Pub Date : 1990-01-01DOI: 10.1016/0041-5553(90)90013-I
D.V. Denisov
The necessary and sufficient conditions for an extremum are expressed in local coordinates. It is shown that in some cases irregularity of the constraints at the extremum points does not affect the form of the necessary conditions. A first-order numerical method with a linear rate of convergence is considered.
{"title":"The use of local coordinates in optimization problems","authors":"D.V. Denisov","doi":"10.1016/0041-5553(90)90013-I","DOIUrl":"10.1016/0041-5553(90)90013-I","url":null,"abstract":"<div><p>The necessary and sufficient conditions for an extremum are expressed in local coordinates. It is shown that in some cases irregularity of the constraints at the extremum points does not affect the form of the necessary conditions. A first-order numerical method with a linear rate of convergence is considered.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 107-109"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90013-I","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73943076","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90113-7
M.V. Reztsov
Some data are obtained which enable the results of previous papers on the averaging of composite plates to be generalized to the case of a composition layer whose structure is restricted by requirement of physical symmetry with respect to the middle plane.
{"title":"The properties of effective modulus of composition plates","authors":"M.V. Reztsov","doi":"10.1016/0041-5553(90)90113-7","DOIUrl":"10.1016/0041-5553(90)90113-7","url":null,"abstract":"<div><p>Some data are obtained which enable the results of previous papers on the averaging of composite plates to be generalized to the case of a composition layer whose structure is restricted by requirement of physical symmetry with respect to the middle plane.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 6","pages":"Pages 103-105"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90113-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75646626","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90157-N
A.S. Buldayev
{"title":"A numerical method of control optimization in delay systems for immune response modelling","authors":"A.S. Buldayev","doi":"10.1016/0041-5553(90)90157-N","DOIUrl":"10.1016/0041-5553(90)90157-N","url":null,"abstract":"","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 5","pages":"Pages 18-28"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90157-N","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75452411","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90107-4
E.V. Zakharov, S.I. Safronov, R.P. Tarasov
It is shown that for boundary value problems with commutative finite-order symmetry groups it is possible to use the concepts of convolution and the Fourier transform for finite groups to reduce considerably the order of the matrix equations used to approximate the original integral equations, and thus to extend the range of problems amenable to numerical analysis. An implementation of this method is considered for boundary value problems with Abelian symmetry group of eighth order, describing a quadrupole-type system. Results of a numerical experiment are presented for this case, enabling the efficiency of the method to be estimated.
{"title":"A method for the numerical solution of integral equations in boundary value problems with finite-order Abelian symmetry groups","authors":"E.V. Zakharov, S.I. Safronov, R.P. Tarasov","doi":"10.1016/0041-5553(90)90107-4","DOIUrl":"10.1016/0041-5553(90)90107-4","url":null,"abstract":"<div><p>It is shown that for boundary value problems with commutative finite-order symmetry groups it is possible to use the concepts of convolution and the Fourier transform for finite groups to reduce considerably the order of the matrix equations used to approximate the original integral equations, and thus to extend the range of problems amenable to numerical analysis. An implementation of this method is considered for boundary value problems with Abelian symmetry group of eighth order, describing a quadrupole-type system. Results of a numerical experiment are presented for this case, enabling the efficiency of the method to be estimated.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 6","pages":"Pages 44-53"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90107-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74209948","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90160-T
V.I. Gryn
{"title":"Determination of the absorption coefficient in the spherically symmetric case","authors":"V.I. Gryn","doi":"10.1016/0041-5553(90)90160-T","DOIUrl":"10.1016/0041-5553(90)90160-T","url":null,"abstract":"","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 5","pages":"Pages 42-54"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90160-T","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81635692","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90102-X
S.L. Logunov
Stability bounds for the solutions of conditionally well-posed problems for the case when the variation and the maximum absolute value of the solutions are bounded by known constants are derived. Differentiation problems, Volterra and Abel integral equations, and convolution equations are considered.
{"title":"Stability bounds for solutions of some conditionally well-posed problems on a set containing discontinuous functions","authors":"S.L. Logunov","doi":"10.1016/0041-5553(90)90102-X","DOIUrl":"10.1016/0041-5553(90)90102-X","url":null,"abstract":"<div><p>Stability bounds for the solutions of conditionally well-posed problems for the case when the variation and the maximum absolute value of the solutions are bounded by known constants are derived. Differentiation problems, Volterra and Abel integral equations, and convolution equations are considered.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 6","pages":"Pages 1-9"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90102-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84260114","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90036-R
Yu.I. Khudak
The existence of a unique global minimum for the maximum of the power reflection coefficient of a single-layer coating in a specified frequency band is proved.
证明了在给定的频带内,单层涂层功率反射系数的最大值存在唯一的全局最小值。
{"title":"The best single-layer brightening coating for a frequency band","authors":"Yu.I. Khudak","doi":"10.1016/0041-5553(90)90036-R","DOIUrl":"10.1016/0041-5553(90)90036-R","url":null,"abstract":"<div><p>The existence of a unique global minimum for the maximum of the power reflection coefficient of a single-layer coating in a specified frequency band is proved.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 238-240"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90036-R","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85834495","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90043-R
I.A. Blatov
A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.
{"title":"The projection method for singularly perturbed boundary-value problems","authors":"I.A. Blatov","doi":"10.1016/0041-5553(90)90043-R","DOIUrl":"10.1016/0041-5553(90)90043-R","url":null,"abstract":"<div><p>A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular “hinged element method”, and also produces a higher order of approximation.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 47-56"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90043-R","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80360164","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 : 1990-01-01DOI: 10.1016/0041-5553(90)90100-7
A.O. Alekseyev, O.G. Alekseyev, V.D. Kiselev
{"title":"The use of duality to determine the branching order of variables and to estimate the bounds in the solution of the knapsack problem","authors":"A.O. Alekseyev, O.G. Alekseyev, V.D. Kiselev","doi":"10.1016/0041-5553(90)90100-7","DOIUrl":"10.1016/0041-5553(90)90100-7","url":null,"abstract":"","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 2","pages":"Pages 199-200"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90100-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81670891","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}