frac{3n}{n+2}$, its uniqueness and regularity for $p ge 1 + frac{2n}{n+2}$. In the case of the second model the existence of the weak solution is proved for $p>1$.
本文研究了具有应力张量$tau ^V(mathbb{e}) = tau (mathbb{e}) - 2mu _1 Delta mathbb{e}$的粘性部分的非牛顿不可压缩流体的Cauchy问题，其中非线性函数$tau (mathbb{e})$满足$tau _{ij}(mathbb{e})e_{ij} ge c|mathbb{e}|^p$或$tau _{ij}(mathbb{e})e_{ij} ge c(|mathbb{e}|^2+|mathbb{e}|^p)$。首先对双极流体模型进行了研究，证明了两种模型$p > 1$弱解的存在性、唯一性和规律性。然后，在高粘度消失$mu _1$条件下，考虑单极流体的柯西问题。对于第一个模型，证明了$p > frac{3n}{n+2}$弱解的存在性，证明了$p ge 1 + frac{2n}{n+2}$弱解的唯一性和正则性。对于第二种模型，证明了$p>1$弱解的存在性。
{"title":"Cauchy problem for the non-newtonian viscous incompressible fluid","authors":"M. Pokorný","doi":"10.21136/am.1996.134320","DOIUrl":"https://doi.org/10.21136/am.1996.134320","url":null,"abstract":"We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $tau ^V(mathbb{e}) = tau (mathbb{e}) - 2mu _1 Delta mathbb{e}$, where the nonlinear function $tau (mathbb{e})$ satisfies $tau _{ij}(mathbb{e})e_{ij} ge c|mathbb{e}|^p$ or $tau _{ij}(mathbb{e})e_{ij} ge c(|mathbb{e}|^2+|mathbb{e}|^p)$. First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for $p > 1$ for both models. Then, under vanishing higher viscosity $mu _1$, the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for $p > frac{3n}{n+2}$, its uniqueness and regularity for $p ge 1 + frac{2n}{n+2}$. In the case of the second model the existence of the weak solution is proved for $p>1$.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"169-201"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74340441","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. This paper concerns an optimal control problem of elliptic singular perturba tions in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained.
{"title":"Singular perturbations in optimal control problem with application to nonlinear structural analysis","authors":"J. Lovísek","doi":"10.21136/am.1996.134328","DOIUrl":"https://doi.org/10.21136/am.1996.134328","url":null,"abstract":"Summary. This paper concerns an optimal control problem of elliptic singular perturba tions in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"58 1","pages":"299-320"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88322904","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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