IF 2.3 2区数学

Journal of Differential Equations Pub Date : 2025-10-17 DOI: 10.1016/j.jde.2025.113838

Imran H. Biswas , Saibal Khan , Guy Vallet

引用次数: 0

State-dependent switching rule design based on polar coordinate method: A case of hybrid unstable subsystem composition 基于极坐标法的状态相关切换规则设计：一种混合不稳定子系统组成实例

IF 3.4 2区数学

Applied Mathematics and Computation Pub Date : 2025-10-17 DOI: 10.1016/j.amc.2025.129767

Juan Wu, Yuandong Wu, Danhong Chen, Yusheng Zhou

{"title":"State-dependent switching rule design based on polar coordinate method: A case of hybrid unstable subsystem composition","authors":"Juan Wu, Yuandong Wu, Danhong Chen, Yusheng Zhou","doi":"10.1016/j.amc.2025.129767","DOIUrl":"10.1016/j.amc.2025.129767","url":null,"abstract":"<div><div>This article investigates switched systems with three types of hybrid unstable subsystems: focus–node, focus–saddle, and node–saddle combinations. The objective is to develop suitable state-dependent switching rules to achieve rapid asymptotic stabilization of the system state to the origin. The proposed switching rule design follows three main steps. First, each subsystem is reformulated in polar coordinates. By analyzing the derivative of the radial distance with respect to the polar angle, a radial increment integral criterion is established to quantify system convergence behavior under both rotational and chattering switching mechanisms. Second, an in-depth analysis is conducted on the intrinsic characteristics of different unstable subsystem combinations. Region partitioning of the phase plane and switching analysis of phase trajectories are carried out based on the relative motion among trajectories. Finally, by leveraging the dynamic properties of subsystem phase trajectories, the most suitable switching mechanism is selected to fully utilize the advantageous features of each subsystem. The corresponding switching lines are then determined by comparing the convergence benefits of the active subsystems under each switching mechanism. Simulation results demonstrate that the resulting state-dependent switching strategy significantly improves convergence rate of the switched system while reducing conservatism.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"513 ","pages":"Article 129767"},"PeriodicalIF":3.4,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323662","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 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

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":"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.","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

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

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

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

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

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, Roger Nichols","doi":"10.1134/S1234567825030024","DOIUrl":"10.1134/S1234567825030024","url":null,"abstract":" Given a self-adjoint operator (H_0) bounded from below in a complex, separable Hilbert space (mathcal H), the corresponding scale of spaces (mathcal H_{+1}(H_0) subset mathcal H subset mathcal H_{-1}(H_0)=[mathcal H_{+1}(H_0)]^*), and a fixed (Vin mathcal B(mathcal H_{+1}(H_0),mathcal H_{-1}(H_0))), we define the operator-valued map (A_V(,cdot,)colon rho(H_0)to mathcal B(mathcal H)) by where (rho(H_0)) denotes the resolvent set of (H_0). Assuming that (A_V(z)) is compact for some (z=z_0in rho(H_0)) and has norm strictly less than one for some (z=E_0in (-infty,0)), we employ an abstract version of Tiktopoulos’ formula to define an operator (H) in (mathcal H) that is formally realized as the sum of (H_0) and (V). We then establish a Birman–Schwinger principle for (H) in which (A_V(,cdot,)) plays the role of the Birman–Schwinger operator: (lambda_0in rho(H_0)) is an eigenvalue of (H) if and only if (1) is an eigenvalue of (A_V(lambda_0)). Furthermore, the geometric (but not necessarily the algebraic) multiplicities of (lambda_0) and (1) as eigenvalues of (H) and (A_V(lambda_0)), respectively, coincide. As a concrete application, we consider one-dimensional Schrödinger operators with (H^{-1}(mathbb{R})) distributional potentials. ","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, Andrey Piatnitski, Vladimir Sloushch, Tatiana Suslina","doi":"10.1134/S1234567825030036","DOIUrl":"10.1134/S1234567825030036","url":null,"abstract":" In (L_2(mathbb R^d)), we consider a selfadjoint operator ({mathbb A}_varepsilon), (varepsilon >0), of the form where (0< alpha < 2). It is assumed that a function (mu(mathbf{x},mathbf{y})) is bounded, positive definite, periodic in each variable, and is such that (mu(mathbf{x},mathbf{y})=mu(mathbf{y},mathbf{x})). A rigorous definition of the operator ({mathbb A}_varepsilon) is given in terms of the corresponding quadratic form. It is proved that the resolvent (({mathbb A}_varepsilon+I)^{-1}) converges in the operator norm on (L_2(mathbb R^d)) to the operator (({mathbb A}^0+I)^{-1}) as (varepsilonto 0). Here, ({mathbb A}^0) is an effective operator of the same form with the constant coefficient (mu^0) equal to the mean value of (mu(mathbf{x},mathbf{y})). We obtain an error estimate of order (O(varepsilon^alpha)) for (0< alpha < 1), (O(varepsilon (1+| operatorname{ln} varepsilon|)^2)) for ( alpha=1), and (O(varepsilon^{2- alpha})) for (1< alpha < 2). In the case where (1< alpha < 2), the result is refined by taking the correctors into account. ","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

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