Pub Date : 2026-02-12DOI: 10.1016/j.geomphys.2026.105795
Xiangdong Yang
In this paper, we introduce the notion of cohomologically symplectic structure on a differentiable stratified space, and we show that the singular symplectic quotient of a symplectic Hamiltonian G-manifold admits a natural cohomologically symplectic structure induced by the original symplectic structure on M.
{"title":"Cohomologically symplectic structures on stratified spaces","authors":"Xiangdong Yang","doi":"10.1016/j.geomphys.2026.105795","DOIUrl":"10.1016/j.geomphys.2026.105795","url":null,"abstract":"<div><div>In this paper, we introduce the notion of cohomologically symplectic structure on a differentiable stratified space, and we show that the singular symplectic quotient <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>0</mn><mo>)</mo><mo>/</mo><mi>G</mi></math></span> of a symplectic Hamiltonian <em>G</em>-manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>ω</mi><mo>,</mo><mi>G</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math></span> admits a natural cohomologically symplectic structure induced by the original symplectic structure on <em>M</em>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"224 ","pages":"Article 105795"},"PeriodicalIF":1.2,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146193180","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 : 2026-02-12DOI: 10.1016/j.camwa.2026.01.042
Xiaozhuang Ma, Lizhen Chen
In this paper, we propose an efficient, fully discrete numerical scheme for the phase field crystal model, combining second-order accuracy in time with spectral accuracy in space. First, we employ a multi-step strategy for time discretization, obtaining a second-order semi-discrete Crank–Nicolson leap-frog scheme. We rigorously prove that this scheme satisfies total mass conservation, unconditional energy stability, and linear, unique solvability. A detailed error analysis confirms its second-order convergence in time. Next, we discretize the semi-discrete scheme in space using the Fourier pseudo-spectral method, ensuring that the fully discrete scheme retains mass conservation and energy dissipation. Convergence and error estimates are also rigorously derived. Numerical experiments demonstrate the scheme’s accuracy and efficiency, particularly in capturing effective energy decay during long-time coarsening dynamics.
{"title":"Stability and error estimate of the second-order Crank–Nicolson leap-frog scheme for the phase field crystal model","authors":"Xiaozhuang Ma, Lizhen Chen","doi":"10.1016/j.camwa.2026.01.042","DOIUrl":"10.1016/j.camwa.2026.01.042","url":null,"abstract":"<div><div>In this paper, we propose an efficient, fully discrete numerical scheme for the phase field crystal model, combining second-order accuracy in time with spectral accuracy in space. First, we employ a multi-step strategy for time discretization, obtaining a second-order semi-discrete Crank–Nicolson leap-frog scheme. We rigorously prove that this scheme satisfies total mass conservation, unconditional energy stability, and linear, unique solvability. A detailed error analysis confirms its second-order convergence in time. Next, we discretize the semi-discrete scheme in space using the Fourier pseudo-spectral method, ensuring that the fully discrete scheme retains mass conservation and energy dissipation. Convergence and error estimates are also rigorously derived. Numerical experiments demonstrate the scheme’s accuracy and efficiency, particularly in capturing effective energy decay during long-time coarsening dynamics.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 1-15"},"PeriodicalIF":2.5,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162101","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 : 2026-02-12DOI: 10.1016/j.chaos.2026.118057
Sarra Senouci, Zhangchun Tang, Mohammed Raouf Senouci, Sid Ali Madoune, Abdelkader Senouci
Synchronizing chaotic systems is a fundamental challenge with significant applications, yet its practical implementation is often hindered by non-ideal channel characteristics such as noise and time delay. This paper introduces a new, robust framework for achieving high-fidelity synchronization in such challenging environments. The primary objective is to develop and validate a control strategy that is resilient to both limited state information and realistic channel imperfections. Our methodology pairs a Luenberger-style state observer with a novel, delay-aware Linear-Quadratic Regulator (LQR) within a master–slave system configuration. The controller explicitly compensates for input delay using a formulation derived from Lyapunov–Krasovskii theory and demonstrates the efficacy of actuating on a single, strategically selected state variable. Simulations conducted over a high-fidelity fiber-optic channel model confirm the framework’s performance. The results demonstrate rapid, precise synchronization that is robust to significant time-varying delays (up to 28ms), achieving settling times as low as 0.8 s while maintaining a steady-state error on the order of 10−5 amidst signal noise and quantization effects. The observer-based partial-state feedback approach successfully matches the performance of full-state feedback, validating its effectiveness. This work presents a comprehensive solution that significantly enhances the feasibility of applying chaos synchronization in real-world systems, proving its stability and robustness against a wide range of initial conditions and channel disturbances.
{"title":"A new framework for robust observer-based synchronization of chaotic systems with a delay-aware LQR controller","authors":"Sarra Senouci, Zhangchun Tang, Mohammed Raouf Senouci, Sid Ali Madoune, Abdelkader Senouci","doi":"10.1016/j.chaos.2026.118057","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118057","url":null,"abstract":"Synchronizing chaotic systems is a fundamental challenge with significant applications, yet its practical implementation is often hindered by non-ideal channel characteristics such as noise and time delay. This paper introduces a new, robust framework for achieving high-fidelity synchronization in such challenging environments. The primary objective is to develop and validate a control strategy that is resilient to both limited state information and realistic channel imperfections. Our methodology pairs a Luenberger-style state observer with a novel, delay-aware Linear-Quadratic Regulator (LQR) within a master–slave system configuration. The controller explicitly compensates for input delay using a formulation derived from Lyapunov–Krasovskii theory and demonstrates the efficacy of actuating on a single, strategically selected state variable. Simulations conducted over a high-fidelity fiber-optic channel model confirm the framework’s performance. The results demonstrate rapid, precise synchronization that is robust to significant time-varying delays (up to <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:mn>28</mml:mn><mml:mspace width=\"0.33em\"></mml:mspace><mml:mi mathvariant=\"normal\">ms</mml:mi></mml:mrow></mml:math>), achieving settling times as low as 0.8 s while maintaining a steady-state error on the order of <mml:math altimg=\"si206.svg\" display=\"inline\"><mml:mrow><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> amidst signal noise and quantization effects. The observer-based partial-state feedback approach successfully matches the performance of full-state feedback, validating its effectiveness. This work presents a comprehensive solution that significantly enhances the feasibility of applying chaos synchronization in real-world systems, proving its stability and robustness against a wide range of initial conditions and channel disturbances.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"10 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146209864","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}
This work presents an innovative spatio-temporal parabolic framework based on fractional calculus, employing both Caputo and Riemann–Liouville derivatives. The primary objective is to enhance traditional super-resolution methods, with a specific focus on multi-frame image reconstruction. The proposed model incorporates a spatially regularized fractional tensor diffusion mechanism that modulates both the magnitude and orientation of diffusion locally across the image domain. Theoretical analysis begins by addressing the model’s well-posedness. Using the Faedo-Galerkin scheme, we first establish the uniqueness and existence of weak solution to an auxiliary problem involving a time-fractional Caputo derivative. Then, leveraging Schauder fixed point theorem, we show the existence of a unique weak solution for our full model. Numerical experiments illustrate the practical capabilities of the approach, showcasing the advantages of fractional order methods in the context of image denoising and super-resolution. Furthermore, tests on real video sequences confirm the model’s robustness and performance in blind reconstruction scenarios. Comparative evaluations with state-of-the-art techniques underline the efficiency of our fractional model in terms of visual quality and detail preservation.
{"title":"Fractional spatio-temporal modeling for enhanced MRI super-resolution from multi-frame data","authors":"Anouar Ben-Loghfyry , Abderrahim Charkaoui , Shengda Zeng","doi":"10.1016/j.camwa.2026.01.037","DOIUrl":"10.1016/j.camwa.2026.01.037","url":null,"abstract":"<div><div>This work presents an innovative spatio-temporal parabolic framework based on fractional calculus, employing both Caputo and Riemann–Liouville derivatives. The primary objective is to enhance traditional super-resolution methods, with a specific focus on multi-frame image reconstruction. The proposed model incorporates a spatially regularized fractional tensor diffusion mechanism that modulates both the magnitude and orientation of diffusion locally across the image domain. Theoretical analysis begins by addressing the model’s well-posedness. Using the Faedo-Galerkin scheme, we first establish the uniqueness and existence of weak solution to an auxiliary problem involving a time-fractional Caputo derivative. Then, leveraging Schauder fixed point theorem, we show the existence of a unique weak solution for our full model. Numerical experiments illustrate the practical capabilities of the approach, showcasing the advantages of fractional order methods in the context of image denoising and super-resolution. Furthermore, tests on real video sequences confirm the model’s robustness and performance in blind reconstruction scenarios. Comparative evaluations with state-of-the-art techniques underline the efficiency of our fractional model in terms of visual quality and detail preservation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 147-185"},"PeriodicalIF":2.5,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146160706","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 : 2026-02-12DOI: 10.1016/j.aim.2026.110852
Daqing Wan , Dingxin Zhang
Using basic properties of perverse sheaves, we give new upper bounds for compactly supported Betti numbers for arbitrary affine varieties in defined by r polynomial equations of degrees at most d. As arithmetic applications, new total degree bounds are obtained for zeta functions of varieties and L-functions of exponential sums over finite fields, improving the classical results of Bombieri, Katz, and Adolphson–Sperber. In the complete intersection case, our total Betti number bound is asymptotically optimal as a function in d. In general, it remains an open problem to find an asymptotically optimal bound as a function in d.
{"title":"Betti number bounds for varieties and exponential sums","authors":"Daqing Wan , Dingxin Zhang","doi":"10.1016/j.aim.2026.110852","DOIUrl":"10.1016/j.aim.2026.110852","url":null,"abstract":"<div><div>Using basic properties of perverse sheaves, we give new upper bounds for compactly supported Betti numbers for arbitrary affine varieties in <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> defined by <em>r</em> polynomial equations of degrees at most <em>d</em>. As arithmetic applications, new total degree bounds are obtained for zeta functions of varieties and L-functions of exponential sums over finite fields, improving the classical results of Bombieri, Katz, and Adolphson–Sperber. In the complete intersection case, our total Betti number bound is asymptotically optimal as a function in <em>d</em>. In general, it remains an open problem to find an asymptotically optimal bound as a function in <em>d</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"490 ","pages":"Article 110852"},"PeriodicalIF":1.5,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174621","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}
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast system after cylindrical blow-up and use a well-known connection between the divergence integral along orbits and transition maps for vector fields. Since properties of the divergence integral depend on the location and multiplicity of singularities, we divide the sliding cycles into different classes, which can then produce different types of cyclicity results. As an example, we apply our results to regularized piecewise linear systems.
{"title":"Cyclicity of sliding cycles with singularities of regularized piecewise smooth visible-invisible two-folds","authors":"Jicai Huang , Renato Huzak , Otavio Henrique Perez , Jinhui Yao","doi":"10.1016/j.jde.2026.114205","DOIUrl":"10.1016/j.jde.2026.114205","url":null,"abstract":"<div><div>In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast system after cylindrical blow-up and use a well-known connection between the divergence integral along orbits and transition maps for vector fields. Since properties of the divergence integral depend on the location and multiplicity of singularities, we divide the sliding cycles into different classes, which can then produce different types of cyclicity results. As an example, we apply our results to regularized piecewise linear systems.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"465 ","pages":"Article 114205"},"PeriodicalIF":2.3,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192806","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 : 2026-02-12DOI: 10.1016/j.cnsns.2026.109829
Juan Sánchez Umbría, Marta Net
Numerical continuation and stability analysis of periodic orbits are used to analyze, under a dynamical systems point of view, the time dependent dynamics that arise from the steady convection of a H2-Xe gas mixture, driven by lateral temperature and low concentration gradients. Both Soret and Dufour effects are taken into account. A bifurcation diagram consisting of sequences of period-doubling and saddle-node bifurcations is unfold. They give rise to a series of nested Feigenbaum cascades in a narrow region of the parameter space. Several types of cyclic and chaotic solutions close to heteroclinic orbits were found in the interval of the control parameter where the periodic orbits are unstable. The relations between them are established.
{"title":"Nested Feigenbaum cascades and Shil’nikov-like dynamics in convection of binary mixtures","authors":"Juan Sánchez Umbría, Marta Net","doi":"10.1016/j.cnsns.2026.109829","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109829","url":null,"abstract":"Numerical continuation and stability analysis of periodic orbits are used to analyze, under a dynamical systems point of view, the time dependent dynamics that arise from the steady convection of a H<mml:math altimg=\"si28.svg\"><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mn mathvariant=\"bold-italic\">2</mml:mn></mml:mrow></mml:msub></mml:math>-Xe gas mixture, driven by lateral temperature and low concentration gradients. Both Soret and Dufour effects are taken into account. A bifurcation diagram consisting of sequences of period-doubling and saddle-node bifurcations is unfold. They give rise to a series of nested Feigenbaum cascades in a narrow region of the parameter space. Several types of cyclic and chaotic solutions close to heteroclinic orbits were found in the interval of the control parameter where the periodic orbits are unstable. The relations between them are established.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"20 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146209872","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 : 2026-02-12DOI: 10.1080/10618600.1993.10474613
Luc Devroye, Peter Epstein, Jörg-Rüdiger Sack
{"title":"On Generating Random Intervals and Hyperrectangles","authors":"Luc Devroye, Peter Epstein, Jörg-Rüdiger Sack","doi":"10.1080/10618600.1993.10474613","DOIUrl":"https://doi.org/10.1080/10618600.1993.10474613","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"90 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169776","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 : 2026-02-12DOI: 10.1080/10618600.2026.2627458
Fuheng Cui, Stephen G. Walker
{"title":"Martingale Posterior Distributions for Log-concave Density Functions","authors":"Fuheng Cui, Stephen G. Walker","doi":"10.1080/10618600.2026.2627458","DOIUrl":"https://doi.org/10.1080/10618600.2026.2627458","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"152 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169912","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}
Søren Dyhr, Ángel González-Prieto, Eva Miranda, Daniel Peralta-Salas
In this paper, we study the Chern–Hamilton energy functional on compact cosymplectic manifolds, fully classifying in dimension 3 those manifolds admitting a critical compatible metric for this functional. This is the case if and only if either the manifold is co-Kähler or if it is a mapping torus of the 2-torus by a hyperbolic toral automorphism and equipped with a suspension cosymplectic structure. Moreover, any critical metric has minimal energy among all compatible metrics. We also exhibit examples of manifolds with first Betti number admitting cosymplectic structures, but such that no cosymplectic structure admits a critical compatible metric.
{"title":"The cosymplectic Chern–Hamilton conjecture","authors":"Søren Dyhr, Ángel González-Prieto, Eva Miranda, Daniel Peralta-Salas","doi":"10.1112/jlms.70453","DOIUrl":"https://doi.org/10.1112/jlms.70453","url":null,"abstract":"<p>In this paper, we study the Chern–Hamilton energy functional on compact cosymplectic manifolds, fully classifying in dimension 3 those manifolds admitting a critical compatible metric for this functional. This is the case if and only if either the manifold is co-Kähler or if it is a mapping torus of the 2-torus by a hyperbolic toral automorphism and equipped with a suspension cosymplectic structure. Moreover, any critical metric has minimal energy among all compatible metrics. We also exhibit examples of manifolds with first Betti number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>b</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$b_1 geqslant 2$</annotation>\u0000 </semantics></math> admitting cosymplectic structures, but such that no cosymplectic structure admits a critical compatible metric.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70453","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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