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Functional Analysis and Its Applications最新文献

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Normal Oscillations of a Pendulum with Cavity Completely Filled with Viscoelastic Fluid (Two-Dimensional Case) 完全充满粘弹性流体空腔的钟摆法向振动（二维情况）
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-10-02 DOI: 10.1134/S1234567826030079
Denis Tsvetkov
{"title":"Normal Oscillations of a Pendulum with Cavity Completely Filled with Viscoelastic Fluid (Two-Dimensional Case)","authors":"Denis Tsvetkov","doi":"10.1134/S1234567826030079","DOIUrl":"10.1134/S1234567826030079","url":null,"abstract":"<p> The two-dimensional problem of normal oscillations of a pendulum with a cavity completely filled with a viscoelastic fluid described by the generalized Oldroyd model is investigated. After formulating the initial-boundary value problem and its operator representation, the properties of the operators involved are examined. The main spectral problem for these operators is formulated and the structure of the corresponding spectrum is studied. A connection is established between the solution of the formulated problem and the eigenvalue problem for a certain operator pencil. Based on this connection, additional information about the structure of the spectrum is obtained. Statements concerning the asymptotic behavior of the eigenvalues are derived and the basis properties of the system of eigenvectors are studied. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 3","pages":"276 - 293"},"PeriodicalIF":0.7,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149098512","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
Generalised Joyal Disks and Higher Operads 广义磁盘和高级操作符
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020084
Boris Shoikhet
{"title":"Generalised Joyal Disks and Higher Operads","authors":"Boris Shoikhet","doi":"10.1134/S1234567826020084","DOIUrl":"10.1134/S1234567826020084","url":null,"abstract":"<p> In this short paper, we announce results on a new construction of higher operads in the sense of Batanin. Our construction is based on a new concept of a generalised Joyal disk. We introduce a funny product on the category of generalised <span>(d)</span>-disks, which makes it possible to generalise the lattice path operad. For each <span>(dge 1)</span>, the generalised lattice path operad <span>(mathcal{L}^d)</span> is a colored symmetric operad with the category of unary operations <span>(Theta_d)</span>. Our goal in this paper is to depict a <span>((d+1))</span>-operad <span>(mathbf{seq}_d)</span> inside the desymmetrisation <span>(mathrm{des}(mathcal{L}^d))</span>. Tamarkin’s operad <span>(mathbf{seq})</span> is a solution for <span>(d=1)</span>. We succeed in constructing such an operad <span>(mathbf{seq}_d)</span> for <span>(d=2,3)</span>, and prove that it is contractible in the topological and dg condensations. For <span>(d&gt;3)</span>, an explicit construction is also provided, but the proof that it is indeed a <span>((d+1))</span>-operad (as well as proving its topological and dg contractibility) relies on combinatorial conjectures which are still open. The symmetrisation theorem is applied to <span>(mathbf{seq}_d)</span>, which potentially gives rise to a <span>(E_{d+1})</span>-algebra structure on <span>(d)</span>-categorical deformation complexes. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"203 - 207"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433692","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
Operator Monotone Functions and Commutativity of (C^*)-Algebras (C^*) -代数的算子单调函数与交换性
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020060
Yifan Liu
{"title":"Operator Monotone Functions and Commutativity of (C^*)-Algebras","authors":"Yifan Liu","doi":"10.1134/S1234567826020060","DOIUrl":"10.1134/S1234567826020060","url":null,"abstract":"<p> We show that if <span>(f)</span> is a nonlinear convex increasing function on <span>(mathbb{R})</span>, <span>(A)</span> is a <span>(C^*)</span>-algebra, and the continuous functional calculus of <span>(f)</span> on <span>(A_{mathrm{sa}})</span> preserves the order of the elements in <span>(A_{mathrm{sa}})</span>, then <span>(A)</span> is commutative. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"197 - 200"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433694","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
Iterated Integrals of Finite- and Infinite-Dimensional Gaussian Processes 有限维和无限维高斯过程的迭代积分
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020023
Artem Kalinichenko
{"title":"Iterated Integrals of Finite- and Infinite-Dimensional Gaussian Processes","authors":"Artem Kalinichenko","doi":"10.1134/S1234567826020023","DOIUrl":"10.1134/S1234567826020023","url":null,"abstract":"<p> In this paper, we find conditions under which the known definitions of iterated integrals of finite-dimensional Gaussian processes could be used to construct integrals of the infinite-dimensional analogues of these processes. In the context of the rough paths theory, our results allow us to carry the existing constructions of finite-dimensional Gaussian rough paths over to the infinite-dimensional case. Using more abstract terms, we define a continuous linear map between the space of Gaussian chaoses generated by some Gaussian processes and the space of chaoses generated by the infinite-dimensional analogues of these processes. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"129 - 146"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433697","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
Exotic Spherical Flexible Octahedra and Counterexamples to the Modified Bellows Conjecture 奇异球面柔性八面体及修正波纹管猜想的反例
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020011
Alexander A. Gaifullin
{"title":"Exotic Spherical Flexible Octahedra and Counterexamples to the Modified Bellows Conjecture","authors":"Alexander A. Gaifullin","doi":"10.1134/S1234567826020011","DOIUrl":"10.1134/S1234567826020011","url":null,"abstract":"<p> In 2014, the author showed that in the three-dimensional spherical space, alongside the three classical types of flexible octahedra constructed by Bricard, there exists a new type of flexible octahedra, which was called exotic. In the present paper, we give a geometric construction for exotic flexible octahedra, describe their configuration spaces, and calculate their volumes. We show that the volume of an exotic flexible octahedron is nonconstant during the flexion, and, moreover, the volume remains nonconstant if we replace any set of vertices of the octahedron with their antipodes. So exotic flexible octahedra are counterexamples to the Modified Bellows Conjecture proposed by the author in 2015. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"107 - 128"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433695","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
Some Nonexistence Results of Systems of Quasilinear Elliptic Inequalities Involving the (Delta_lambda)-Laplacian 涉及(Delta_lambda) - laplace的拟线性椭圆不等式系统的一些不存在性结果
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020035
Thi Lieu Le, Ba Phuong Le, Quang Thanh Khuat, Thi Minh Nguyet Tran
{"title":"Some Nonexistence Results of Systems of Quasilinear Elliptic Inequalities Involving the (Delta_lambda)-Laplacian","authors":"Thi Lieu Le,&nbsp;Ba Phuong Le,&nbsp;Quang Thanh Khuat,&nbsp;Thi Minh Nguyet Tran","doi":"10.1134/S1234567826020035","DOIUrl":"10.1134/S1234567826020035","url":null,"abstract":"<p> In this paper, we establish some nonexistence results of a quasilinear elliptic inequality </p><p> and a system of quasilinear elliptic inequalities </p><p> where <span>(nabla_lambda=(lambda_1partial_{x_1},lambda_2partial_{x_2},dots,lambda_Npartial_{x_N}))</span> and <span>(lambda_i)</span>, <span>(i=1,2,dots,N)</span> are some functions. Here, <span>(p,widetilde{p}&gt;1)</span>, <span>(q, widetilde{q}geq 0)</span>, and <span>(w,h, widetilde{w}, widetilde{h} in L^1_{mathrm{loc}}(mathbb R^N))</span> are nonnegative functions satisfying some growth conditions at infinity. In particular, our results can be seen as a generalization of some results of Mitidieri and Pokhozhaev from the Laplace operator to the <span>(Delta_lambda)</span>-Laplacian. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"147 - 161"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433698","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 Combinatorial and Ergodic Properties of Certain Classes of Interval Translation Mappings 论区间平移映射的组合性和遍历性
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020059
Alexandra Skripchenko, Valentin Chernyi
{"title":"On Combinatorial and Ergodic Properties of Certain Classes of Interval Translation Mappings","authors":"Alexandra Skripchenko,&nbsp;Valentin Chernyi","doi":"10.1134/S1234567826020059","DOIUrl":"10.1134/S1234567826020059","url":null,"abstract":"<p> In this paper, we study a special class of interval translation mappings introduced in 2007 by H. Bruin. We prove that a typical map of infinite type is uniquely ergodic and provide an upper bound for the Hausdorff dimension of the parameter set that gives rise to the interval translation mappings of infinite type. Moreover, we prove that such interval translation mappings have sublinear combinatorial complexity. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"180 - 196"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433760","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
Localization of Eigenfunctions Near the Vertices in Dirichlet’s Faceted Cup Dirichlet面杯中顶点附近特征函数的局部化
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020047
Sergei Nazarov
{"title":"Localization of Eigenfunctions Near the Vertices in Dirichlet’s Faceted Cup","authors":"Sergei Nazarov","doi":"10.1134/S1234567826020047","DOIUrl":"10.1134/S1234567826020047","url":null,"abstract":"<p> We study the spectrum of the Dirichlet problem for the Laplace operator in a thin-walled domain shaped as an upright faceted cup with a regular polygon as the base. We obtain restrictions on the relative thickness of the bottom that ensure localization of the first few eigenfunctions in a neighborhood of the vertices of the base. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"162 - 179"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433693","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 Moutard Type Transformation for Matrix Pairs of Generalized Analytic Functions 广义解析函数矩阵对的Moutard型变换
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-07-10 DOI: 10.1134/S1234567826020072
Yi C. Huang
{"title":"On the Moutard Type Transformation for Matrix Pairs of Generalized Analytic Functions","authors":"Yi C. Huang","doi":"10.1134/S1234567826020072","DOIUrl":"10.1134/S1234567826020072","url":null,"abstract":"<p> We present a seemingly overlooked property of the Moutard transformation considered by Novikov and Taimanov for matrix pairs of generalized analytic functions. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 2","pages":"201 - 202"},"PeriodicalIF":0.7,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148433696","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 Commuting Differential Operators of Rank 2 Corresponding to Trigonal Spectral Curves of Genus 3 3属三角谱曲线对应的2阶可交换微分算子
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010088
Matvey Ivlev
{"title":"On Commuting Differential Operators of Rank 2 Corresponding to Trigonal Spectral Curves of Genus 3","authors":"Matvey Ivlev","doi":"10.1134/S1234567826010088","DOIUrl":"10.1134/S1234567826010088","url":null,"abstract":"<p> The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications in soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank <span>(l&gt;1)</span> has not been solved in the general case. In all known examples of operators of rank <span>(l&gt;1)</span>, the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"102 - 106"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579671","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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