Pub Date : 2024-11-28DOI: 10.1016/j.jmaa.2024.129091
Zhen-Hang Yang , Feng Qi
The bivariate homogeneous functions of two parameters are also called the bivariate means of two parameters. In the paper, the authors survey some results published since 2005 about monotonicity, logarithmic convexity, and Schur convexity of the bivariate homogeneous functions of two parameters, review the Minkowski, Hölder, Chebyshev, and Hermite–Hadamard type inequalities for the bivariate homogeneous functions of two parameters, and exhibit comparisons of the bivariate homogeneous functions of two parameters. Applying these results, the authors derive and remark some nice inequalities for the bivariate homogeneous functions of two parameters.
{"title":"Bivariate homogeneous functions of two parameters: Monotonicity, convexity, comparisons, and functional inequalities","authors":"Zhen-Hang Yang , Feng Qi","doi":"10.1016/j.jmaa.2024.129091","DOIUrl":"10.1016/j.jmaa.2024.129091","url":null,"abstract":"<div><div>The bivariate homogeneous functions of two parameters are also called the bivariate means of two parameters. In the paper, the authors survey some results published since 2005 about monotonicity, logarithmic convexity, and Schur convexity of the bivariate homogeneous functions of two parameters, review the Minkowski, Hölder, Chebyshev, and Hermite–Hadamard type inequalities for the bivariate homogeneous functions of two parameters, and exhibit comparisons of the bivariate homogeneous functions of two parameters. Applying these results, the authors derive and remark some nice inequalities for the bivariate homogeneous functions of two parameters.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129091"},"PeriodicalIF":1.2,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmaa.2024.129083
Sergey A. Timoshin , Alexander A. Tolstonogov
We consider a sweeping process with a triple perturbation defined on a separable Hilbert space. The values of the moving set are time- and state-dependent prox-regular sets. The perturbation is given by the sum of three multivalued mappings having different semicontinuity properties with respect to the state variable. The first mapping with closed, possibly, nonconvex values is lower semicontinuous. The second one with closed convex values has weakly sequentially closed graph. The values of the third mapping can be both convex and nonconvex closed sets. This mapping has closed graph at the points where it is convex-valued. At a point therein its value is a nonconvex set, the mapping is lower semicontinuous on a neighborhood of this point. Usually, the latter mapping is called a mapping with mixed semicontinuity properties. We prove the existence of a solution to our sweeping process. To this aim, we propose a new method that is not related to the catching-up algorithm or its modifications often used in the existence proofs for sweeping processes. We use classical approaches based on a priori estimates and a fixed-point argument for multivalued mappings. Our existence result is completely new and it implies the existing results for the considered class of sweeping processes with state-dependent moving sets.
{"title":"State-dependent prox-regular sweeping process with a general nonconvex composed perturbation","authors":"Sergey A. Timoshin , Alexander A. Tolstonogov","doi":"10.1016/j.jmaa.2024.129083","DOIUrl":"10.1016/j.jmaa.2024.129083","url":null,"abstract":"<div><div>We consider a sweeping process with a triple perturbation defined on a separable Hilbert space. The values of the moving set are time- and state-dependent prox-regular sets. The perturbation is given by the sum of three multivalued mappings having different semicontinuity properties with respect to the state variable. The first mapping with closed, possibly, nonconvex values is lower semicontinuous. The second one with closed convex values has weakly sequentially closed graph. The values of the third mapping can be both convex and nonconvex closed sets. This mapping has closed graph at the points where it is convex-valued. At a point therein its value is a nonconvex set, the mapping is lower semicontinuous on a neighborhood of this point. Usually, the latter mapping is called a mapping with mixed semicontinuity properties. We prove the existence of a solution to our sweeping process. To this aim, we propose a new method that is not related to the catching-up algorithm or its modifications often used in the existence proofs for sweeping processes. We use classical approaches based on a priori estimates and a fixed-point argument for multivalued mappings. Our existence result is completely new and it implies the existing results for the considered class of sweeping processes with state-dependent moving sets.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129083"},"PeriodicalIF":1.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmaa.2024.129087
Bochra Belhadji , Mama Abdelli , Akram Ben Aissa , Khaled Zennir
We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
{"title":"Global existence and stabilization of the quasilinear Petrovsky equation with localized nonlinear damping","authors":"Bochra Belhadji , Mama Abdelli , Akram Ben Aissa , Khaled Zennir","doi":"10.1016/j.jmaa.2024.129087","DOIUrl":"10.1016/j.jmaa.2024.129087","url":null,"abstract":"<div><div>We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129087"},"PeriodicalIF":1.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmaa.2024.129082
Scott Harman
For the Laplacian in spherical and hyperbolic spaces, Robin eigenvalues in two dimensions and Dirichlet eigenvalues in higher dimensions are shown to satisfy scaling inequalities analogous to the standard scale invariance of the Euclidean Laplacian. These results extend work of Langford and Laugesen to Robin problems and to Dirichlet problems in higher dimensions. In addition, scaled Robin eigenvalues behave exotically as the domain expands to a 2-sphere, tending to the spectrum of an exterior Robin problem.
{"title":"Scaling inequalities and limits for Robin and Dirichlet eigenvalues","authors":"Scott Harman","doi":"10.1016/j.jmaa.2024.129082","DOIUrl":"10.1016/j.jmaa.2024.129082","url":null,"abstract":"<div><div>For the Laplacian in spherical and hyperbolic spaces, Robin eigenvalues in two dimensions and Dirichlet eigenvalues in higher dimensions are shown to satisfy scaling inequalities analogous to the standard scale invariance of the Euclidean Laplacian. These results extend work of Langford and Laugesen to Robin problems and to Dirichlet problems in higher dimensions. In addition, scaled Robin eigenvalues behave exotically as the domain expands to a 2-sphere, tending to the spectrum of an exterior Robin problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129082"},"PeriodicalIF":1.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmaa.2024.129090
Malay Mandal , Kunal Mukherjee , Issan Patri
The mixed q-deformed Araki-Woods -algebras are simple when the underlying Hilbert space in the construction is infinite-dimensional and the analytic generator of the associated orthogonal representation is bounded.
当构造中的底层Hilbert空间为无限维且相关正交表示的解析生成器有界时，混合q-变形Araki-Woods C -代数是简单的。
{"title":"On the simplicity of certain mixed q-deformed Araki-Woods C⁎-algebras","authors":"Malay Mandal , Kunal Mukherjee , Issan Patri","doi":"10.1016/j.jmaa.2024.129090","DOIUrl":"10.1016/j.jmaa.2024.129090","url":null,"abstract":"<div><div>The mixed <em>q</em>-deformed Araki-Woods <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras are simple when the underlying Hilbert space in the construction is infinite-dimensional and the analytic generator of the associated orthogonal representation is bounded.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129090"},"PeriodicalIF":1.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmaa.2024.129086
Nguyen Viet Phuong , Ta Thi Hoai An
In this paper, we will give a better upper bound for the defect relation for a class of holomorphic maps, this result is generalized to hypersurfaces from the hyperplane case in [9]. More precisely, let be hypersurfaces in general position, and let be holomorphic map of lower order μ, such that for all . If then
{"title":"Defect relations for holomorphic curves of finite lower order intersecting hypersurfaces","authors":"Nguyen Viet Phuong , Ta Thi Hoai An","doi":"10.1016/j.jmaa.2024.129086","DOIUrl":"10.1016/j.jmaa.2024.129086","url":null,"abstract":"<div><div>In this paper, we will give a better upper bound for the defect relation for a class of holomorphic maps, this result is generalized to hypersurfaces from the hyperplane case in <span><span>[9]</span></span>. More precisely, let <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> be hypersurfaces in general position, and let <span><math><mi>f</mi><mo>:</mo><mi>C</mi><mo>→</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>C</mi><mo>)</mo></math></span> be holomorphic map of lower order <em>μ</em>, such that <span><math><mi>f</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>⊄</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for all <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>q</mi></math></span>. If <span><math><mn>0</mn><mo><</mo><mi>μ</mi><mo>≤</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> then<span><span><span><math><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>q</mi></mrow></munderover><msub><mrow><mi>δ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>≤</mo><mi>n</mi><mo>.</mo></math></span></span></span></div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129086"},"PeriodicalIF":1.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.jmaa.2024.129080
Arup Chattopadhyay, Supratim Jana
In the classical Hardy space , it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator . It appears in this paper that kernels of finite rank perturbations of Hankel operators are almost shift invariant as well as nearly -invariant with finite defect. This allows us to obtain a structure of the kernel in several important cases by applying a recent theorem due to Chalendar, Gallardo, and Partington.
{"title":"Kernels of perturbed Hankel operators","authors":"Arup Chattopadhyay, Supratim Jana","doi":"10.1016/j.jmaa.2024.129080","DOIUrl":"10.1016/j.jmaa.2024.129080","url":null,"abstract":"<div><div>In the classical Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. It appears in this paper that kernels of finite rank perturbations of Hankel operators are almost shift invariant as well as nearly <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-invariant with finite defect. This allows us to obtain a structure of the kernel in several important cases by applying a recent theorem due to Chalendar, Gallardo, and Partington.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129080"},"PeriodicalIF":1.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.jmaa.2024.129078
Aaron Melman
We derive zero inclusion sectors for both analytic and harmonic trinomials, as well as sector dependent lower bounds on the magnitudes of their zeros. In addition, we determine the minimum and maximum number of zeros of a harmonic trinomial from basic arguments. Examples illustrate the theory.
{"title":"Zero location for analytic and harmonic trinomials","authors":"Aaron Melman","doi":"10.1016/j.jmaa.2024.129078","DOIUrl":"10.1016/j.jmaa.2024.129078","url":null,"abstract":"<div><div>We derive zero inclusion sectors for both analytic and harmonic trinomials, as well as sector dependent lower bounds on the magnitudes of their zeros. In addition, we determine the minimum and maximum number of zeros of a harmonic trinomial from basic arguments. Examples illustrate the theory.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129078"},"PeriodicalIF":1.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive analytic formulas for the alternating projection method applied to the cone of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to and a 3-plane whose intersection is a singleton with singularity degree 2.
{"title":"Analytic formulas for alternating projection sequences for the positive semidefinite cone and an application to convergence analysis","authors":"Hiroyuki Ochiai , Yoshiyuki Sekiguchi , Hayato Waki","doi":"10.1016/j.jmaa.2024.129070","DOIUrl":"10.1016/j.jmaa.2024.129070","url":null,"abstract":"<div><div>We derive analytic formulas for the alternating projection method applied to the cone <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> and a 3-plane whose intersection is a singleton with singularity degree 2.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129070"},"PeriodicalIF":1.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.jmaa.2024.129072
Chris Vales
This work is concerned with the spectral analysis of a piezoelectric energy harvesting model based on a coupled bending-torsion beam. After building the problem's operator setting and showing that the governing operator is nonselfadjoint with a purely discrete spectrum, we derive an asymptotic approximation of its spectrum. In doing so, we also prove that the addition of energy harvesting can be viewed as a weak perturbation of the underlying beam dynamics, in the sense that no piezoelectric parameters appear in the spectral approximation's first two orders of magnitude. We conclude by outlining future work based on numerical simulations.
{"title":"Spectral analysis of a coupled bending-torsion beam energy harvester: asymptotic results","authors":"Chris Vales","doi":"10.1016/j.jmaa.2024.129072","DOIUrl":"10.1016/j.jmaa.2024.129072","url":null,"abstract":"<div><div>This work is concerned with the spectral analysis of a piezoelectric energy harvesting model based on a coupled bending-torsion beam. After building the problem's operator setting and showing that the governing operator is nonselfadjoint with a purely discrete spectrum, we derive an asymptotic approximation of its spectrum. In doing so, we also prove that the addition of energy harvesting can be viewed as a weak perturbation of the underlying beam dynamics, in the sense that no piezoelectric parameters appear in the spectral approximation's first two orders of magnitude. We conclude by outlining future work based on numerical simulations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129072"},"PeriodicalIF":1.2,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号