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Segmentation in Measure Spaces 度量空间中的分段
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-20 DOI: 10.1007/s00245-024-10134-5
Salvador Moll, Vicent Pallardó-Julià, Marcos Solera
{"title":"Segmentation in Measure Spaces","authors":"Salvador Moll,&nbsp;Vicent Pallardó-Julià,&nbsp;Marcos Solera","doi":"10.1007/s00245-024-10134-5","DOIUrl":"10.1007/s00245-024-10134-5","url":null,"abstract":"<div><p>We consider an abstract concept of <i>perimeter measure space</i> as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10134-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140681329","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}
引用次数: 0
Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models 跳跃扩散模型中效用最大化的前向后向 SDEs 系统
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-20 DOI: 10.1007/s00245-024-10114-9
Marina Santacroce, Paola Siri, Barbara Trivellato
{"title":"Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models","authors":"Marina Santacroce,&nbsp;Paola Siri,&nbsp;Barbara Trivellato","doi":"10.1007/s00245-024-10114-9","DOIUrl":"10.1007/s00245-024-10114-9","url":null,"abstract":"<div><p>We consider the classical problem of maximizing the expected utility of terminal net wealth with a final random liability in a simple jump-diffusion model. In the spirit of Horst et al. (Stoch Process Appl 124(5):1813–1848, 2014) and Santacroce and Trivellato (SIAM J Control Optim 52(6):3517–3537, 2014), under suitable conditions the optimal strategy is expressed in implicit form in terms of a forward backward system of equations. Some explicit results are presented for the pure jump model and for exponential utilities.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10114-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887955","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}
引用次数: 0
Stability Results for Novel Serially-Connected Magnetizable Piezoelectric and Elastic Smart-System Designs 新型串联可磁化压电和弹性智能系统设计的稳定性结果
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-16 DOI: 10.1007/s00245-024-10129-2
Mohammad Akil, Serge Nicaise, Ahmet Özkan Özer, Virginie Régnier
{"title":"Stability Results for Novel Serially-Connected Magnetizable Piezoelectric and Elastic Smart-System Designs","authors":"Mohammad Akil,&nbsp;Serge Nicaise,&nbsp;Ahmet Özkan Özer,&nbsp;Virginie Régnier","doi":"10.1007/s00245-024-10129-2","DOIUrl":"10.1007/s00245-024-10129-2","url":null,"abstract":"<div><p>In this paper, the stability of longitudinal vibrations for transmission problems of two smart-system designs are studied: (i) a serially-connected elastic–piezoelectric–elastic design with a local damping acting only on the piezoelectric layer and (ii) a serially-connected piezoelectric–elastic design with a local damping acting on the elastic part only. Unlike the existing literature, piezoelectric layers are considered magnetizable, and therefore, a fully-dynamic PDE model, retaining interactions of electromagnetic fields (due to Maxwell’s equations) with the mechanical vibrations, is considered. The design (i) is shown to have exponentially stable solutions. However, the nature of the stability of solutions of the design (ii), whether it is polynomial or exponential, is dependent entirely upon the arithmetic nature of a quotient involving all physical parameters. Furthermore, a polynomial decay rate is provided in terms of a measure of irrationality of the quotient. Note that this type of result is totally new (see Theorem 1.3 and Condition <span>(mathrm {mathbf {(H_{Pol})}})</span>). The main tool used throughout the paper is the multipliers technique which requires an adaptive selection of cut-off functions together with a particular attention to the sharpness of the estimates to optimize the results.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887893","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}
引用次数: 0
The Kuznetsov and Blackstock Equations of Nonlinear Acoustics with Nonlocal-in-Time Dissipation 具有非局部时间耗散的非线性声学库兹涅佐夫和布莱克斯托克方程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-16 DOI: 10.1007/s00245-024-10130-9
Barbara Kaltenbacher, Mostafa Meliani, Vanja Nikolić
{"title":"The Kuznetsov and Blackstock Equations of Nonlinear Acoustics with Nonlocal-in-Time Dissipation","authors":"Barbara Kaltenbacher,&nbsp;Mostafa Meliani,&nbsp;Vanja Nikolić","doi":"10.1007/s00245-024-10130-9","DOIUrl":"10.1007/s00245-024-10130-9","url":null,"abstract":"<div><p>In ultrasonics, nonlocal quasilinear wave equations arise when taking into account a class of heat flux laws of Gurtin–Pipkin type within the system of governing equations of sound motion. The present study extends previous work by the authors to incorporate nonlocal acoustic wave equations with quadratic gradient nonlinearities which require a new approach in the energy analysis. More precisely, we investigate the Kuznetsov and Blackstock equations with dissipation of fractional type and identify a minimal set of assumptions on the memory kernel needed for each equation. In particular, we discuss the physically relevant examples of Abel and Mittag–Leffler kernels. We perform the well-posedness analysis uniformly with respect to a small parameter on which the kernels depend and which can be interpreted as the sound diffusivity or the thermal relaxation time. We then analyze the limiting behavior of solutions with respect to this parameter, and how it is influenced by the specific class of memory kernels at hand. Through such a limiting study, we relate the considered nonlocal quasilinear equations to their limiting counterparts and establish the convergence rates of the respective solutions in the energy norm.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10130-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887675","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}
引用次数: 0
Generalized (varphi )-Pullback Attractors for Evolution Processes and Application to a Nonautonomous Wave Equation 演化过程的广义 $$varphi $$-Pullback 吸引子及其在非自治波方程中的应用
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-15 DOI: 10.1007/s00245-024-10133-6
Matheus C. Bortolan, Tomás Caraballo, Carlos Pecorari Neto
{"title":"Generalized (varphi )-Pullback Attractors for Evolution Processes and Application to a Nonautonomous Wave Equation","authors":"Matheus C. Bortolan,&nbsp;Tomás Caraballo,&nbsp;Carlos Pecorari Neto","doi":"10.1007/s00245-024-10133-6","DOIUrl":"10.1007/s00245-024-10133-6","url":null,"abstract":"<div><p>In this work we define the <i>generalized</i> <span>(varphi )</span>-<i>pullback attractors</i> for evolution processes in complete metric spaces, which are compact and positively invariant families, that <i>pullback attract</i> bounded sets with a rate determined by a decreasing function <span>(varphi )</span> that vanishes at infinity, called <i>decay function</i>. We find conditions under which a given evolution process has a generalized <span>(varphi )</span>-pullback attractor, both in the discrete and in the continuous cases. We present a result for the special case of generalized polynomial pullback attractors, and apply it to obtain such an object for a nonautonomous wave equation.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140699876","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}
引用次数: 0
Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations with Reflection 带反射的双时标随机偏微分方程的平均原理
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI: 10.1007/s00245-024-10123-8
Zhishan Ma, Juan Yang
{"title":"Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations with Reflection","authors":"Zhishan Ma,&nbsp;Juan Yang","doi":"10.1007/s00245-024-10123-8","DOIUrl":"10.1007/s00245-024-10123-8","url":null,"abstract":"<div><p>In this work, we consider a system of fast and slow time-scale stochastic partial differential equations with reflection, where the slow component is the one-dimensional stochastic Burgers equation, the fast component is the stochastic reaction-diffusion equation, and both the fast and slow components have two reflecting walls. The well-posedness of this system is established. Our approach is based on the penalized method by giving the delicate estimation of the penalized terms, which do not resort to splitting the reflected system into stochastic system without reflection and deterministic system with reflection. Then by means of penalized method and combining the classical Khasminskii’s time discretization, we prove the averaging principle for a class of reflected stochastic partial differential equations. In particular, due to the existence and uniqueness of invariant measure for fast component with frozen slow component, the ergodicity for frozen equations are given for different initial function spaces, which plays an important role.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593033","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}
引用次数: 0
Optimal Control for Suppression of Singularity in Chemotaxis via Flow Advection 通过流动平流抑制趋化奇点的优化控制
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI: 10.1007/s00245-024-10122-9
Weiwei Hu, Ming-Jun Lai, Jinsil Lee
{"title":"Optimal Control for Suppression of Singularity in Chemotaxis via Flow Advection","authors":"Weiwei Hu,&nbsp;Ming-Jun Lai,&nbsp;Jinsil Lee","doi":"10.1007/s00245-024-10122-9","DOIUrl":"10.1007/s00245-024-10122-9","url":null,"abstract":"<div><p>This work focuses on the optimal control design for suppressing the singularity formation in chemotaxis governed by the parabolic-elliptic Patlak–Keller–Segel (PKS) system via flow advection. The main idea of this work lies in utilizing flow advection for enhancing diffusion as to control the nonlinear behavior of the system. The objective is to determine an optimal strategy for adjusting flow strength so that the possible finite time blow-up of the solution can be suppressed. Rigorous proof of the existence of an optimal solution and derivation of first-order optimality conditions for solving such a solution are presented. Spline collocation methods are employed for solving the optimality conditions. Numerical experiments based on 2D cellular flows in a rectangular domain are conducted to demonstrate our ideas and designs.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592893","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}
引用次数: 0
Global Zero-Relaxation Limit for a Two-Fluid Euler–Poisson System 双流体欧拉-泊松系统的全局零振荡极限
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI: 10.1007/s00245-024-10131-8
Cunming Liu, Han Sheng
{"title":"Global Zero-Relaxation Limit for a Two-Fluid Euler–Poisson System","authors":"Cunming Liu,&nbsp;Han Sheng","doi":"10.1007/s00245-024-10131-8","DOIUrl":"10.1007/s00245-024-10131-8","url":null,"abstract":"<div><p>We study the relaxation problem for a two-fluid Euler-Poisson system. We prove the global-in-time convergence of the system for smooth solutions near the constant equilibrium states. The limit system is the two-fluid drift-diffusion system as the relaxation time tends to zero. In the proof, we establish uniform energy estimates of smooth solutions for all the parameters and the time. These estimates allow us to pass to the limit in the system to obtain the limit system. Moreover, the global convergence rate of the solutions is obtained by stream function techniques.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592911","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}
引用次数: 0
From Non-local to Local Navier–Stokes Equations 从非局部纳维-斯托克斯方程到局部纳维-斯托克斯方程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI: 10.1007/s00245-024-10128-3
Oscar Jarrín, Geremy Loachamín
{"title":"From Non-local to Local Navier–Stokes Equations","authors":"Oscar Jarrín,&nbsp;Geremy Loachamín","doi":"10.1007/s00245-024-10128-3","DOIUrl":"10.1007/s00245-024-10128-3","url":null,"abstract":"<div><p>Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier–Stokes equations, which involve the fractional Laplacian operator <span>((-Delta )^{frac{alpha }{2}})</span> with <span>(alpha &lt;2)</span>, converge to a solution of the classical case, with <span>(-Delta )</span>, when <span>(alpha )</span> goes to 2. Precisely, in the setting of mild solutions, we prove uniform convergence in the <span>(L^{infty }_{t,x})</span>-space and derive a precise convergence rate, revealing some phenomenological effects. As a bi-product, we prove strong convergence in the <span>(L^{p}_{t}L^{q}_{x})</span>-space. Finally, our results are also generalized to the coupled setting of the Magnetic-hydrodynamic system.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593129","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}
引用次数: 0
On the Continuity of the Projection Mapping from Strategic Measures to Occupation Measures in Absorbing Markov Decision Processes 论吸收马尔可夫决策过程中从战略措施到职业措施的投影映射的连续性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-12 DOI: 10.1007/s00245-024-10124-7
Alexey Piunovskiy, Yi Zhang
{"title":"On the Continuity of the Projection Mapping from Strategic Measures to Occupation Measures in Absorbing Markov Decision Processes","authors":"Alexey Piunovskiy,&nbsp;Yi Zhang","doi":"10.1007/s00245-024-10124-7","DOIUrl":"10.1007/s00245-024-10124-7","url":null,"abstract":"<div><p>In this paper, we prove the following assertion for an absorbing Markov decision process (MDP) with the given initial distribution, which is also assumed to be semi-continuous: the continuity of the projection mapping from the space of strategic measures to the space of occupation measures, both endowed with their weak topologies, is equivalent to the MDP model being uniformly absorbing. An example demonstrates, among other interesting scenarios, that for an absorbing (but not uniformly absorbing) semi-continuous MDP with the given initial distribution, the space of occupation measures can fail to be compact in the weak topology.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10124-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593132","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}
引用次数: 0
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