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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献

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On the type of the meromorphic function of finite order 有限阶亚纯函数的类型
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-06-01 DOI: 10.35634/vm230202
M.V. Kabanko
{"title":"On the type of the meromorphic function of finite order","authors":"M.V. Kabanko","doi":"10.35634/vm230202","DOIUrl":"https://doi.org/10.35634/vm230202","url":null,"abstract":"Let $f(z)$ be a meromorphic function on the complex plane of finite order $rho>0$. Let $rho(r)$ be a proximate order in the sense of Boutroux such that $limsuplimits_{rtoinfty}rho(r)=rho$, $liminflimits_{rtoinfty}rho(r)=alpha>0$. If $[alpha]<alphaleqslantrho<[alpha]+1$ then the types of $T(r,f)$ and $|N|(r,f)$ coincide with respect to $rho(r)$. If there are integers between $alpha$ and $rho$, then the resulting criterion is formulated in terms of the upper density of zeros and poles of the function $f$ and their argument symmetry.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136281136","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
$Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type 具有广义型积分约束的微分寻优对策
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-06-01 DOI: 10.35634/vm230208
B. Samatov, M. A. Horilov, B. Juraev
{"title":"$Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type","authors":"B. Samatov, M. A. Horilov, B. Juraev","doi":"10.35634/vm230208","DOIUrl":"https://doi.org/10.35634/vm230208","url":null,"abstract":"The paper investigates a differential game of simple pursuit, when the controls of two opposing players are subject to integral constraints of a generalized type. The generalization of the proposed restriction lies in the fact that it includes previously known restrictions such as integral, geometric, linear, exponential and their mixtures. In general, it includes 25 types of pursuit problems with such different types of constraints. To solve the pursuit problem under such generalized constraints, we propose a parallel pursuit strategy ($Pi$-strategy for short) and find sufficient conditions for the solvability of this problem. At the end of the article, tables are provided that list each particular type of game, the conditions for its solvability, the resolving function (which determines the corresponding $Pi$-strategy), and the time of capture.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74703916","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: 2
Letter to the Editor: Correction to the “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition” [Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2023, vol. 33, issue 1, pp. 90-102] 给编者的信:对“具有非局部条件的抛物型积分-微分方程的核确定问题”的修正[j]。Udmurt。麦可大学。Komp 'yut。《Nauki, 2023》，第33卷，第1期，第90-102页。
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-06-01 DOI: 10.35634/vm230213
D.Q. Durdiev, J. J. Jumaev, D. Atoev
{"title":"Letter to the Editor: Correction to the “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition” [Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2023, vol. 33, issue 1, pp. 90-102]","authors":"D.Q. Durdiev, J. J. Jumaev, D. Atoev","doi":"10.35634/vm230213","DOIUrl":"https://doi.org/10.35634/vm230213","url":null,"abstract":"In this note we give a complete correct formulation and proof of Lemma 1 of [1].","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79684390","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
Potential theory on an analytic surface 解析曲面上的势论
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230101
B. Abdullaev, Kh.Q. Kamolov
{"title":"Potential theory on an analytic surface","authors":"B. Abdullaev, Kh.Q. Kamolov","doi":"10.35634/vm230101","DOIUrl":"https://doi.org/10.35634/vm230101","url":null,"abstract":"The work is devoted to the theory of pluripotential on analytic surfaces. The pluripotential theory on the complex space ${mathbb C}^{n},$ as well as on the Stein complex manifold $Xsubset{mathbb C}^{N}$ (without a singular set) have been studied in enough detail. In this work, we propose a new approach for studying the main objects of potential theory on an analytic set with a non-empty singular (critical) set.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82114051","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 some properties of *-integral 关于*积分的一些性质
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230105
{"title":"On some properties of *-integral","authors":"","doi":"10.35634/vm230105","DOIUrl":"https://doi.org/10.35634/vm230105","url":null,"abstract":"This work continues the author's research on the theory of regulated functions and *-integral. The possibility to express a regulated function as a sum of right-continuous and left-continuous functions (called $rl$-representation) is studied. A limit theorem for the *-integral is proved. It allows approximating discontinuous integrands and integrators by sequences of absolutely continuous functions. A new result on $delta$-correctness of the solution of an ordinary linear differential equation with generalized functions in coefficients is proved. This solution is defined via a quasi-differential equation. A formula for the total variation of an indefinite *-integral of a $sigma$-continuous function with respect to a function of bounded variation is given. It generalizes the well-known formula for computing the total variation of an absolutely continuous function. The formula is also interesting in the case of an indefinite $RS$-integral.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73860949","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 eigenelements of a two-dimensional Steklov-type boundary value problem for the Lamé operator lam<s:1>算子的二维steklov型边值问题的特征元
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230104
D. B. Davletov, O. B. Davletov, R.R. Davletova, A. Ershov
{"title":"On eigenelements of a two-dimensional Steklov-type boundary value problem for the Lamé operator","authors":"D. B. Davletov, O. B. Davletov, R.R. Davletova, A. Ershov","doi":"10.35634/vm230104","DOIUrl":"https://doi.org/10.35634/vm230104","url":null,"abstract":"In this paper, we study a two-dimensional Steklov-type boundary value problem for the Lamé operator in a half-strip, which is the limiting problem for a singularly perturbed boundary-value problem in a half-strip with a small hole. A theorem on the existence of eigenelements of the boundary value problem under study is proved. In particular, we obtain estimates for the eigenvalues expressed in terms of the Lamé constants and a parameter that determines the width of the half-strip, and refine the structure of the corresponding eigenfunctions, which determines their behavior as their argument move away from the base of the half-strip. Moreover, explicit expressions for the eigenvalues of the limiting boundary value problem are found up to the solution of a system of algebraic equations. The results obtained in this paper will make it possible to construct and rigorously justify an asymptotic expansion of the eigenvalue of a singularly perturbed boundary value problem in a half-strip with a small round hole in powers of a small parameter that determines the diameter of the hole.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87584825","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
The method of resolving functions for solving a pursuit problem with integral constraints on player controls 求解带有玩家控制的积分约束的追踪问题的函数的方法
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230107
N. Mamadaliev, K. Mustapokulov, G. M. Abdualimova
{"title":"The method of resolving functions for solving a pursuit problem with integral constraints on player controls","authors":"N. Mamadaliev, K. Mustapokulov, G. M. Abdualimova","doi":"10.35634/vm230107","DOIUrl":"https://doi.org/10.35634/vm230107","url":null,"abstract":"In this paper, we study pursuit game problems described by a system of equations with a retarded argument under integral constraints on the players' controls. The proposed scheme uses the ideas of the method of resolving functions. Modifications of methods (i.e., the first and so-called third methods) [1,3,12] of pursuit are proposed in the case when integral constraints are imposed on the players' controls. Sufficient conditions are obtained for the possibility of completing the pursuit in a finite time.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82995428","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
Non-linear wave propagation in a weakly compressible Kelvin-Voigt liquid containing bubbly clusters 含气泡团的弱可压缩Kelvin-Voigt液体中的非线性波传播
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230112
Y. B. Chukkol, I. Bello, M. Abdullahi
{"title":"Non-linear wave propagation in a weakly compressible Kelvin-Voigt liquid containing bubbly clusters","authors":"Y. B. Chukkol, I. Bello, M. Abdullahi","doi":"10.35634/vm230112","DOIUrl":"https://doi.org/10.35634/vm230112","url":null,"abstract":"The effect of bubble-bubble interaction on wave propagation in homogeneous weakly compressible viscoelastic bubbly flow is investigated using the reductive perturbation method. The bubble dynamics equation is derived using the kinetic energy conservation approach. The bubble dynamics and mixture equations are coupled with the equation of state for gas to investigate the shock wave propagation phenomenon in the mixture. A two-dimensional Korteweg-de VriesBurger (KdVB) equation in terms of a pressure profile is derived. It is found that the bubble-bubble interaction has no effect when using the parameters under our consideration.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81787207","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 Shimoda's Theorem 关于下田定理
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230102
A. Atamuratov, K.K. Rasulov
{"title":"On Shimoda's Theorem","authors":"A. Atamuratov, K.K. Rasulov","doi":"10.35634/vm230102","DOIUrl":"https://doi.org/10.35634/vm230102","url":null,"abstract":"The present work is devoted to Shimoda's Theorem on the holomorphicity of a function $f(z,w)$ which is holomorphic by $win V$ for each fixed $zin U$ and is holomorphic by $zin U$ for each fixed $win E$, where $Esubset V$ is a countable set with at least one limit point in $V$. Shimoda proves that in this case $f(z,w)$ is holomorphic in $Utimes V$ except for a nowhere dense closed subset of $Utimes V$. We prove the converse of this result, that is for an arbitrary given nowhere dense closed subset of $U$, $Ssubset U$, there exists a holomorphic function, satisfying Shimoda's Theorem on $Utimes Vsubset {mathbb C}^{2}$, that is not holomorphic on $Stimes V$. Moreover, we observe conditions which imply empty exception sets on Shimoda's Theorem and prove generalizations of Shimoda's Theorem.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78793622","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
Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition 一类具有非局部条件的抛物型积分微分方程的核确定问题
IF 0.5
Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2023-03-01 DOI: 10.35634/vm230106
D.Q. Durdiev, J. J. Jumaev, D. Atoev
{"title":"Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition","authors":"D.Q. Durdiev, J. J. Jumaev, D. Atoev","doi":"10.35634/vm230106","DOIUrl":"https://doi.org/10.35634/vm230106","url":null,"abstract":"In this paper, an inverse problem for a one-dimensional integro-differential heat equation is investigated with nonlocal initial-boundary and integral overdetermination conditions. We use the Fourier method and the Schauder principle to investigate the solvability of the direct problem. Further, the problem is reduced to an equivalent closed system of integral equations with respect to unknown functions. Existence and uniqueness of the solution of the integral equations are proved using a contractive mapping. Finally, using the equivalency, the existence and uniqueness of the classical solution is obtained.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72464121","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: 1
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