In the paper, we find the sharp estimate of the best approximation, by entire functions of exponential type not greater than $sigma$, for functions $f(x)$ from the class $W^r H^{omega}$ such that $limlimits_{x rightarrow -infty} f(x) = limlimits_{x rightarrow infty} f(x) = 0$,$$A_{sigma}(W^r H^{omega}_0)_C = frac{1}{sigma^{r+1}} intlimits_0^{pi} Phi_{pi, r}(t)omega'(t/sigma)dt$$for $sigma > 0$, $r = 1, 2, 3, ldots$ and concave modulus of continuity.Also, we calculate the supremum$$suplimits_{substack{fin L^{(r)}f ne const}} frac{sigma^r A_{sigma}(f)_L}{omega (f^{(r)}, pi/sigma)_L} = frac{K_L}{2}$$
{"title":"Sharp estimates of approximation of classes of differentiable functions by entire functions","authors":"V. Babenko, A.Yu. Gromov","doi":"10.15421/247701","DOIUrl":"https://doi.org/10.15421/247701","url":null,"abstract":"In the paper, we find the sharp estimate of the best approximation, by entire functions of exponential type not greater than $sigma$, for functions $f(x)$ from the class $W^r H^{omega}$ such that $limlimits_{x rightarrow -infty} f(x) = limlimits_{x rightarrow infty} f(x) = 0$,$$A_{sigma}(W^r H^{omega}_0)_C = frac{1}{sigma^{r+1}} intlimits_0^{pi} Phi_{pi, r}(t)omega'(t/sigma)dt$$for $sigma > 0$, $r = 1, 2, 3, ldots$ and concave modulus of continuity.Also, we calculate the supremum$$suplimits_{substack{fin L^{(r)}f ne const}} frac{sigma^r A_{sigma}(f)_L}{omega (f^{(r)}, pi/sigma)_L} = frac{K_L}{2}$$","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"617 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77621209","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 propose the algorithm of covering a graph by chains of types that satisfy bounds for length and total weight of a chain.
在本文中，我们提出了用满足链的长度和总权的界限的类型链覆盖图的算法。
{"title":"On one algorithm of covering a graph by heterogeneous chains","authors":"N.A. Likholat","doi":"10.15421/247731","DOIUrl":"https://doi.org/10.15421/247731","url":null,"abstract":"In the paper, we propose the algorithm of covering a graph by chains of types that satisfy bounds for length and total weight of a chain.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77680735","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 study the equations of movement of a rod and other simplest rectilinear bodies. We have found some of their regular solutions, which can be used to construct periodic solutions, close to these regular ones.
{"title":"On regular movements of a material rod","authors":"L. Boiko","doi":"10.15421/247724","DOIUrl":"https://doi.org/10.15421/247724","url":null,"abstract":"We study the equations of movement of a rod and other simplest rectilinear bodies. We have found some of their regular solutions, which can be used to construct periodic solutions, close to these regular ones.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"205 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77471588","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 absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.
{"title":"Absolute summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods","authors":"N. I. Volkova, N. Novikova","doi":"10.15421/247715","DOIUrl":"https://doi.org/10.15421/247715","url":null,"abstract":"We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86163910","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 absolute summability of Fourier integrals and conjugate Fourier integrals by Voronoi-Nerlund method.
利用Voronoi-Nerlund方法建立了傅里叶积分和共轭傅里叶积分的绝对可和性条件。
{"title":"Absolute summability of conjugate Fourier integrals by Voronoi-Nerlund method","authors":"N. I. Volkova, N.P. Ogol","doi":"10.15421/247716","DOIUrl":"https://doi.org/10.15421/247716","url":null,"abstract":"We establish conditions of absolute summability of Fourier integrals and conjugate Fourier integrals by Voronoi-Nerlund method.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81387266","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 provide one of possible ways to reduce the time of transitive process of models tuning in the identification problems, which is: forced search for extremum of system state criterion.
提出了一种减少辨识问题中模型调优传递过程时间的方法，即系统状态准则的强制极值搜索。
{"title":"Algorithm of search identification with forced search for extremum","authors":"A. Mikhalev, L. V. Korol","doi":"10.15421/247732","DOIUrl":"https://doi.org/10.15421/247732","url":null,"abstract":"We provide one of possible ways to reduce the time of transitive process of models tuning in the identification problems, which is: forced search for extremum of system state criterion.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86209002","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 have found the best linear polynomial methods of approximation of continuous periodic functions of multiple variables in uniform metric with concave modulus of continuity.
在连续模为凹模的一致度量下，我们找到了逼近多变量连续周期函数的最佳线性多项式方法。
{"title":"On multidimensional Jackson's theorem","authors":"S. Pichugov","doi":"10.15421/247708","DOIUrl":"https://doi.org/10.15421/247708","url":null,"abstract":"We have found the best linear polynomial methods of approximation of continuous periodic functions of multiple variables in uniform metric with concave modulus of continuity.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87251082","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 have found exact values of approximation in uniform metric by interpolative infinitely differentiable splines on the classes $W^r_{L_p}$.
在类W^r_{L_p}$上，我们得到了用插值无限可微样条近似一致度量的精确值。
{"title":"Exact values of approximation by infinitely differentiable splines on some classes of functions","authors":"V. L. Velikіn","doi":"10.15421/247703","DOIUrl":"https://doi.org/10.15421/247703","url":null,"abstract":"We have found exact values of approximation in uniform metric by interpolative infinitely differentiable splines on the classes $W^r_{L_p}$.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"64 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72579677","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 stress-deformed state of elastic system that consists of the elliptic bottom, the ring, and the conic shell. The ring is under arbitrary load, which acts in its plane.On the base of the principal differential dependencies of design of the planar circular ring, we obtain the expressions for tensions, momentum, and the angle of rotation of lateral section.
{"title":"Asymptotic research of deformations and stresses of the ring that sustains the seam of elliptic bottom and conic shell","authors":"B. N. Yakovlev","doi":"10.15421/247736","DOIUrl":"https://doi.org/10.15421/247736","url":null,"abstract":"In the paper, we consider stress-deformed state of elastic system that consists of the elliptic bottom, the ring, and the conic shell. The ring is under arbitrary load, which acts in its plane.On the base of the principal differential dependencies of design of the planar circular ring, we obtain the expressions for tensions, momentum, and the angle of rotation of lateral section.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"182 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81941483","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 have found order asymptotic estimates of approximations, in the strong sense, relative to given matrix of classes of continuous periodic functions of two variables by some trigonometric polynomials.
在本文中，我们用一些三角多项式找到了与给定的二元连续周期函数类的矩阵有关的强意义上的阶渐近估计。
{"title":"On approximation, in the strong sense, of functions of two variables by trigonometric polynomials","authors":"V. V. Lipovik, N. P. Khoroshko","doi":"10.15421/247706","DOIUrl":"https://doi.org/10.15421/247706","url":null,"abstract":"In the paper, we have found order asymptotic estimates of approximations, in the strong sense, relative to given matrix of classes of continuous periodic functions of two variables by some trigonometric polynomials.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90442149","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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