A $p$-parametric robot manipulator is a mapping $g$ of $mathbb{R}^p$ into the homogeneous space $P=(C_6times C_6)/mathop{rm Diag}(C_6times C_6)$ represented by the formula $g(u_1,u_2,dots ,u_p)=exp (u_1 X^1)cdot dots cdot exp (u_p X^p)$, where $C_6$ is the Lie group of all congruences of $E_3$ and $X^1,X^2,dots ,X^p$ are fixed vectors from the Lie algebra of $C_6$. In this paper the $3$-parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University in Prague.
{"title":"3-parametric robot manipulator with intersecting axes","authors":"Jerzy Gądek","doi":"10.21136/AM.1995.134284","DOIUrl":"https://doi.org/10.21136/AM.1995.134284","url":null,"abstract":"A $p$-parametric robot manipulator is a mapping $g$ of $mathbb{R}^p$ into the homogeneous space $P=(C_6times C_6)/mathop{rm Diag}(C_6times C_6)$ represented by the formula $g(u_1,u_2,dots ,u_p)=exp (u_1 X^1)cdot dots cdot exp (u_p X^p)$, where $C_6$ is the Lie group of all congruences of $E_3$ and $X^1,X^2,dots ,X^p$ are fixed vectors from the Lie algebra of $C_6$. In this paper the $3$-parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University in Prague.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"63 1","pages":"131-145"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73915995","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. In this paper, two algorithms are proposed to so l ve systems of a l gebraic equations generated by a discretization procedure of the weak formu l ation of boundary va l ue prob l ems for systems of non l inear e ll iptic equations. The first a l gorithm, Newton-CG-MG, is suitab l e for systems with gradient mappings, whi l e the second, Newton-CE-MG, can be app l ied to more genera l systems. Convergence theorems are proved and app l ication to the semiconductor device mode ll ing is described.
{"title":"Convergent algorithms suitable for the solution of the semiconductor device equations","authors":"Miroslav Pospíšek","doi":"10.21136/am.1995.134283","DOIUrl":"https://doi.org/10.21136/am.1995.134283","url":null,"abstract":"Summary. In this paper, two algorithms are proposed to so l ve systems of a l gebraic equations generated by a discretization procedure of the weak formu l ation of boundary va l ue prob l ems for systems of non l inear e ll iptic equations. The first a l gorithm, Newton-CG-MG, is suitab l e for systems with gradient mappings, whi l e the second, Newton-CE-MG, can be app l ied to more genera l systems. Convergence theorems are proved and app l ication to the semiconductor device mode ll ing is described.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"28 1","pages":"107-130"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86127797","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":"A matrix constructive method for the analytic-numerical solution of coupled partial differential systems","authors":"L. Jódar, E. Navarro, M. Ferrer","doi":"10.21136/am.1995.134302","DOIUrl":"https://doi.org/10.21136/am.1995.134302","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"39 1","pages":"391-400"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85744350","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-quadratic estimators in a special structure of thelinear model","authors":"G. Wimmer","doi":"10.21136/am.1995.134282","DOIUrl":"https://doi.org/10.21136/am.1995.134282","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84237891","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 paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and their bases are given by the so-called fundamental splines.
{"title":"Interpolating and smoothing biquadratic spline","authors":"R. Kučera","doi":"10.21136/am.1995.134298","DOIUrl":"https://doi.org/10.21136/am.1995.134298","url":null,"abstract":"The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and their bases are given by the so-called fundamental splines.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"19 1","pages":"339-356"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77932588","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 describe a numerical method for the equation $u_t + pu_x - varepsilon u_{xx} = f$ in $(0,1) times (0,T)$ with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.
{"title":"An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection","authors":"J. Dalík, H. Růžičková","doi":"10.21136/am.1995.134300","DOIUrl":"https://doi.org/10.21136/am.1995.134300","url":null,"abstract":"We describe a numerical method for the equation $u_t + pu_x - varepsilon u_{xx} = f$ in $(0,1) times (0,T)$ with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"183 1","pages":"367-380"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77484058","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":"Double points on characteristics","authors":"O. Röschel","doi":"10.21136/am.1995.134301","DOIUrl":"https://doi.org/10.21136/am.1995.134301","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"1 1","pages":"381-390"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77519509","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 explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $ple 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p-1$. Numerical results are presented which demonstrate that constant step size TSRK can be both effectively and efficiently used in an Euler equation solver. Furthermore, a comparison with a variable step size formulation shows that in these solvers the variable step size formulation offers no advantages compared to the constant step size implementation.
{"title":"Explicit two-step Runge-Kutta methods","authors":"Z. Jackiewicz, R. Renaut, M. Zennaro","doi":"10.21136/am.1995.134306","DOIUrl":"https://doi.org/10.21136/am.1995.134306","url":null,"abstract":"The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $ple 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p-1$. Numerical results are presented which demonstrate that constant step size TSRK can be both effectively and efficiently used in an Euler equation solver. Furthermore, a comparison with a variable step size formulation shows that in these solvers the variable step size formulation offers no advantages compared to the constant step size implementation.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"121 1","pages":"433-456"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74692542","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":"Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model","authors":"G. Wimmer","doi":"10.21136/AM.1995.134305","DOIUrl":"https://doi.org/10.21136/AM.1995.134305","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"47 1","pages":"411-431"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82426804","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":"Proceedings of the 2nd Summer Conference Numerical Modelling in Continuum Mechanics. Preface","authors":"M. Feistauer, R. Rannacher, K. Kozel","doi":"10.21136/am.1995.134288","DOIUrl":"https://doi.org/10.21136/am.1995.134288","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"107 1","pages":"161-162"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77412627","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：