相关论文: Stability in Phase Retrieval: Characterizing Condi…

The Laplacian $\Delta_{\mathbb{S}^{n-1}}$ on the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ has the property that it can explicitly be expressed in terms of $\Lambda$, the Dirichlet-to-Neumann map of the unit ball, as…

Before proving (unconditional) energy stability for gradient flows, most existing studies either require a strong Lipschitz condition regarding the non-linearity or certain $L^{\infty}$ bounds on the numerical solutions (the maximum…

Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…

The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bilevel optimization. An example of such a Lipschitzian property…

Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…

In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…

In this paper we try to complete the stability analysis for an abstract system of coupled hyperbolic and parabolic equations $$ \left\{ \begin{array}{lll} \ds u_{tt} + Au - A^\alpha w = 0, \\ w_t + A^\alpha u_t + A^\beta w = 0,\\ u(0) =…

We introduce stability conditions (in the sense of King) for representable modules of continuous quivers of type A along with a special criteria called the four point condition. The stability conditions are defined using a generalization of…

In this note we prove that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map…

We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…

Propagation-based X-ray phase contrast enables nanoscale imaging of biological tissue by probing not only the attenuation, but also the real part of the refractive index of the sample. Since only intensities of diffracted waves can be…

We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation…

Hundred twenty years after the fundamental work of Poincar\'e, the statistics of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime,…

This paper is Part II of a series on global existence and asymptotic behavior of positive solutions to \begin{equation*} \begin{cases} \displaystyle u_t=\Delta u-\chi_0\nabla\cdot\left(\frac{u^m}{(1+v)^\beta}\nabla…

We consider a one dimensional affine switched system obtained from a formal limit of a two dimensional linear system. We show this is equivalent to minimising the average digit in beta representations with unrestricted digits. We give a…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

We establish the concept of $\alpha$-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either $\alpha(x)=1$ or $0\leq \alpha(x)<1$ for all $x\in \mathbb{R}$. Furthermore, we investigate the Lipschitz…

In this paper, we investigate the uniform regularity and asymptotic behavior of solutions to the following Lotka-Volterra type system of strong competition with Dirichlet boundary conditions: \begin{align*} \left\{ \begin{array}{ll} -\Delta…

We establish the conditioned stochastic stability of equilibrium states for H\"older potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient…