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Lichnerowicz Laplacian from the Point of View of the Bochner Technique 从 Bochner 技术的角度看 Lichnerowicz Laplacian
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030179
I. A. Aleksandrova, S. E. Stepanov, I. I. Tsyganok
{"title":"Lichnerowicz Laplacian from the Point of View of the Bochner Technique","authors":"I. A. Aleksandrova, S. E. Stepanov, I. I. Tsyganok","doi":"10.1134/s0001434624030179","DOIUrl":"https://doi.org/10.1134/s0001434624030179","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Vanishing theorems for the kernels of Lichnerowicz and Hodge Laplacians on a complete Riemannian manifold are proved, and the eigenvalues of a Lichnerowicz Laplacian on a closed Riemannian manifold are estimated. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573487","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 an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space 论巴拿赫空间中非凸值分式微分夹杂的初值问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030088
V. V. Obukhovskii, G. G. Petrosyan, M. S. Soroka
{"title":"On an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space","authors":"V. V. Obukhovskii, G. G. Petrosyan, M. S. Soroka","doi":"10.1134/s0001434624030088","DOIUrl":"https://doi.org/10.1134/s0001434624030088","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Based on fixed point theory for condensing operators, an initial value problem for semilinear differential inclusions of fractional order <span>(qin(1,2))</span> in Banach spaces is studied. It is assumed that the linear part of the inclusion generates a family of cosine operator functions and the nonlinear part is a multivalued map with nonconvex values. Local and global existence theorems for mild solutions of the initial value problem are proved. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573364","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
To the Continuation of Solution Germs 为继续解决病菌问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030350
N. A. Shananin
{"title":"To the Continuation of Solution Germs","authors":"N. A. Shananin","doi":"10.1134/s0001434624030350","DOIUrl":"https://doi.org/10.1134/s0001434624030350","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In the note, by a model example of a linear partial differential equation, it is demonstrated how the properties of continuation of germs of generalized solutions are changed depending on the type of differential system generated by the principal real-analytic symbol of the equation and on whether the infinitely differentiable coefficient at the lowest term of the equation belongs to the class of real-analytic functions. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573499","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
Piercing Hyperplane Theorem 穿透超平面定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030349
Burak Ünveren, Guy Barokas
{"title":"Piercing Hyperplane Theorem","authors":"Burak Ünveren, Guy Barokas","doi":"10.1134/s0001434624030349","DOIUrl":"https://doi.org/10.1134/s0001434624030349","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We prove that any strictly convex and closed set in <span>(mathbb{R}^n)</span> is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set <span>(C)</span> unless <span>(C)</span> is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573498","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 Generation of the Groups $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ and $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ by Three Involutions Two of Which Commute. II 论 $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ 和 $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ 群的生成--三个旋回 其中两个相交.二
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030015
M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, T. B. Shaipova
{"title":"On the Generation of the Groups $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ and $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ by Three Involutions Two of Which Commute. II","authors":"M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, T. B. Shaipova","doi":"10.1134/s0001434624030015","DOIUrl":"https://doi.org/10.1134/s0001434624030015","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We complete the solution of the problem on the existence of generating triplets of involutions two of which commute for the special linear group <span>(mathrm{SL}_n(mathbb{Z}+imathbb{Z}))</span> and the projective special linear group <span>(mathrm{PSL}_n(mathbb{Z}+imathbb{Z}))</span> over the ring of Gaussian integers. The answer has only been unknown for <span>(mathrm{SL}_5)</span>, <span>(mathrm{PSL}_6)</span>, and <span>(mathrm{SL}_{10})</span>. We explicitly indicate the generating triples of involutions in these three cases, and we make a significant use of computer calculations in the proof. Taking into account the known results for the problem under consideration, as a consequence, we obtain the following two statements. The group <span>(mathrm{SL}_n(mathbb{Z}+imathbb{Z}))</span> (respectively, <span>(mathrm{PSL}_n(mathbb{Z}+imathbb{Z}))</span>) is generated by three involutions two of which commute if and only if <span>(ngeq 5)</span> and <span>(nneq 6)</span> (respectively, if <span>(ngeq 5)</span>). </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573358","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
Generalized Multiple Multiplicative Fourier Transform and Estimates of Integral Moduli of Continuity 广义多重傅立叶变换和连续性积分模量估算
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030246
S. S. Volosivets
{"title":"Generalized Multiple Multiplicative Fourier Transform and Estimates of Integral Moduli of Continuity","authors":"S. S. Volosivets","doi":"10.1134/s0001434624030246","DOIUrl":"https://doi.org/10.1134/s0001434624030246","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper presents the properties of generalized multiple multiplicative Fourier transforms. Also, upper and lower bounds are given for the integral modulus of continuity in terms of the mentioned Fourier transforms, and the bound in <span>(L^2)</span> is unimprovable. As a corollary, an analog of Titchmarsh’s equivalence theorem for the multiplicative Fourier transform is obtained. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573489","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
A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean 关于具有里兹均值的傅里叶级数的 $$L^1$$ 收敛性的说明
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s000143462403009x
H. S. Özarslan, M. Ö. Şakar
{"title":"A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean","authors":"H. S. Özarslan, M. Ö. Şakar","doi":"10.1134/s000143462403009x","DOIUrl":"https://doi.org/10.1134/s000143462403009x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, the problem of <span>(L^1)</span>-convergence of Fourier series with quasi-monotone coefficients is handled by using the <span>((bar{N},p_n))</span>-mean. Also, an example is given about the Fourier series of a signal (function) <span>(f)</span> and its <span>((bar{N},p_n))</span> mean. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573477","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
Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix 具有部分退化扩散矩阵的柯尔莫哥洛夫方程的哈斯明斯基定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030155
S. V. Shaposhnikov, D. V. Shatilovich
{"title":"Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix","authors":"S. V. Shaposhnikov, D. V. Shatilovich","doi":"10.1134/s0001434624030155","DOIUrl":"https://doi.org/10.1134/s0001434624030155","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The stationary Kolmogorov equation with partially degenerate diffusion matrix and discontinuous drift coefficient is studied. Sufficient conditions for the existence of a probability solution are obtained. Examples demonstrating the sharpness of these conditions are given. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573482","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 Existence and Properties of Convex Extensions of Boolean Functions 论布尔函数凸扩展的存在和性质
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030210
D. N. Barotov
{"title":"On the Existence and Properties of Convex Extensions of Boolean Functions","authors":"D. N. Barotov","doi":"10.1134/s0001434624030210","DOIUrl":"https://doi.org/10.1134/s0001434624030210","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the problem of the existence of a convex extension of any Boolean function <span>(f(x_1,x_2,dots,x_n))</span> to the set <span>([0,1]^n)</span>. A convex extension <span>(f_C(x_1,x_2,dots,x_n))</span> of an arbitrary Boolean function <span>(f(x_1,x_2,dots,x_n))</span> to the set <span>([0,1]^n)</span> is constructed. On the basis of the constructed convex extension <span>(f_C(x_1,x_2,dots,x_n))</span>, it is proved that any Boolean function <span>(f(x_1,x_2,dots,x_n))</span> has infinitely many convex extensions to <span>([0,1]^n)</span>. Moreover, it is proved constructively that, for any Boolean function <span>(f(x_1,x_2,dots,x_n))</span>, there exists a unique function <span>(f_{DM}(x_1,x_2,dots,x_n))</span> being its maximal convex extensions to <span>([0,1]^n)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573488","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
Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation 用第一近似法研究微分系统的完全振荡、旋转和徘徊特性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030313
I. N. Sergeev
{"title":"Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation","authors":"I. N. Sergeev","doi":"10.1134/s0001434624030313","DOIUrl":"https://doi.org/10.1134/s0001434624030313","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573496","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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