Related papers: Parametrizing the abstract Ellentuck theorem
We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…
We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup. This…
Certain famous combinatorial sequences, such as the Catalan numbers and the Motzkin numbers, when taken modulo a prime power, can be computed by finite automata. Many theorems about such sequences can therefore be proved using Walnut, which…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
In this paper we show an abstract theorem that can be used to prove the existence of solution for a class of elliptic equation considered in Berestycki-Lions \cite{berest} and related problems. Moreover, we use the abstract theorem to show…
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite…
We unify the recently developed abstract theories of universal series and extended universal series to include sums of the form $\sum_{k=0}^n a_k x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\geq k\geq 0}$ in a topological vector…
We incorporate into the empirical measure the auxiliary information given by a finite collection of expectation in an optimal information geometry way. This allows to unify several methods exploiting a side information and to uniquely…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
A general solution of the Batalin-Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin-Vilkovisky master equation is also established. Superfields…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address…
Using the universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain geometric hypothesis the best approximations (in the sense of…
A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
We generalize the Brezzi-Rappaz-Raviart approximation theorem, which allows to obtain existence and a priori error estimates for approximations of solutions to some nonlinear partial differential equations. Our contribution lies in the fact…
We give an explicit formulae for obtaining the translation symmetries in the cartesian product $X^N$, where $N$ is some positive integer and $X$ is some finite set. Moreover, we obtain some fundamental results from elementary number theory.
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…