{"title":"On some new sharp embedding theorems in area Nevanlinna spaces and related problems","authors":"R. Shamoyan","doi":"10.31029/demr.15.3","DOIUrl":"https://doi.org/10.31029/demr.15.3","url":null,"abstract":"We provide some new sharp embedding theorems for analytic area Nevanlinna spaces in the unit disk extending some previously known assertions in various directions.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132494708","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}
{"title":"A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation","authors":"É. Abduragimov","doi":"10.31029/demr.11.5","DOIUrl":"https://doi.org/10.31029/demr.11.5","url":null,"abstract":"A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{primeprime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x in [0,1]$, $y in R$ and satisfies the condition $a_0 x^{gamma}y^p leq f(x,y) leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $gamma geq 0$ -- constants.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"357 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121634720","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}
{"title":"A numerical method for solving the Cauchy problem for ODEs using a system of polynomials generated by a system of modified Laguerre polynomials","authors":"G. Akniyev, R. Gadzhimirzaev","doi":"10.31029/demr.12.2","DOIUrl":"https://doi.org/10.31029/demr.12.2","url":null,"abstract":"In this paper, we consider a numerical realization of an iterative method for solving the Cauchy problem for ordinary differential equations, based on representing the solution in the form of a Fourier series by the system of polynomials ${L_{1,n}(x;b)}_{n=0}^infty$, orthonormal with respect to the Sobolev-type inner product $$ langle f,grangle=f(0)g(0)+int_{0}^infty f'(x)g'(x)rho(x;b)dx $$ and generated by the system of modified Laguerre polynomials ${L_{n}(x;b)}_{n=0}^infty$, where $b>0$. In the approximate calculation of the Fourier coefficients of the desired solution, the Gauss -- Laguerre quadrature formula is used.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125909843","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}
{"title":"Computer simulation of phase transitions of the Heisenberg antiferromagnetic model","authors":"M. Ramazanov, A. Murtazaev","doi":"10.31029/demr.11.3","DOIUrl":"https://doi.org/10.31029/demr.11.3","url":null,"abstract":"Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. \u0000 The phase transitions of this model are studied. \u0000 The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors $r = J_2 / J_1$ in the range $0.0 leq r leq 1.0$. \u0000 The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116641604","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}
{"title":"About the convergence of the Fourier transform","authors":"Mohamed-Ahmed Boudref","doi":"10.31029/demr.15.1","DOIUrl":"https://doi.org/10.31029/demr.15.1","url":null,"abstract":"The main result is the proof of the theorems, the results of which one can\u0000characterize as a weak form of the formula for the inversion of the bi-dimmensional Fourier transform. Sufficient conditions on a function are obtained for a weak (of degree $r$) convergence of bi-dimmensional Fourier transform for a function $f(x;y)$. These conditions have an integral form and describe the behavior of the function near the border of a rectangle. A similar theorem is proved, in which the Fourier transform of a function $f$ is replaced by the Fourier transform of another function $g$, the norm of the central difference of which does not exceed the norm of the central difference of $f$.\u0000The principal objective is to study the behavior of the Fourier transform of \u0000$g$ and $f$.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116550191","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}
{"title":"О приближенном решении краевой задачи с разрывным решением","authors":"A. Ramazanov, A. Ramazanov","doi":"10.31029/demr.15.2","DOIUrl":"https://doi.org/10.31029/demr.15.2","url":null,"abstract":"Через сплайн-функции по трехточечным рациональным интерполянтам построено приближенное решение краевой задачи: $y^prime +p(x) y=f(x)$, $y(a)=A$, $y(b)=B$. При этом функции $p(x)$ и $f(x)$ считаются непрерывными на отрезке $[a,b]$ и допускается, что существует решение $y(x)$, которое может иметь разрыв первого рода со скачком в заданной точке $tauin(a,b)$.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122607021","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}
{"title":"On new parametric representations of certain classes of subharmonic functions in the unit disk","authors":"R. Shamoyan","doi":"10.31029/demr.13.5","DOIUrl":"https://doi.org/10.31029/demr.13.5","url":null,"abstract":"We define new spaces of subharmonic functions in the unit disk and provide characterizations of these new classes of functions via parametric representation.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117086946","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}
{"title":"On the approximation of $ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants","authors":"A. Ramazanov, V. Magomedova","doi":"10.31029/demr.11.4","DOIUrl":"https://doi.org/10.31029/demr.11.4","url":null,"abstract":"For the function $f(x)=exp(-x)$, $xin [0,+infty)$ on grids of nodes $Delta: 0=x_0<x_1<dots $ with $x_nto +infty$ we construct rational spline-functions such that $R_k(x,f, Delta)=R_i(x,f)A_{i,k}(x)linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $xin[x_{i-1}, x_i]$ $(i=1,2,dots)$ and $k=1,2,dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=alpha_j+beta_j(x-x_j)+gamma_j/(x+1)$ $(j=1,2,dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)equiv R_1(x,f)$.\u0000\u0000Bounds for the convergence rate of $R_k(x,f, Delta)$ with $f(x)=exp(-x)$, $xin [0,+infty)$, are found.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115346298","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}
{"title":"The approximation of piecewise smooth functions by trigonometric Fourier sums","authors":"M. Magomed-Kasumov","doi":"10.31029/demr.12.3","DOIUrl":"https://doi.org/10.31029/demr.12.3","url":null,"abstract":"We obtain exact order-of-magnitude estimates of piecewise smooth functions approximation by trigonometric Fourier sums. It is shown that in continuity points Fourier series of piecewise Lipschitz function converges with rate $ln n/n$. If function $f$ has a piecewise absolutely continuous derivative then it is proven that in continuity points decay order of Fourier series remainder $R_n(f,x)$ for such function is equal to $1/n$. We also obtain exact order-of-magnitude estimates for $q$-times differentiable functions with piecewise smooth $q$-th derivative. In particular, if $f^{(q)}(x)$ is piecewise Lipschitz then $|R_n(f,x)| le c(x)frac{ln n}{n^{q+1}}$ in continuity points of $f^{(q)}(x)$ and $sup_{x in [0,2pi]}|R_n(f,x)| le frac{c}{n^q}$. In case when $f^{(q)}(x)$ has piecewise absolutely continuous derivative it is shown that $|R_n(f,x)| le frac{c(x)}{n^{q+1}}$ in continuity points of $f^{(q)}(x)$. As a consequence of the last result convergence rate estimate of Fourier series to continuous piecewise linear functions is obtained.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126963658","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}
{"title":"Обратная задача для интегро-дифференциального уравнения с обобщенным оператором Уизема высокой степени","authors":"T. Yuldashev, S. Bolbekov","doi":"10.31029/demr.15.4","DOIUrl":"https://doi.org/10.31029/demr.15.4","url":null,"abstract":"Изучены вопросы разрешимости и определения неизвестного коэффициента в обратной задаче для одного интегро-дифференциального уравнения в частных производных с многомерным обобщенным оператором Уизема высокой степени. С помощью выражения дифференциальных уравнений в частных производных высокого порядка через суперпозицию дифференциальных операторов в частных производных первого порядка представлено рассматриваемое уравнение высшего порядка как обыкновенное интегро-дифференциальное уравнение, описывающее изменение неизвестной функции вдоль характеристик. Доказана однозначная разрешимость прямой задачи методом последовательных приближений. Получена оценка сходимости итерационного процесса Пикара. Определение неизвестного коэффициента сведено к решению интегрального уравнения Вольтерра первого рода.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133821991","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}