Related papers: On linear Harbourne constants
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this paper we consider invariant formulation of nonlinear (Lagrangian…
Discussion of the constancy, or otherwise, of the various so-called universal constants which abound in physics has continued for many years. However, relatively recent observations, which appear to indicate a variation in the value of the…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants.
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
Construction of the gauge-invariant variables for the linear metric perturbation, which was proposed in the paper [K. Nakamura, arXiv:1101.1147], is discussed through an alternative approach. Our starting point of the construction of the…
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
We prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. We clarify the cancellations that take place between the two aforementioned…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
An equation is obtained to find the Lagrangian for a one-dimensional autonomous system. The continuity of the first derivative of its constant of motion is assumed. This equation is solved for a generic nonconservative autonomous system…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
Computations involving invariant random vectors are directly related to the theory of invariants (cf. e.g \cite{Weing_1}). Some simple observations along these lines are presented in this paper. We note in particular that sum of elements of…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…