Related papers: Two Applications of Desargues' Theorem
In this article we prove several reciprocity theorems for some infinite-dimensional dual pairs of representations on Bargmann-Segal-Fock spaces.
Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for…
We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…
We consider some applications of the non-homogeneous second order integral equation of Fox. Some new solutions to Fox's integral equation are discussed in relation to number theory.
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…
In this paper, we investigate the configuration theorems of Desargues and Pappus in a synthetic geometric way. We provide a bridge between the two configurations with a third one that can be considered a specification for both. We do not…
In this paper we show an index theorem for gerbes
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…
In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
We give a formula for matrix exponentials and partial fraction decompositions.
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
Thermodynamic systems involving reversible and non-reversible heat transfer are used to derive integral inequalities expected from the Second of Law of Thermodynamics. Then, the inequalities are proved and generalized to higher dimensions…
We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
A very simple but useful almost sure convergence theorem of probability is given.
We use duality in the manner of Serre to generalize a theorem of Hedenmalm on solution of the $\bar \partial $ equation with inverse of the weight in H\"ormander $\displaystyle L^{2}$ estimates.\
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…