In this paper we establish sufficient conditions of summability, by functional method of G.F. Voronoi, of Fourier integral of a function $f(t) in L_{(-infty, infty)}$.
本文利用G.F. Voronoi的泛函方法，建立了一个函数$f(t) in L_{(-infty, infty)}$的傅里叶积分的可和性的充分条件。
{"title":"Summation of trigonometric Fourier integrals by method of G.F. Voronoi","authors":"L. G. Bojtsun","doi":"10.15421/247714","DOIUrl":"https://doi.org/10.15421/247714","url":null,"abstract":"In this paper we establish sufficient conditions of summability, by functional method of G.F. Voronoi, of Fourier integral of a function $f(t) in L_{(-infty, infty)}$.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77866728","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}
We construct the algorithm that implements forced search for extremum of unimodal criterion. We provide results of mathematical modelling on a computer.
构造了强制搜索单峰准则极值的算法。我们在计算机上提供数学建模的结果。
{"title":"Algorithm of forced search for extremum of unimodal criterion","authors":"L. V. Korol","doi":"10.15421/247728","DOIUrl":"https://doi.org/10.15421/247728","url":null,"abstract":"We construct the algorithm that implements forced search for extremum of unimodal criterion. We provide results of mathematical modelling on a computer.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75743082","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}
We establish necessary and sufficient conditions for ${ alpha_k(x) }$ to satisfy such that the product $prodlimits_{k=1}^{infty} [1+alpha_k(x) U_k(x)]$ converges uniformly under the condition that ${ U_k(x) }$ belongs to a given class.
{"title":"On uniform convergence of infinite products","authors":"K. M. Slepenchuk, G. A. Barbashova","doi":"10.15421/247720","DOIUrl":"https://doi.org/10.15421/247720","url":null,"abstract":"We establish necessary and sufficient conditions for ${ alpha_k(x) }$ to satisfy such that the product $prodlimits_{k=1}^{infty} [1+alpha_k(x) U_k(x)]$ converges uniformly under the condition that ${ U_k(x) }$ belongs to a given class.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81696996","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}
In the paper, for the set of two homogeneous differential equations (in Novozhilov sense) that describes non-axial-symmetric deformation of rotation hull, which is under arbitrary edge load, we obtain by elliptic method the approximate solutions for elliptic and conic shells. We find expressions for transitions.
{"title":"Asymptotic research of deformations of elliptic bottom and conic shell","authors":"B. N. Yakovlev","doi":"10.15421/247737","DOIUrl":"https://doi.org/10.15421/247737","url":null,"abstract":"In the paper, for the set of two homogeneous differential equations (in Novozhilov sense) that describes non-axial-symmetric deformation of rotation hull, which is under arbitrary edge load, we obtain by elliptic method the approximate solutions for elliptic and conic shells. We find expressions for transitions.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86236418","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}
In the paper, we consider approximations of nonperiodic functions defined on $[-1, 1]$ by algebraic polynomials in $L_p$ metric ($0 < p < 1$).In particular, for some classes we provide the constructive characteristic in the same metric.
本文研究了在$L_p$度量($0 < p < 1$)中定义在$[- 1,1]$上的非周期函数的代数多项式逼近。特别是，对于某些类，我们在相同的度量中提供了建设性特征。
{"title":"On approximation of nonperiodic functions by algebraic polynomials in $L_p$ metric ($0 < p < 1$)","authors":"L. B. Khodak","doi":"10.15421/247710","DOIUrl":"https://doi.org/10.15421/247710","url":null,"abstract":"In the paper, we consider approximations of nonperiodic functions defined on $[-1, 1]$ by algebraic polynomials in $L_p$ metric ($0 < p < 1$).In particular, for some classes we provide the constructive characteristic in the same metric.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88558831","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}
We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.
{"title":"Tauberian theorems in the case of strong summability in degree $p$ of double series","authors":"T.N. Yarkovaia","doi":"10.15421/247721","DOIUrl":"https://doi.org/10.15421/247721","url":null,"abstract":"We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87102385","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}
By means of Fourier-Chebyshev operators we construct, by approximative method, the generalized polynomial that approximates the solution of Goursat problem with constant coefficients. We obtain the efficient estimate of this approximation.
{"title":"On numerical solution by method of V.K. Dzyadyk of Goursat problem with constant coefficients","authors":"V. P. Burlachenko, Y. Romanenko","doi":"10.15421/247726","DOIUrl":"https://doi.org/10.15421/247726","url":null,"abstract":"By means of Fourier-Chebyshev operators we construct, by approximative method, the generalized polynomial that approximates the solution of Goursat problem with constant coefficients. We obtain the efficient estimate of this approximation.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81316584","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}
The problem about the bend of circular plate of variable thickness under specifically selected laws of rigidity change is reduced to the ordinary differential equation with variable coefficients of polynomial kind. The construction of the approximate solution of equation that satisfies boundary conditions is realized by means of canonical polynomials and $tau$-method of Lantzosh.
{"title":"Canonical polynomials in the problem about the bend of circular plate of variable thickness","authors":"O. Bugrim, Ye.S. Sinaiskii","doi":"10.15421/247725","DOIUrl":"https://doi.org/10.15421/247725","url":null,"abstract":"The problem about the bend of circular plate of variable thickness under specifically selected laws of rigidity change is reduced to the ordinary differential equation with variable coefficients of polynomial kind. The construction of the approximate solution of equation that satisfies boundary conditions is realized by means of canonical polynomials and $tau$-method of Lantzosh.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85118329","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}
We obtain conditions of $L$-summability of series, associated with Fourier series.
得到了傅里叶级数的L -可和性的条件。
{"title":"$L$-summability of series, associated with Fourier series","authors":"Ye.M. Kilberg","doi":"10.15421/247717","DOIUrl":"https://doi.org/10.15421/247717","url":null,"abstract":"We obtain conditions of $L$-summability of series, associated with Fourier series.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81156785","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}
We establish conditions of $|gamma|_p$- and $[gamma]_p$-summability in degree $p geqslant 1$ of $r$ times differentiated Fourier series at the point where $gamma = | gamma_{nk} |$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.
{"title":"Absolute and strong summability in degree $p geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods","authors":"N. Polovina","doi":"10.15421/247719","DOIUrl":"https://doi.org/10.15421/247719","url":null,"abstract":"We establish conditions of $|gamma|_p$- and $[gamma]_p$-summability in degree $p geqslant 1$ of $r$ times differentiated Fourier series at the point where $gamma = | gamma_{nk} |$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83072569","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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