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Researches in Mathematics最新文献

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On the best choice of nodes at interpolation of functions by even Hermitian splines 偶厄米样条函数插值中节点的最佳选择
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247707
A. D. Malysheva
{"title":"On the best choice of nodes at interpolation of functions by even Hermitian splines","authors":"A. D. Malysheva","doi":"10.15421/247707","DOIUrl":"https://doi.org/10.15421/247707","url":null,"abstract":"We have found exact values of deviation of even Hermitian splines on some classes of functions and pointed out the best choice of nodes at approximation of concrete functions by these splines.","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":"89828908","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 series, associated with Fourier series, by matrix methods 级数的绝对和强和度$p geqslant 1$，与傅里叶级数有关，由矩阵方法
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247718
N. Polovina
{"title":"Absolute and strong summability in degree $p geqslant 1$ of series, associated with Fourier series, by matrix methods","authors":"N. Polovina","doi":"10.15421/247718","DOIUrl":"https://doi.org/10.15421/247718","url":null,"abstract":"We establish conditions of $|gamma|_p$- and $[gamma]_p$-summability in degree $p geqslant 1$ of series, associated with Fourier series, at the point where $gamma = | gamma_{nk} |$ is the matrix of transformation of series to sequence.","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":"75527486","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 solution of one linear problem with initial and boundary conditions 一类具有初始条件和边界条件的线性问题的解
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247729
S. Kritskaia
{"title":"On solution of one linear problem with initial and boundary conditions","authors":"S. Kritskaia","doi":"10.15421/247729","DOIUrl":"https://doi.org/10.15421/247729","url":null,"abstract":"We solve one boundary problem of fourth order with initial conditions, that appears, for example, when one solves the problem about lateral oscillations of elastic-viscous-relaxating rod of variable profile with variable momentum of inertia with freely supported ends.","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":"85149777","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
To the question of approximation of continuous periodic functions by trigonometric polynomials 用三角多项式逼近连续周期函数的问题
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247711
V. Shalaev
{"title":"To the question of approximation of continuous periodic functions by trigonometric polynomials","authors":"V. Shalaev","doi":"10.15421/247711","DOIUrl":"https://doi.org/10.15421/247711","url":null,"abstract":"In the paper, it is proved that$$1 - frac{1}{2n} leqslant suplimits_{substack{f in Cf ne const}} frac{E_n(f)_C}{omega_2(f; pi/n)_C} leqslant inflimits_{L_n in Z_n(C)} suplimits_{substack{f in Cf ne const}} frac{| f - L_n(f) |_C}{omega_2 (f; pi/n)_C} leqslant 1$$where $omega_2(f; t)_C$ is the modulus of smoothness of the function $f in C$, $E_n(f)_C$ is the best approximation by trigonometric polynomials of the degree not greater than $n-1$ in uniform metric, $Z_n(C)$ is the set of linear bounded operators that map $C$ to the subspace of trigonometric polynomials of degree not greater than $n-1$.","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":"81370803","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 one problem, associated with lateral oscillations of elastic-viscous-relaxating rod 在一个问题上，与弹性粘松弛杆的横向振动有关
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247734
D. Rogach
{"title":"On one problem, associated with lateral oscillations of elastic-viscous-relaxating rod","authors":"D. Rogach","doi":"10.15421/247734","DOIUrl":"https://doi.org/10.15421/247734","url":null,"abstract":"We obtain the solution of the problem about lateral oscillations of elastic-viscous-relaxating rod of finite length, variable profile, and variable momentum of rotation inertia of rod elements about the axis that is perpendicular to oscillation plane.","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":"75486091","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 differential inequalities of S.A. Chaplygin related to limit Cauchy problem for sets of ordinary differential equations of first order 关于一阶常微分方程集极限柯西问题的s.a.chplygin微分不等式
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247723
I. I. Bezvershenko
{"title":"On differential inequalities of S.A. Chaplygin related to limit Cauchy problem for sets of ordinary differential equations of first order","authors":"I. I. Bezvershenko","doi":"10.15421/247723","DOIUrl":"https://doi.org/10.15421/247723","url":null,"abstract":"We prove a theorem on differential inequalities related to limit Cauchy problem for the set of ordinary differential equations$$y' = f(x,y,z),$$z' = varphi(x,y,z)$$with boundary conditions$$limlimits_{x rightarrow infty} y(x) = y(infty) = y_0, ; limlimits_{x rightarrow infty} z(x) = z(infty) = z_0$$","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75439805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On one extremal property of Korovkin's means 关于科洛夫金均值的一个极值性质
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247702
V. Babenko, S. Pichugov
{"title":"On one extremal property of Korovkin's means","authors":"V. Babenko, S. Pichugov","doi":"10.15421/247702","DOIUrl":"https://doi.org/10.15421/247702","url":null,"abstract":"We point out that$$inflimits_{L in L_n} suplimits_{substack{f in C_{2pi}f ne const}} frac{max | f(x) - L(f, x) |}{omega^*_2(f, pi/n + 1)} = frac{1}{2}$$where $C_{2pi}$ is the space of periodic continuous functions on real domain, $L_n$ is the set of linear operators that map $C_{2pi}$ to the set of trigonometric polynomials of order no greater than $n$ ($n = 0,1,ldots$), $omega_2(f, t) = suplimits_{x, |h| leqslant t} |f(x-h) - 2f(x) + f(x+h)|$, $omega^*_2(f, t)$ is the concave hull of the function $omega_2(f, t)$. In this equality, the infimum is attained for Korovkin's means.","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":"74790522","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
Research of solution of the problem about longitudinal oscillation of heterogeneous rod in presence of linear law of relaxation and after-effect 存在线性松弛律和后效的非均质杆纵向振荡问题的求解方法研究
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247730
S. Kritskaia
{"title":"Research of solution of the problem about longitudinal oscillation of heterogeneous rod in presence of linear law of relaxation and after-effect","authors":"S. Kritskaia","doi":"10.15421/247730","DOIUrl":"https://doi.org/10.15421/247730","url":null,"abstract":"We obtain the solution of the problem about longitudinal impact of heterogeneous rod in presence of linear law of relaxation and after-effect in case when one end of rod is connected to some mass, and the other undergoes the impact by some load, we conduct the research of this solution.","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":"75077149","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
Exact values of the best mean approximations by algebraic polynomials of $W^r_L$ classes ($r=1,2$) $W^r_L$类($r=1,2$)的代数多项式的最佳均值逼近的精确值
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247705
V. Kofanov
{"title":"Exact values of the best mean approximations by algebraic polynomials of $W^r_L$ classes ($r=1,2$)","authors":"V. Kofanov","doi":"10.15421/247705","DOIUrl":"https://doi.org/10.15421/247705","url":null,"abstract":"In the paper, we have found the supremum of the best mean approximations by algebraic polynomials of differentiable functions from $W^r_L$ classes for $r=1,2$.","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":"74320094","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 absolute summability in degree $p$ of double series 二重级数p阶绝对可和情况下的陶伯利定理
Researches in Mathematics Pub Date : 2021-10-06 DOI: 10.15421/247722
T.N. Yarkovaia
{"title":"Tauberian theorems in the case of absolute summability in degree $p$ of double series","authors":"T.N. Yarkovaia","doi":"10.15421/247722","DOIUrl":"https://doi.org/10.15421/247722","url":null,"abstract":"We establish a Tauberian theorem in the case of absolute 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":"79140084","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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