Related papers: Characteristic Function, Schur Parameters and Pseu…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
Some new relations on skew Schur function differences are established both combinatorially using Sch\"utzenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
We introduce two new bases of QSym, the flipped extended Schur functions and the backward extended Schur functions, as well as their duals in NSym, the flipped shin functions and the backward shin functions. These bases are the images of…
The notion of supershift generalizes that one of superoscillation and expresses the fact that the sampling of a function in an interval allows to compute the values of the function outside the interval. In a previous paper we discussed the…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
We give an equivalent condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [6] and…
A central notion of physics is the rate of change. While mathematically the concept of derivative represents an idealization of the linear growth, power law types of non-linearities even in noiseless physical signals cause derivative…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…
New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border…
In this paper, we provide a combinatorial characterization of the elements of Schur ultrafilters on countable commutative groups. Using this characterization, we construct a free Schur ultrafilter on $\mathbb Z$ that is not infinitary…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
This article considers testing for mean-level shifts in functional data. The class of the famous Darling-Erd\H{o}s-type cumulative sums (CUSUM) procedures is extended to functional time series under short range dependence conditions which…
Symplectic $Q$-functions are a symplectic analogue of Schur $Q$-functions and defined as the $t=-1$ specialization of Hall--Littlewood functions associated with the root system of type $C$. In this paper we prove that symplectic…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…