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Global well-posedness and vanishing viscosity limit of the compressible elastic system in three dimensions 三维可压缩弹性系统的全局适定性和消失黏度极限
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-10-17 DOI: 10.1016/j.jde.2025.113849
Guochun Wu , Wenbin Zhao
{"title":"Global well-posedness and vanishing viscosity limit of the compressible elastic system in three dimensions","authors":"Guochun Wu ,&nbsp;Wenbin Zhao","doi":"10.1016/j.jde.2025.113849","DOIUrl":"10.1016/j.jde.2025.113849","url":null,"abstract":"<div><div>The compressible elastodynamics is a typical example of systems with different wave speeds, which are difficult to be solved due to lack of symmetries. In general, the nonlinear interactions among the pressure waves are so strong that the global existence of classical solutions cannot be expected. In this article we investigate a specific example, namely the compressible Mooney–Rivlin materials, of which both the interactions among the pressure waves and among the shear waves satisfy the null conditions respectively. With delicate analysis of the linear system, we manage to identify all the good unknowns in a simpler form which are essential to exploit the null conditions for extra time decay. The approach to the a priori energy estimates applies to both inviscid and viscous systems, and enables us to justify the vanishing viscosity limit result.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"453 ","pages":"Article 113849"},"PeriodicalIF":2.3,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325324","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
Generation of Virtual Populations for Quantitative Systems Pharmacology Through Advanced Sampling Methods. 通过先进的采样方法为定量系统药理学生成虚拟种群。
IF 2.2 4区 数学
Bulletin of Mathematical Biology Pub Date : 2025-10-17 DOI: 10.1007/s11538-025-01532-z
Miriam Schirru, Tristan Brier, Maxime Petit, Didier Zugaj, Pierre-Olivier Tremblay, Fahima Nekka
{"title":"Generation of Virtual Populations for Quantitative Systems Pharmacology Through Advanced Sampling Methods.","authors":"Miriam Schirru, Tristan Brier, Maxime Petit, Didier Zugaj, Pierre-Olivier Tremblay, Fahima Nekka","doi":"10.1007/s11538-025-01532-z","DOIUrl":"https://doi.org/10.1007/s11538-025-01532-z","url":null,"abstract":"<p><p>Virtual population (Vpop) generation is a central component of quantitative systems pharmacology (QSP), involving the sampling of parameter sets that represent physiologically plausible patients (PPs) and capture observed inter-individual variability in clinical outcomes. This approach poses challenges due to the high dimensionality and often non-identifiability nature of many QSP models. In this study, we evaluate the performance of the DREAM(ZS) algorithm, a multi-chain adaptive Markov chain Monte Carlo (MCMC) method for generating Vpop. Using the Van De Pas model of cholesterol metabolism as a case study, we compare DREAM(ZS) to the single-chain Metropolis-Hastings (MH) algorithm adopted by Rieger et al. Our comparison focuses on convergence behavior, parametric diversity, and posterior coverage, in relation to the ability of each method to explore complex parameter distributions and maintain outcomes correlations. DREAM(ZS) demonstrates superior exploration of the parameter space, reducing boundary accumulation effects common in traditional MH sampling, and restoring parameter correlation structures. These advantages are attributed in part to its adaptive proposal mechanism and the use of a bias-corrected likelihood formulation, which together contribute to a better parameters space sampling without compromising model fit. Our findings contribute to the ongoing development of efficient sampling methodologies for high-dimensional biological models, introducing a promising and easy to use alternative for Vpop generation in QSP, expanding the methodological approaches for in silico trial simulation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 11","pages":"165"},"PeriodicalIF":2.2,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145312197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum advantage and CSP complexity 量子优势和CSP复杂性
IF 1.2 1区 数学
Journal of Combinatorial Theory Series B Pub Date : 2025-10-17 DOI: 10.1016/j.jctb.2025.10.002
Lorenzo Ciardo
{"title":"Quantum advantage and CSP complexity","authors":"Lorenzo Ciardo","doi":"10.1016/j.jctb.2025.10.002","DOIUrl":"10.1016/j.jctb.2025.10.002","url":null,"abstract":"<div><div>Information-processing tasks modelled by homomorphisms between relational structures can witness quantum advantage when entanglement is used as a computational resource. We prove that the occurrence of quantum advantage is determined by the same algebraic structure (known as the polymorphism minion) that captures the complexity of CSPs. We investigate the connection between the minion of quantum advantage and other known minions controlling CSP tractability and width. In this way, we make use of complexity results from the algebraic theory of CSPs to characterise the occurrence of quantum advantage in the case of graphs, and to obtain new necessary and sufficient conditions in the case of arbitrary relational structures.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"176 ","pages":"Pages 404-439"},"PeriodicalIF":1.2,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145332382","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}
引用次数: 0
Asymptotic Completeness for Short-Range (N)-Body Systems Revisited 近程(N) -体系统的渐近完备性
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030097
Erik Skibsted
{"title":"Asymptotic Completeness for Short-Range (N)-Body Systems Revisited","authors":"Erik Skibsted","doi":"10.1134/S1234567825030097","DOIUrl":"10.1134/S1234567825030097","url":null,"abstract":"<p> We review Yafaev’s approach to asymptotic completeness for systems of particles mutually interacting with short-range potentials. The resulting theory is based on computation of commutators with time-independent (mostly bounded) observables yielding a sufficient supply of Kato smoothness bounds. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"330 - 346"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145315638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Surface Waves on Infinite Boundaries 无限边界上的表面波
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030115
Dmitrii Yafaev
{"title":"Surface Waves on Infinite Boundaries","authors":"Dmitrii Yafaev","doi":"10.1134/S1234567825030115","DOIUrl":"10.1134/S1234567825030115","url":null,"abstract":"<p> We develop scattering theory for the Laplace operator in the half-space with Robin type boundary conditions on the boundary plane. In particular, we show that, in addition to usual space waves living in cones and described by standard wave operators, surface waves may arise in this problem. They are localized in parabolic neighbourhoods of the boundary. We find conditions on the boundary coefficient ensuring the existence of surface waves. Several open problems are formulated. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"366 - 389"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1234567825030115.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Density results using the method of fundamental solutions for a fluid-structure interaction problem 流固耦合问题基本解方法的密度结果
IF 3.4 2区 数学
Applied Mathematics and Computation Pub Date : 2025-10-17 DOI: 10.1016/j.amc.2025.129769
Tielei Zhu , Zhihao Ge
{"title":"Density results using the method of fundamental solutions for a fluid-structure interaction problem","authors":"Tielei Zhu ,&nbsp;Zhihao Ge","doi":"10.1016/j.amc.2025.129769","DOIUrl":"10.1016/j.amc.2025.129769","url":null,"abstract":"<div><div>We propose two numerical methods i.e., the method of fundamental solutions (MFS) and the coupling of the MFS and the plane waves method, for solving a fluid-structure interaction scattering problem numerically in two and three dimensions, which are both free of irregular frequencies. It is shown that the acoustic fields can be approximated in the <span><math><msup><mi>H</mi><mn>1</mn></msup></math></span>-norm by the fundamental solutions of the Helmholtz equation placed at distinct source points, whereas elastic fields are approximated in the same norm either by the fundamental solutions of the Navier equations at different locations or by the plane waves of the Navier equations with distinct directions. Some numerical examples are performed to show the behaviors of our methods for the two-dimensional case.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"512 ","pages":"Article 129769"},"PeriodicalIF":3.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145326081","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
New Remarks on the Scattering for a Perturbed Polyharmonic Operator 关于摄动多谐算子散射的新注记
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030085
Grigori Rozenblum
{"title":"New Remarks on the Scattering for a Perturbed Polyharmonic Operator","authors":"Grigori Rozenblum","doi":"10.1134/S1234567825030085","DOIUrl":"10.1134/S1234567825030085","url":null,"abstract":"<p> We obtain sufficient conditions for the perturbation of the power of the resolvent of the polyharmonic operator under a perturbation by a highly singular potential to belong to Schatten classes. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"321 - 329"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Generalized Birman–Schwinger Principle and Applications to One-Dimensional Schrödinger Operators with Distributional Potentials 广义Birman-Schwinger原理及其在一维Schrödinger分布势算子中的应用
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030024
Fritz Gesztesy, Roger Nichols
{"title":"A Generalized Birman–Schwinger Principle and Applications to One-Dimensional Schrödinger Operators with Distributional Potentials","authors":"Fritz Gesztesy,&nbsp;Roger Nichols","doi":"10.1134/S1234567825030024","DOIUrl":"10.1134/S1234567825030024","url":null,"abstract":"<p> Given a self-adjoint operator <span>(H_0)</span> bounded from below in a complex, separable Hilbert space <span>(mathcal H)</span>, the corresponding scale of spaces <span>(mathcal H_{+1}(H_0) subset mathcal H subset mathcal H_{-1}(H_0)=[mathcal H_{+1}(H_0)]^*)</span>, and a fixed <span>(Vin mathcal B(mathcal H_{+1}(H_0),mathcal H_{-1}(H_0)))</span>, we define the operator-valued map <span>(A_V(,cdot,)colon rho(H_0)to mathcal B(mathcal H))</span> by </p><p> where <span>(rho(H_0))</span> denotes the resolvent set of <span>(H_0)</span>. Assuming that <span>(A_V(z))</span> is compact for some <span>(z=z_0in rho(H_0))</span> and has norm strictly less than one for some <span>(z=E_0in (-infty,0))</span>, we employ an abstract version of Tiktopoulos’ formula to define an operator <span>(H)</span> in <span>(mathcal H)</span> that is formally realized as the sum of <span>(H_0)</span> and <span>(V)</span>. We then establish a Birman–Schwinger principle for <span>(H)</span> in which <span>(A_V(,cdot,))</span> plays the role of the Birman–Schwinger operator: <span>(lambda_0in rho(H_0))</span> is an eigenvalue of <span>(H)</span> if and only if <span>(1)</span> is an eigenvalue of <span>(A_V(lambda_0))</span>. Furthermore, the geometric (but not necessarily the algebraic) multiplicities of <span>(lambda_0)</span> and <span>(1)</span> as eigenvalues of <span>(H)</span> and <span>(A_V(lambda_0))</span>, respectively, coincide. </p><p> As a concrete application, we consider one-dimensional Schrödinger operators with <span>(H^{-1}(mathbb{R}))</span> distributional potentials. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"224 - 250"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homogenization of the Lévy-type Operators lcv型算子的均匀化
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-10-17 DOI: 10.1134/S1234567825030036
Elena Zhizhina, Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina
{"title":"Homogenization of the Lévy-type Operators","authors":"Elena Zhizhina,&nbsp;Andrey Piatnitski,&nbsp;Vladimir Sloushch,&nbsp;Tatiana Suslina","doi":"10.1134/S1234567825030036","DOIUrl":"10.1134/S1234567825030036","url":null,"abstract":"<p> In <span>(L_2(mathbb R^d))</span>, we consider a selfadjoint operator <span>({mathbb A}_varepsilon)</span>, <span>(varepsilon &gt;0)</span>, of the form </p><p> where <span>(0&lt; alpha &lt; 2)</span>. It is assumed that a function <span>(mu(mathbf{x},mathbf{y}))</span> is bounded, positive definite, periodic in each variable, and is such that <span>(mu(mathbf{x},mathbf{y})=mu(mathbf{y},mathbf{x}))</span>. A rigorous definition of the operator <span>({mathbb A}_varepsilon)</span> is given in terms of the corresponding quadratic form. It is proved that the resolvent <span>(({mathbb A}_varepsilon+I)^{-1})</span> converges in the operator norm on <span>(L_2(mathbb R^d))</span> to the operator <span>(({mathbb A}^0+I)^{-1})</span> as <span>(varepsilonto 0)</span>. Here, <span>({mathbb A}^0)</span> is an effective operator of the same form with the constant coefficient <span>(mu^0)</span> equal to the mean value of <span>(mu(mathbf{x},mathbf{y}))</span>. We obtain an error estimate of order <span>(O(varepsilon^alpha))</span> for <span>(0&lt; alpha &lt; 1)</span>, <span>(O(varepsilon (1+| operatorname{ln} varepsilon|)^2))</span> for <span>( alpha=1)</span>, and <span>(O(varepsilon^{2- alpha}))</span> for <span>(1&lt; alpha &lt; 2)</span>. In the case where <span>(1&lt; alpha &lt; 2)</span>, the result is refined by taking the correctors into account. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 3","pages":"251 - 257"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Perron’s Method in the Dirichlet Problem for the Soft Laplacian on a Stratified Set 分层集上软拉普拉斯算子Dirichlet问题的Perron方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-17 DOI: 10.1134/S1064562424602658
N. S. Dairbekov, O. M. Penkin, D. V. Savasteev
{"title":"Perron’s Method in the Dirichlet Problem for the Soft Laplacian on a Stratified Set","authors":"N. S. Dairbekov,&nbsp;O. M. Penkin,&nbsp;D. V. Savasteev","doi":"10.1134/S1064562424602658","DOIUrl":"10.1134/S1064562424602658","url":null,"abstract":"<p>The solvability of the Dirichlet problem for the soft Laplacian on a stratified set is proved using a modification of the well-known Perron method.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 1","pages":"16 - 19"},"PeriodicalIF":0.6,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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