Pub Date : 2025-03-04DOI: 10.1007/s10208-025-09702-0
Buyang Li, Yifei Wu
This article is concerned with the construction and analysis of new time discretizations for the KdV equation on a torus for low-regularity solutions below (H^1). New harmonic analysis tools, including averaging approximations to the exponential phase functions and trilinear estimates of the KdV operator, are established for the construction and analysis of time discretizations with higher convergence orders under low-regularity conditions. In addition, new perturbation techniques are introduced to establish stability estimates of time discretizations under low-regularity conditions without using filters when the energy techniques fail. The proposed method is proved to be convergent with order (gamma ) (up to a logarithmic factor) in (L^2) under the regularity condition (uin C([0,T];H^gamma )) for (gamma in (0,1]).
本文关注环上 KdV 方程对于低于 (H^1)的低规则解的新时间离散的构造和分析。本文建立了新的谐波分析工具，包括指数相位函数的平均近似和 KdV 算子的三线性估计，用于构建和分析低规则性条件下具有更高收敛阶数的时间离散。此外，还引入了新的扰动技术，当能量技术失效时，无需使用滤波器即可建立低规则性条件下时间离散的稳定性估计。在 (gamma in C([0,T];H^gamma )) 为 (gamma in (0,1])的规则性条件下，所提出的方法被证明在 (L^2) 中以 (gamma )阶收敛（达到对数因子）。
{"title":"An Unfiltered Low-Regularity Integrator for the KdV Equation with Solutions Below $$mathbf{H^1}$$","authors":"Buyang Li, Yifei Wu","doi":"10.1007/s10208-025-09702-0","DOIUrl":"https://doi.org/10.1007/s10208-025-09702-0","url":null,"abstract":"<p>This article is concerned with the construction and analysis of new time discretizations for the KdV equation on a torus for low-regularity solutions below <span>(H^1)</span>. New harmonic analysis tools, including averaging approximations to the exponential phase functions and trilinear estimates of the KdV operator, are established for the construction and analysis of time discretizations with higher convergence orders under low-regularity conditions. In addition, new perturbation techniques are introduced to establish stability estimates of time discretizations under low-regularity conditions without using filters when the energy techniques fail. The proposed method is proved to be convergent with order <span>(gamma )</span> (up to a logarithmic factor) in <span>(L^2)</span> under the regularity condition <span>(uin C([0,T];H^gamma ))</span> for <span>(gamma in (0,1])</span>.</p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":"59 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.ffa.2025.102607
Christian Weiß
The classic example of a low-discrepancy sequence in is with and . Here we address the non-linear case and show that a polynomial f generates a low-discrepancy sequence in if and only if it is a permutation polynomial . By this it is possible to construct non-linear examples of low-discrepancy sequences in for all primes p. Moreover, we prove a criterion which decides for any given polynomial in with if it generates a low-discrepancy sequence. We also discuss connections to the theories of Poissonian pair correlations and real discrepancy.
{"title":"Polynomial p-adic low-discrepancy sequences","authors":"Christian Weiß","doi":"10.1016/j.ffa.2025.102607","DOIUrl":"10.1016/j.ffa.2025.102607","url":null,"abstract":"<div><div>The classic example of a low-discrepancy sequence in <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is <span><math><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><mi>a</mi><mi>n</mi><mo>+</mo><mi>b</mi></math></span> with <span><math><mi>a</mi><mo>∈</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>×</mo></mrow></msubsup></math></span> and <span><math><mi>b</mi><mo>∈</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. Here we address the non-linear case and show that a polynomial <em>f</em> generates a low-discrepancy sequence in <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> if and only if it is a permutation polynomial <span><math><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mspace></mspace><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. By this it is possible to construct non-linear examples of low-discrepancy sequences in <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> for all primes <em>p</em>. Moreover, we prove a criterion which decides for any given polynomial in <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> with <span><math><mi>p</mi><mo>∈</mo><mrow><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo></mrow></math></span> if it generates a low-discrepancy sequence. We also discuss connections to the theories of Poissonian pair correlations and real discrepancy.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"105 ","pages":"Article 102607"},"PeriodicalIF":1.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552862","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 : 2025-03-04DOI: 10.1007/s00039-025-00708-y
Xin Fu, Hans-Joachim Hein, Xumin Jiang
We give an example of a family of smooth complex algebraic surfaces of degree 6 in (mathbb{CP}^{3}) developing an isolated elliptic singularity. We show via a gluing construction that the unique Kähler-Einstein metrics of Ricci curvature −1 on these sextics develop a complex hyperbolic cusp in the limit, and that near the tip of the forming cusp a Tian-Yau gravitational instanton bubbles off.
{"title":"A Continuous Cusp Closing Process for Negative Kähler-Einstein Metrics","authors":"Xin Fu, Hans-Joachim Hein, Xumin Jiang","doi":"10.1007/s00039-025-00708-y","DOIUrl":"https://doi.org/10.1007/s00039-025-00708-y","url":null,"abstract":"<p>We give an example of a family of smooth complex algebraic surfaces of degree 6 in <span>(mathbb{CP}^{3})</span> developing an isolated elliptic singularity. We show via a gluing construction that the unique Kähler-Einstein metrics of Ricci curvature −1 on these sextics develop a complex hyperbolic cusp in the limit, and that near the tip of the forming cusp a Tian-Yau gravitational instanton bubbles off.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"2 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143539114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.chaos.2025.116185
Hongshuai Wu , Tina P. Benko , Haojie Xu , Kuan Zou , Changwei Huang
The study of the impact of social learners on collective decision-making within a group has attracted considerable attention, but studies considering the influence of social learners on collective performance under different interaction ranges are still limited. In this study, we investigate the collective decision-making dynamics driven by merit and conformity within a structured population with limited interaction ranges. Our numerical simulation results show that when the fraction of social learners surpasses a critical threshold, a bistable state emerges, where the majority may eventually support either the higher- or lower-merit option. Furthermore, the critical threshold of the proportion of social learners is influenced not only by the relative merit of the two options but also by the interaction range of social learners. A larger relative merit leads to a higher critical threshold, while a larger interaction range results in a lower critical threshold.
{"title":"The impact of social learners on collective decision-making across varying interaction ranges","authors":"Hongshuai Wu , Tina P. Benko , Haojie Xu , Kuan Zou , Changwei Huang","doi":"10.1016/j.chaos.2025.116185","DOIUrl":"10.1016/j.chaos.2025.116185","url":null,"abstract":"<div><div>The study of the impact of social learners on collective decision-making within a group has attracted considerable attention, but studies considering the influence of social learners on collective performance under different interaction ranges are still limited. In this study, we investigate the collective decision-making dynamics driven by merit and conformity within a structured population with limited interaction ranges. Our numerical simulation results show that when the fraction of social learners surpasses a critical threshold, a bistable state emerges, where the majority may eventually support either the higher- or lower-merit option. Furthermore, the critical threshold of the proportion of social learners is influenced not only by the relative merit of the two options but also by the interaction range of social learners. A larger relative merit leads to a higher critical threshold, while a larger interaction range results in a lower critical threshold.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116185"},"PeriodicalIF":5.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.chaos.2025.116240
Yufei Fan , Xueyu Meng , Jun Liu , Jun-Chao Ma , Zhiqiang Cai , Shubin Si
Effective optimization of prevention and control measures can significantly organize the spread of infectious diseases. In this paper, we construct an SIQRSV (Susceptible-Infected-Quarantined-Recovered-Susceptible-Vaccinated) compartmental model for infectious diseases on complex networks to study the infection mechanism. Specifically, we analyze the impact mechanism of infection rates, consider network heterogeneity, and examine the influence of network topology on disease spread. Using a system of differential equations, we can elucidate the disease transmission process. Furthermore, we obtain the disease-free equilibrium point of the system in its steady state. By constructing an autonomous equation, we derive the basic reproduction number of the system, and further validate it using the next-generation matrix method. Additionally, through the Jacobian matrix, we demonstrate the stability of the disease-free equilibrium points. Subsequently, based on the compartmental model, we consider the costs of treatment, control measures, and vaccination to construct a Hamiltonian system to optimize the quarantine rate. Finally, we conduct simulation experiments based on our proposed model on various networks, including BA scale-free networks and four empirical networks. The results indicate that compared to random quarantine measures, our optimized measures can effectively suppress the spread of infectious diseases, thereby providing theoretical support for policymakers in formulating control measures.
{"title":"Hamiltonian optimal control of quarantine against epidemic spreading on complex networks","authors":"Yufei Fan , Xueyu Meng , Jun Liu , Jun-Chao Ma , Zhiqiang Cai , Shubin Si","doi":"10.1016/j.chaos.2025.116240","DOIUrl":"10.1016/j.chaos.2025.116240","url":null,"abstract":"<div><div>Effective optimization of prevention and control measures can significantly organize the spread of infectious diseases. In this paper, we construct an SIQRSV (Susceptible-Infected-Quarantined-Recovered-Susceptible-Vaccinated) compartmental model for infectious diseases on complex networks to study the infection mechanism. Specifically, we analyze the impact mechanism of infection rates, consider network heterogeneity, and examine the influence of network topology on disease spread. Using a system of differential equations, we can elucidate the disease transmission process. Furthermore, we obtain the disease-free equilibrium point of the system in its steady state. By constructing an autonomous equation, we derive the basic reproduction number of the system, and further validate it using the next-generation matrix method. Additionally, through the Jacobian matrix, we demonstrate the stability of the disease-free equilibrium points. Subsequently, based on the compartmental model, we consider the costs of treatment, control measures, and vaccination to construct a Hamiltonian system to optimize the quarantine rate. Finally, we conduct simulation experiments based on our proposed model on various networks, including BA scale-free networks and four empirical networks. The results indicate that compared to random quarantine measures, our optimized measures can effectively suppress the spread of infectious diseases, thereby providing theoretical support for policymakers in formulating control measures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116240"},"PeriodicalIF":5.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.chaos.2025.116169
Sudhir Singh , K. Manikandan , K. Sakkaravarthi
The rogue wave phenomenon continues to attract ever-increasing interest in both theoretical and experimental exploration, with higher-dimensional nonlinear soliton models possessing more fascinating evolutionary dynamics. This motivated the present work to study the evolutionary characteristics of lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model with complex dispersion-nonlinearity coefficients by constructing explicit solutions through the Hirota bilinearization technique and generalized recursive polynomials. With systematic analysis of the solutions, we reveal the dynamical features and various pattern formation strategies of lump–rogue waves and provide extensive graphical demonstrations. The results are discussed elaborately with certain possible future directions. The observed results can be helpful for enhancing the understanding of localized nonlinear evolutionary waves.
{"title":"Evolutionary higher-order lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model: Insights on the dynamical patterns through explicit solutions","authors":"Sudhir Singh , K. Manikandan , K. Sakkaravarthi","doi":"10.1016/j.chaos.2025.116169","DOIUrl":"10.1016/j.chaos.2025.116169","url":null,"abstract":"<div><div>The rogue wave phenomenon continues to attract ever-increasing interest in both theoretical and experimental exploration, with higher-dimensional nonlinear soliton models possessing more fascinating evolutionary dynamics. This motivated the present work to study the evolutionary characteristics of lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model with complex dispersion-nonlinearity coefficients by constructing explicit solutions through the Hirota bilinearization technique and generalized recursive polynomials. With systematic analysis of the solutions, we reveal the dynamical features and various pattern formation strategies of lump–rogue waves and provide extensive graphical demonstrations. The results are discussed elaborately with certain possible future directions. The observed results can be helpful for enhancing the understanding of localized nonlinear evolutionary waves.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116169"},"PeriodicalIF":5.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-03DOI: 10.1007/s43034-025-00415-7
Xiaoyan Li, Yunan Cui
In this paper, criteria for strong U-points and H-property in Orlicz sequence spaces equipped with the p-Amemiya norm ((1< p<infty )) are given. Next, compactly locally uniform rotundity and locally uniform rotundity of these spaces are deduced. Obtained results broaden the knowledge about these notions in Orlicz sequence spaces equipped with the p-Amemiya norm.
{"title":"On some local geometry of Orlicz sequence spaces equipped with the p-Amemiya norm","authors":"Xiaoyan Li, Yunan Cui","doi":"10.1007/s43034-025-00415-7","DOIUrl":"10.1007/s43034-025-00415-7","url":null,"abstract":"<div><p>In this paper, criteria for strong U-points and H-property in Orlicz sequence spaces equipped with the <i>p</i>-Amemiya norm <span>((1< p<infty ))</span> are given. Next, compactly locally uniform rotundity and locally uniform rotundity of these spaces are deduced. Obtained results broaden the knowledge about these notions in Orlicz sequence spaces equipped with the <i>p</i>-Amemiya norm.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533168","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 construct two classes of Zalcman-type domains, on which the Bergman distance functions exhibit certain pre-described boundary behaviors. Such examples also lead to generalizations of uniform perfectness in the sense of Pommerenke. These weakly uniformly perfect conditions can be characterized in terms of the logarithm capacity. We obtain lower estimates for the boundary behaviors of Bergman kernel functions on such domains.
{"title":"Bergman functions on weakly uniformly perfect domains","authors":"Yuanpu Xiong, Zhiyuan Zheng","doi":"10.1112/jlms.70107","DOIUrl":"https://doi.org/10.1112/jlms.70107","url":null,"abstract":"<p>We construct two classes of Zalcman-type domains, on which the Bergman distance functions exhibit certain pre-described boundary behaviors. Such examples also lead to generalizations of uniform perfectness in the sense of Pommerenke. These weakly uniformly perfect conditions can be characterized in terms of the logarithm capacity. We obtain lower estimates for the boundary behaviors of Bergman kernel functions on such domains.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-03DOI: 10.1016/j.aim.2025.110187
Jianchun Chu , Man-Chun Lee , Jintian Zhu
In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves in [3]. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.
{"title":"Homological n-systole in (n + 1)-manifolds and bi-Ricci curvature","authors":"Jianchun Chu , Man-Chun Lee , Jintian Zhu","doi":"10.1016/j.aim.2025.110187","DOIUrl":"10.1016/j.aim.2025.110187","url":null,"abstract":"<div><div>In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves in <span><span>[3]</span></span>. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110187"},"PeriodicalIF":1.5,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-03DOI: 10.1016/j.jfa.2025.110895
Anton Tselishchev
For any sequence of positive numbers such that we provide an explicit simple construction of -bounded Markushevich basis in a separable Hilbert space which is not strong, or, in other terminology, is not hereditary complete; this condition on the sequence is sharp. Using a finite-dimensional version of this construction, Dvoretzky's theorem and a construction of Vershynin, we conclude that in any Banach space for any sequence of positive numbers such that there exists a -bounded Markushevich basis which is not a Schauder basis after any permutation of its elements.
{"title":"Almost Auerbach, Markushevich and Schauder bases in Hilbert and Banach spaces","authors":"Anton Tselishchev","doi":"10.1016/j.jfa.2025.110895","DOIUrl":"10.1016/j.jfa.2025.110895","url":null,"abstract":"<div><div>For any sequence of positive numbers <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> such that <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>∞</mo></math></span> we provide an explicit simple construction of <span><math><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>-bounded Markushevich basis in a separable Hilbert space which is not strong, or, in other terminology, is not hereditary complete; this condition on the sequence <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> is sharp. Using a finite-dimensional version of this construction, Dvoretzky's theorem and a construction of Vershynin, we conclude that in any Banach space for any sequence of positive numbers <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> such that <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mo>∞</mo></math></span> there exists a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>-bounded Markushevich basis which is not a Schauder basis after any permutation of its elements.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 1","pages":"Article 110895"},"PeriodicalIF":1.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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