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Asymptotics of Fundamental Solutions of Parabolic Problems 抛物线问题基本解的渐近性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010176
V. G. Danilov
{"title":"Asymptotics of Fundamental Solutions of Parabolic Problems","authors":"V. G. Danilov","doi":"10.1134/s0001434624010176","DOIUrl":"https://doi.org/10.1134/s0001434624010176","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We present several methods for constructing the asymptotics of the fundamental solution of Fokker–Planck–Kolmogorov-type parabolic equations with a small parameter both for small and finite positive times. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Rational Spline Solutions of Differential Equations with Singularities in the Coefficients of the Derivatives 论微分方程的有理样条解法与微分系数的奇异性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010061
V. G. Magomedova, A.-R. K. Ramazanov
{"title":"On Rational Spline Solutions of Differential Equations with Singularities in the Coefficients of the Derivatives","authors":"V. G. Magomedova, A.-R. K. Ramazanov","doi":"10.1134/s0001434624010061","DOIUrl":"https://doi.org/10.1134/s0001434624010061","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For one generalization of the Riemann differential equation, we obtain sufficient conditions for the approximability by twice continuously differentiable rational interpolation spline functions. To solve the corresponding boundary value problem numerically, a tridiagonal system of linear algebraic equations is constructed and conditions on the coefficients of the differential equation are found guaranteeing the uniqueness of the solution of such Estimates of the deviation of the discrete solution of the boundary value problem from the exact solution on a grid are presented. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Solutions of the One-Dimensional Goldshtik Problem 论一维高兹提克问题的解决方案
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010024
O. V. Baskov, D. K. Potapov
{"title":"On Solutions of the One-Dimensional Goldshtik Problem","authors":"O. V. Baskov, D. K. Potapov","doi":"10.1134/s0001434624010024","DOIUrl":"https://doi.org/10.1134/s0001434624010024","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems 季霍诺夫型反应扩散系统的周期抛物线问题解的存在性、渐近性和李亚普诺夫稳定性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s000143462401022x
N. N. Nefedov
{"title":"Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems","authors":"N. N. Nefedov","doi":"10.1134/s000143462401022x","DOIUrl":"https://doi.org/10.1134/s000143462401022x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems are obtained. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparison of Purely Greedy and Orthogonal Greedy Algorithm 纯粹贪心算法与正交贪心算法的比较
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010048
K. S. Vishnevetskiy
{"title":"Comparison of Purely Greedy and Orthogonal Greedy Algorithm","authors":"K. S. Vishnevetskiy","doi":"10.1134/s0001434624010048","DOIUrl":"https://doi.org/10.1134/s0001434624010048","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Conditions for a dictionary in a Hilbert space are obtained that are necessary or sufficient for the coincidence of purely greedy and orthogonal greedy algorithms with respect to this dictionary. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming 论数学编程问题的二阶充分最优条件
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010140
A. V. Arutyunov, S. E. Zhukovskiy
{"title":"On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming","authors":"A. V. Arutyunov, S. E. Zhukovskiy","doi":"10.1134/s0001434624010140","DOIUrl":"https://doi.org/10.1134/s0001434624010140","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the constrained optimization problem for a smooth function defined on a Banach space with smooth constraints of equality and inequality type. We show that for this problem, under the known sufficient second-order optimality conditions, the set of Lagrange multipliers can be replaced by a smaller set. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Sum of Negative Eigenvalues of the Three-Dimensional Schrödinger Operator 论三维薛定谔算子的负特征值之和
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010139
A. R. Aliev, E. H. Eyvazov
{"title":"On the Sum of Negative Eigenvalues of the Three-Dimensional Schrödinger Operator","authors":"A. R. Aliev, E. H. Eyvazov","doi":"10.1134/s0001434624010139","DOIUrl":"https://doi.org/10.1134/s0001434624010139","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> M. Demuth and G. Katriel (arXiv: math.SP/0802.2032) proved the finiteness of the sum of negative eigenvalues of the <span>(d)</span>-dimensional Schrödinger operator under certain conditions on the electrical potential for <span>(dge 4)</span>. They also posed the following question: Is the restriction <span>(dge 4)</span> a disadvantage of the method, or does it reflect the actual situation? In the present paper, we prove that the technique in the cited paper also works for the three-dimensional Schrödinger operator with Kato potential whose negative part is an integrable function and that this method does not apply to the two-dimensional Schrödinger operator. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dominant Sets for Model Spaces in Several Variables 多变量模型空间的主集
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010127
A. B. Aleksandrov, E. S. Dubtsov
{"title":"Dominant Sets for Model Spaces in Several Variables","authors":"A. B. Aleksandrov, E. S. Dubtsov","doi":"10.1134/s0001434624010127","DOIUrl":"https://doi.org/10.1134/s0001434624010127","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>(I)</span> be an inner function in the domain <span>(mathcal{D}=B_{n_1}times B_{n_2}times dots times B_{n_k})</span>, where <span>(B_n)</span> is the open unit ball in <span>(mathbb{C}^n)</span>, <span>(nge 1)</span>. We construct dominant sets for the space <span>(H^2 ominus I H^2)</span>, where <span>(H^2= H^2(mathcal{D}))</span> is the standard Hardy space. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Algebraic Properties of Integrals of Products of Some Hypergeometric Functions 论某些超几何函数乘积积分的代数特性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010164
V. A. Gorelov
{"title":"On Algebraic Properties of Integrals of Products of Some Hypergeometric Functions","authors":"V. A. Gorelov","doi":"10.1134/s0001434624010164","DOIUrl":"https://doi.org/10.1134/s0001434624010164","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Indefinite integrals of products of generalized hypergeometric functions satisfying first- order differential equations are considered. Necessary and sufficient conditions for the algebraic independence of the set of these integrals and of their values at algebraic points are studied. All algebraic identities arising in this case are found in closed form. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded $$p$$ -Variation 有界 $$p$$ 变量的连续周期函数的傅里叶级数均匀收敛率估计
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-04-22 DOI: 10.1134/s0001434624010243
T. Yu. Semenova
{"title":"Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded $$p$$ -Variation","authors":"T. Yu. Semenova","doi":"10.1134/s0001434624010243","DOIUrl":"https://doi.org/10.1134/s0001434624010243","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We obtain an estimate for the convergence rate of the Fourier series of a continuous periodic function in terms of the modulus of continuity of the function and the value of its <span>(p)</span>-variation. We prove that the leading term of the estimate is sharp. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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