Related papers: The slope robustly determines convex functions
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely…
In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz…
The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent polynomial-time classification of point clouds required a…
The problem of finding the minimizer of a sum of convex functions is central to the field of distributed optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the…
The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…
The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved…
A recent line of ground-breaking results for permutation-based SGD has corroborated a widely observed phenomenon: random permutations offer faster convergence than with-replacement sampling. However, is random optimal? We show that this…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings.…
We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on $\mathbb{R}^N$ to have a (locally strongly) convex inverse. We show under suitable conditions that if the gradient of each component of…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
The self-consistent cranking method is tested by comparing the cranking calculations in the interacting boson model with the exact results obtained from the SU(3) and O(6) dynamical symmetries and from numerical diagonalization. The method…
This work studies the dependence of the solution with respect to interface geometric perturbations in a multiscaled coupled Darcy flow system in direct variational formulation. A set of admissible perturbation functions and a sense of…