Results 31 to 40 of about 1,868 (82)
Convergence and nonconvergence in a nonlocal gradient flow
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract We study the asymptotic convergence as t→∞$t\rightarrow \infty$ of solutions of ∂tu=−f(u)+∫f(u)$\partial _t u=-f(u)+\int f(u)$, a nonlocal differential equation that is formally a gradient flow in a constant‐mass subspace of L2$L^2$ arising from simplified models of phase transitions. In case the solution takes finitely many values, we provide
Sangmin Park, Robert L. Pego
wiley +1 more source
Neural Lyapunov Control for Caputo Fractional‐Order Systems
International Journal of Intelligent Systems, Volume 2025, Issue 1, 2025.This article presents a novel neural network–based approach for designing effective control policies for Caputo‐type nonlinear fractional‐order systems. The proposed approach iteratively refines the neural network to generate a control policy that stabilizes the system within a predefined neighborhood around the zero equilibrium.
Xiaoya Gao +4 more
wiley +1 more source
A Modified Approach to Distributed Bregman ADMM for a Class of Nonconvex Consensus Problems
Journal of Mathematics, Volume 2025, Issue 1, 2025.This article presents a refined iteration of the distributed Bregman alternating direction method of multipliers (ADMM) tailored to tackle nonconvex consensus issues, especially those with multiple blocks. The reliability of this novel approach is established through demonstrating its robust convergence under specific conditions.
Zhonghui Xue +3 more
wiley +1 more source
Towards optimal spatio‐temporal decomposition of control‐related sum‐of‐squares programs
International Journal of Robust and Nonlinear Control, Volume 34, Issue 18, Page 11847-11867, December 2024.Abstract This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting of the time and state space.
Vít Cibulka +2 more
wiley +1 more source
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract We construct a differentiable locally Lipschitz function f$f$ in RN$\mathbb {R}^{N}$ with the property that for every convex body K⊂RN$K\subset \mathbb {R}^N$ there exists x¯∈RN$\bar{x} \in \mathbb {R}^N$ such that K$K$ coincides with the set ∂Lf(x¯)$\partial _L f(\bar{x})$ of limits of derivatives {Df(xn)}n⩾1$\lbrace Df(x_n)\rbrace _{n ...
Aris Daniilidis +2 more
wiley +1 more source
Microflexiblity and local integrability of horizontal curves
Mathematische Nachrichten, Volume 297, Issue 9, Page 3252-3287, September 2024.Abstract Let ξ$\xi$ be an analytic bracket‐generating distribution. We show that the subspace of germs that are singular (in the sense of control theory) has infinite codimension within the space of germs of smooth curves tangent to ξ$\xi$. We formalize this as an asymptotic statement about finite jets of tangent curves.
Álvaro del Pino, Tobias Shin
wiley +1 more source
, 2019 A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ can be written as a composite with the Hilbert map.
Herbig, Hans-Christian +1 more
core +1 more source
Tropical refined curve counting via motivic integration
, 2018 We propose a geometric interpretation of Block and G\"ottsche's refined tropical curve counting invariants in terms of virtual $\chi_{-y}$-specializations of motivic measures of semialgebraic sets in relative Hilbert schemes.
Nicaise, Johannes +2 more
core +1 more source
Polynomial Diffusions and Applications in Finance
, 2016 This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities ...
Filipovic, Damir, Larsson, Martin
core +1 more source
Convex Hulls of Algebraic Sets [PDF]
, 2010 This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals.
Gouveia, João, Thomas, Rekha R.
core