Related papers: A Leibniz/NSA comparison
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We compare the metric and the Palatini formalism to obtain the Einstein equations in the presence of higher-order curvature corrections that consist of contractions of the Riemann tensor, but not of its derivatives. We find that there is a…
We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
An investigation of the comparative efficiency of the different methods in which {\pi} is cal- culated. This thesis will compare and contrast five different methods in calculating {\pi} by first deriving the various proofs to each method…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
In this paper, we introduce compatible ternary Leibniz algebras, (dual)Nijenhuis pairs from the second-order deformation of ternary Leibniz algebras with a representarion and study the invariance of certains operators (generalized…
We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein-Friedmann equations. These analogies produce an effective Lagrangian and…
The response function to an external prove is evaluated using the ring approximation in nuclear matter. Contrary to what it is usually assumed, it is shown that the summation of the ring series and the solution of the Dyson's equation are…
Approximate Bayesian computation (ABC) has gained popularity in recent years owing to its easy implementation, nice interpretation and good performance. Its advantages are more visible when one encounters complex models where maximum…
We examine a proof by Craig Alan Feinstein that P is not equal to NP. We present counterexamples to claims made in his paper and expose a flaw in the methodology he uses to make his assertions. The fault in his argument is the incorrect use…
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces…
Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population…
We look for the optimal range of Lebesque exponents for which inhomogeneous Strichartz estimates are valid. We show that it is larger than the one given by admissible exponents for homogeneous estimates. We prove inhomogeneous estimates…
We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…
We develop refinements of the Levenshtein bound in $q$-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. The first relevant cases are…
We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{ \pm 1\}$ only. A basic case of our results states that for…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
This paper focuses on the biderivations of 4-dimensional nilpotent complex Leibniz algebras. Using the existing classification of these algebras, we develop algorithms to compute derivations, antiderivations, and biderivations as pairs of…
For relational monadic formulas (the L\"owenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in…