Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献

On some sets sufficient for holomorphic continuation of functions with generalized boundary Morera property 关于具有广义边界Morera性质的函数的全纯延拓的充分集

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230307

A.M. Kytmanov, S.G. Myslivets

引用次数: 0

On a cube and subspace projections 在立方体和子空间投影上

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230302

A.A. Boykov, A.V. Seliverstov

{"title":"On a cube and subspace projections","authors":"A.A. Boykov, A.V. Seliverstov","doi":"10.35634/vm230302","DOIUrl":"https://doi.org/10.35634/vm230302","url":null,"abstract":"We consider the arrangement of vertices of a unit multidimensional cube, an affine subspace, and its orthogonal projections onto coordinate subspaces. Upper and lower bounds on the subspace dimension are given under which some orthogonal projection always preserves the incidence relation between the subspace and cube vertices. Some oblique projections are also considered. Moreover, a brief review of the history of the development of multidimensional descriptive geometry is given. Analytic and synthetic methods in geometry diverged since the 17th century. Although both synthesis and analysis are tangled, from this time forth many geometers as well as engineers keep up a nice distinction. One can find references to the idea of higher-dimensional spaces in the 18th-century works, but proper development has been since the middle of the 19th century. Soon such works have appeared in Russian. Next, mathematicians generalized their theories to many dimensions. Our new results are obtained by both analytic and synthetic methods. They illustrate the complexity of pseudo-Boolean programming problems because reducing the problem dimension by orthogonal projection meets obstacles in the worst case.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135686320","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 semi-analytical approximation of the normal derivative of the simple layer potential near the boundary of a two-dimensional domain 二维域边界附近简单层势法向导数的半解析近似

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230304

D.Yu. Ivanov

{"title":"On one semi-analytical approximation of the normal derivative of the simple layer potential near the boundary of a two-dimensional domain","authors":"D.Yu. Ivanov","doi":"10.35634/vm230304","DOIUrl":"https://doi.org/10.35634/vm230304","url":null,"abstract":"On the basis of piecewise quadratic interpolation, semi-analytical approximations of the normal derivative of the simple layer potential near and on the boundary of a two-dimensional domain are obtained. To calculate the integrals formed after the interpolation of the density function, exact integration over the variable $rho=(r^{2}-d^{2})^{1/2} $ is used, where $d$ and $r$ are the distances from the observed point to the boundary of the domain and to the boundary point of integration, respectively. The study proves the stable convergence of such approximations with cubic velocity uniformly near the boundary of the class $C^{5}$, as well as on the boundary itself. It is also proved that, by analogy with the exact function, the approximations suffer a discontinuity at the boundary, the magnitude of which is proportional to the values of the interpolated density function, but they can be extended on the boundary to functions that are continuous either on a closed internal border domain or on a closed external one. Theoretical conclusions about uniform convergence are confirmed by the results of calculating the normal derivative near the boundary of a unit circle.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135686322","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

Integration of the negative order Korteweg-de Vries equation by the inverse scattering method 反散射法积分负阶Korteweg-de Vries方程

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230309

G.U. Urazboev, I.I. Baltaeva, O.B. Ismoilov

引用次数: 0

On Banach spaces of regulated functions of several variables. An analogue of the Riemann integral 关于多变量正则函数的Banach空间。黎曼积分的类比

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230301

V.N. Baranov, V.I. Rodionov, A.G. Rodionova

{"title":"On Banach spaces of regulated functions of several variables. An analogue of the Riemann integral","authors":"V.N. Baranov, V.I. Rodionov, A.G. Rodionova","doi":"10.35634/vm230301","DOIUrl":"https://doi.org/10.35634/vm230301","url":null,"abstract":"The paper introduces the concept of a regulated function of several variables $fcolon Xtomathbb R$, where $Xsubseteq mathbb R^n$. The definition is based on the concept of a special partition of the set $X$ and the concept of oscillation of the function $f$ on the elements of the partition. It is shown that every function defined and continuous on the closure $X$ of the open bounded set $X_0subseteqmathbb R^n$, is regulated (belongs to the space $langle{rm G(}X),|cdot |rangle$). The completeness of the space ${rm G}(X)$ in the $sup$-norm $|cdot|$ is proved. This is the closure of the space of step functions. In the second part of the work, the space ${rm G}^J(X)$ is defined and studied, which differs from the space ${rm G}(X)$ in that its definition uses $J$-partitions instead of partitions, whose elements are Jordan measurable open sets. The properties of the space ${rm G}(X)$ listed above carry over to the space ${rm G}^J(X)$. In the final part of the paper, the notion of $J$-integrability of functions of several variables is defined. It is proved that if $X$ is a Jordan measurable closure of an open bounded set $X_0subseteqmathbb R^n$, and the function $fcolon Xtomathbb R$ is Riemann integrable, then it is $J$-integrable. In this case, the values of the integrals coincide. All functions $fin{rm G}^J(X)$ are $J$-integrable.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135686321","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

A hybrid model of population dynamics with refuge-regime: regularization and self-organization 人口动态与难民制度的混合模型:正规化与自组织

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230306

A.N. Kirillov, A.M. Sazonov

引用次数: 0

Quotient and transversal mappings for topological quasigroups 拓扑拟群的商与横映射

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230308

S.V. Ludkowski

引用次数: 0

Generation of adaptive hexahedral meshes from surface and voxel geometric models 从表面和体素几何模型生成自适应六面体网格

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230310

A.S. Karavaev, S.P. Kopysov

引用次数: 0

Inverse problems for the beam vibration equation with involution 带对合的梁振动方程的反问题

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230305

A.B. Imanbetova, Abdissalam Sarsenbi, Bolat Seilbekov

引用次数: 0

On the growth of solutions of complex linear differential equations with analytic coefficients in $overline{mathbb{C}}backslash{z_{0}}$ of finite logarithmic order 有限对数阶$overline{mathbb{C}}backslash{z_{0}}$中具有解析系数的复线性微分方程解的增长

Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-09-01 DOI: 10.35634/vm230303

Abdelkader Dahmani, Benharrat Belaïdi

引用次数: 0