Related papers: Determining equations for higher-order decompositi…

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.

We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization of the operator. This could also be validated by…

We derive a set of easy rules to follow when estimating the coefficients of operators in an effective Lagrangian. In particular, we emphasize how to estimate the size of coefficients originating from irrelevant interactions in the…

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…

For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.

In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.

We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…

On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.

We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…

The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by…

The main aim of this article is to establish an $L_p$-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the…

Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…

In this note, we are interested in the *-version of various special functions. Noting that many special functions are defined by integrals involving the exponential functions, we define *-special functions by similar integral formula…

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

In this note, we review the latest qualitative results, referring to the Li\'enard Equation, in the framework of non-conformable, generalized and fractional differential operators.

We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of…

For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest…