Related papers: A Leibniz/NSA comparison
We study certain kind of polynomials associated with Lissajous curves, called Chebyshev-Lissajous polynomials. We investigate their irreducibilities over the real numbers and complex numbers, thus comfirming two conjectures proposed by…
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties.…
In this article, we relax the Bayesianity assumption in the now-traditional model of Bayesian Persuasion introduced by Kamenica & Gentzkow. Unlike preexisting approaches -- which have tackled the possibility of the receiver (Bob) being…
Development of bibliometric techniques has reached such a level as to suggest their integration or total substitution for classic peer review in the national research assessment exercises, as far as the hard sciences are concerned. In this…
LS is a particular type of computational processes simulating living tissue. They use an unlimited branching process arising from the simultaneous substitutions of some words instead of letters in some initial word. This combines the…
This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in \cite{ab} can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic…
We examine some recent scholarship on Leibniz's philosophy of the infinitesimal calculus. We indicate difficulties that arise in articles by Bassler, Knobloch, and Arthur, due to a denial to Leibniz's infinitesimals of the status of…
In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the perspective point of intersection at infinite distance…
We shall show that although Palatini f(R)-theories are equivalent to Brans-Dicke theories, still the first pass the Mercury precession of perihelia test, while the second do not. We argue that the two models are not physically equivalent…
We study polynomial approximation on a $d$-cube, where $d$ is large, and compare interpolation on sparse grids, aka Smolyak's algorithm (SA), with a simple least squares method based on randomly generated points (LS) using standard…
The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric $\h$ on its annhilator vector bundle. In particular, the possible dimensions of the…
If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…
We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…
In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology,…
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the…
A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The…
In this paper, the structure of the second relative homology and the relative stem cover of the direct sum of two pairs of Leibniz algebras are determined by means of the non-abelian tensor product of Leibniz algebras. We also characterize…