Related papers: Stability of a class of action functionals dependi…
We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equation under which the zero solution is asymptotically stable.…
We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable…
This paper investigates the stability properties of the spectrum of the classical Steklov problem under domain perturbation. We find conditions which guarantee the spectral stability and we show their optimality. We emphasize the fact that…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the $\Delta_2$-condition in terms of their directional derivatives. Furthermore we study related basic…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3]…
We analyze the role of the force-dependent kinetics of motor proteins in the stability of antiparallel arrays of polar filaments, such as those in the mitotic spindle. We determine the possible stable structures and show that there exists…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J.…
In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $\delta$-stationary points near an isolated local minimum point $x^*$ is…
A periodic homogenization result of nonconvex integral functionals in the vectorial case with convex bounded constraints on gradients is proved. The class of integrands considered have singular behavior near the boundary of the convex set…
This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…
The asymptotic stability of several homological invariants of the graded pieces of a graded module has attracted quite a lot of attention over the last decades. We provide in this text several stability results together with estimates of…