Related papers: On norming systems of linear equations

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

In this paper we continue our research on the concept of liken. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in $\mathbb{R}$. The most important examples of…

Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…

A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and Paul for real scalars. In this paper, we give a different…

Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…

We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm…

This paper introduces a novel approach to design of functional H_\infty filters for a class of nonlinear descriptor systems subjected to disturbances. Departing from conventional assumptions regarding system regularity, we adopt a more…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear…

A characterization of t-normed integrals was obtained in \cite{CLM} for finite compacta and in \cite{Rad} for the general case. Such characterization establishes a correspondence between the space of capacities and homogeneous respect…

We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed…

This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…

Consider a smooth one-parameter family t -> f_t of dynamical systems f_t, with |t|<epsilon. Assume that for all t (or for many t close to t=0) the map f_t admits a unique SRB invariant probability measure m_t. We say that linear response}…

In a countably normed space which is a linear space equipped with a countable number of pair-wise compatible norms, we prove the existence of a common nearest point (in all norms) from a point outside a nonempty subset if this subset is…

Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…

Normed spaces appear to have very little going for them: aside from the hackneyed linear structure, you get a norm whose only virtue, aside from separating points, is the Triangle Inequality. What could you possibly prove with that? As it…

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…

The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…

Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…