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Researches in Mathematics最新文献

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Summation of trigonometric Fourier integrals by method of G.F. Voronoi 用G.F. Voronoi的方法求和三角傅立叶积分
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247714
L. G. Bojtsun
{"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}
引用次数: 0
Algorithm of forced search for extremum of unimodal criterion 单峰准则极值的强制搜索算法
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247728
L. V. Korol
{"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}
引用次数: 0
On uniform convergence of infinite products 关于无穷积的一致收敛
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247720
K. M. Slepenchuk, G. A. Barbashova
{"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}
引用次数: 0
Asymptotic research of deformations of elliptic bottom and conic shell 椭圆底与圆锥壳变形的渐近研究
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247737
B. N. Yakovlev
{"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}
引用次数: 0
On approximation of nonperiodic functions by algebraic polynomials in $L_p$ metric ($0 < p < 1$) $L_p$度量($0 < p < 1$)中非周期函数的代数多项式逼近
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247710
L. B. Khodak
{"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}
引用次数: 0
Tauberian theorems in the case of strong summability in degree $p$ of double series 二重级数阶$p$强可和情况下的Tauberian定理
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247721
T.N. Yarkovaia
{"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}
引用次数: 0
On numerical solution by method of V.K. Dzyadyk of Goursat problem with constant coefficients 常系数Goursat问题的V.K. Dzyadyk方法数值解
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247726
V. P. Burlachenko, Y. Romanenko
{"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}
引用次数: 0
Canonical polynomials in the problem about the bend of circular plate of variable thickness 变厚圆板弯曲问题中的正则多项式
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247725
O. Bugrim, Ye.S. Sinaiskii
{"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}
引用次数: 0
$L$-summability of series, associated with Fourier series L -级数的可和性，与傅里叶级数有关
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247717
Ye.M. Kilberg
{"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}
引用次数: 0
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 用矩阵法求$r$倍微分傅里叶级数和$r$倍微分共轭傅里叶级数在$p geqslant 1$次上的绝对和强求和性
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247719
N. Polovina
{"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}
引用次数: 0
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