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Contemporary Mathematics. Fundamental Directions最新文献

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On Solution of First-Order Linear Systems of Partial Differential Equations 一阶线性偏微分方程组的解
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-549-563
V. Zadorozhniy, L. Y. Kabantsova
{"title":"On Solution of First-Order Linear Systems of Partial Differential Equations","authors":"V. Zadorozhniy, L. Y. Kabantsova","doi":"10.22363/2413-3639-2021-67-3-549-563","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-549-563","url":null,"abstract":"Explicit formulas for the first-order partial differential equations system solving were obtained. Solution found for the system with initial conditions. Calculation examples establishing statements truth mentioned. Searching for partial differential equations system solution mathematical expectation became more difficult issue as partial differential equations system with random processes coefficients were covered. Gaussian coefficients and uniformly distributed random process cases examples has been reviewed.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127616674","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
An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects 具有霍尔效应和离子滑移效应的磁流体动力学改进爆破判据
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-526-534
S. Gala, M. Ragusa
{"title":"An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects","authors":"S. Gala, M. Ragusa","doi":"10.22363/2413-3639-2021-67-3-526-534","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-526-534","url":null,"abstract":"In this work, we consider the magnetohydrodynamics system with the Hall and ion-slip effects in R3. The main result is a sufficient condition for regularity on a time interval [0,T] expressed in terms , of the norm of the homogeneous Besov space B˙,0{dot{B}_{infty,infty}^0} with respect to the pressure and the BMO-norm with respect to the gradient of the magnetic field, respectively \u0000∫0T(‖Δπ(t)‖B˙∞,∞02/3+‖ΔB(t)‖BMO2)dt∞{int_{0}^{T} ({| Delta pi(t)|}^{2/3}_{dot{B}_{infty,infty}^0} + {| Delta B (t)|}^{2}_{BMO} ) dt","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"318 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116289220","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: 3
On the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain 无限域上高阶椭圆型方程广义Neumann问题的可解性
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-564-575
B. Koshanov, A. Soldatov
{"title":"On the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain","authors":"B. Koshanov, A. Soldatov","doi":"10.22363/2413-3639-2021-67-3-564-575","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-564-575","url":null,"abstract":"We consider the generalized Neumann problem for a 2lth-order elliptic equation with constant real higher-order coefficients in an infinite domain containing the exterior of some circle and bounded by a sufficiently smooth contour. It consists in specifying of the (kj-1){(k_j - 1)}th-order normal derivatives where 1≤k1...kl≤2l{1le k_1 < ... < k_l le 2l}; for kj=j{k_j = j} it turns into the Dirichlet problem, and for kj=j+1{k_j = j +1} into the Neumann problem. Under certain assumptions about the coefficients of the equation at infinity, a necessary and sufficient condition for the Fredholm property of this problem is obtained and a formula for its index in Holder spaces is given.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125746363","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
Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform 与随机过程相关的方程:半群方法和傅立叶变换
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-2-324-348
I. Melnikova, U. A. Alekseeva, V. A. Bovkun
{"title":"Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform","authors":"I. Melnikova, U. A. Alekseeva, V. A. Bovkun","doi":"10.22363/2413-3639-2021-67-2-324-348","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-2-324-348","url":null,"abstract":"The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations - stochastic differential equations (SDEs) - and deterministic equations for the probabilistic characteristics of processes determined by random perturbations. The resulting deterministic pseudodifferential equations are investigated by semigroup methods and Fourier transform methods.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126470764","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 Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients 变系数微分-差分方程第二边值问题的广义解
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-576-595
A. Skubachevskii, N. Ivanov
{"title":"On Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients","authors":"A. Skubachevskii, N. Ivanov","doi":"10.22363/2413-3639-2021-67-3-576-595","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-576-595","url":null,"abstract":"We consider the second boundary-value problem for a second-order differential-difference equation with variable coefficients on the interval (0,d). We investigate the existence of a generalized solution and obtain conditions on the right-hand side of the equation which ensure the smoothness of generalized solutions on the entire interval (0,d).","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114273132","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: 5
Delay Differential Equations with Differentiable Solution Operators on Open Domains in C((-∞, 0], Rn) and Processes for Volterra Integro-Differential Equations C((-∞，0]，Rn)开域上具有可微解算子的时滞微分方程及Volterra积分微分方程的过程
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-483-506
H. Walther
{"title":"Delay Differential Equations with Differentiable Solution Operators on Open Domains in C((-∞, 0], Rn) and Processes for Volterra Integro-Differential Equations","authors":"H. Walther","doi":"10.22363/2413-3639-2021-67-3-483-506","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-483-506","url":null,"abstract":"For autonomous delay differential equations x'(t)=f(xt){x'(t)=f(x_t)} we construct a continuous semiflow of continuously differentiable solution operators x0xt{x_0 to x_t}, t0{t le 0}, on open subsets of the Frechet space C((-,0],Rn){C((-infty, 0], R^n)}. For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application, we obtain processes which incorporate all solutions of Volterra integro-differential equations x'(t)=∫0tk(t,s)h(x(s))ds{x'(t)={int_0}^t k(t,s) h(x(s)) ds}.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123219707","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
Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities 具有不可积正则奇异点的任意阶微分算子谱分析的正逆问题
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-2-408-421
V. Yurko
{"title":"Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities","authors":"V. Yurko","doi":"10.22363/2413-3639-2021-67-2-408-421","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-2-408-421","url":null,"abstract":"A short review is presented of results on the spectral theory of arbitrary order ordinary differential operators with non-integrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117218860","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
On Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability 可和变序Lebesgue空间中的Holder不等式
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-472-482
V. Burenkov, T. Tararykova
{"title":"On Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability","authors":"V. Burenkov, T. Tararykova","doi":"10.22363/2413-3639-2021-67-3-472-482","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-472-482","url":null,"abstract":"In this paper, we introduce a new version of the definition of a quasi-norm (in particular, a norm) in Lebesgue spaces with variable order of summability. Using it, we prove an analogue of Holders inequality for such spaces, which is more general and more precise than those known earlier.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128003049","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
Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals 多重傅立叶级数和积分的广义局部化和几乎处处可和性
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-4-634-653
R. Ashurov
{"title":"Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals","authors":"R. Ashurov","doi":"10.22363/2413-3639-2021-67-4-634-653","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-4-634-653","url":null,"abstract":"It is well known that Luzins conjecture has a positive solution for one-dimensional trigonometric Fourier series, but in the multidimensional case it has not yet found its confirmation for spherical partial sums of multiple Fourier series. Historically, progress in solving Luzins hypothesis has been achieved by considering simpler problems. In this paper, we consider three of these problems for spherical partial sums: the principle of generalized localization, summability almost everywhere, and convergence almost everywhere of multiple Fourier series of smooth functions. A brief overview of the work in these areas is given and unsolved problems are mentioned and new problems are formulated. Moreover, at the end of the work, a new result on the convergence of spherical sums for functions from Sobolev classes is proved.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116137850","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
Weak and Strong Asymptotics of Orthogonal Polynomials with «Varying» Weight 变权正交多项式的弱渐近和强渐近
Contemporary Mathematics. Fundamental Directions Pub Date : 2021-12-15 DOI: 10.22363/2413-3639-2021-67-3-427-441
A. I. Aptekarev
{"title":"Weak and Strong Asymptotics of Orthogonal Polynomials with «Varying» Weight","authors":"A. I. Aptekarev","doi":"10.22363/2413-3639-2021-67-3-427-441","DOIUrl":"https://doi.org/10.22363/2413-3639-2021-67-3-427-441","url":null,"abstract":"We consider sequences of orthogonal polynomials with varying weights, i.e., depending on the number of the polynomial. We obtain extensions of applicability classes of well-known asymptotic formulas for large numbers.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121831786","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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