Related papers: An extension of the classical derivative
Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalised to find the general form of the…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
The paper contains an interesting generalization of the classical Taylor expansion formula and four applications
We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local…
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
One of the happiest accidents in all math is the ease of transforming a function to and taking derivatives in the Fourier frequency domain. But in order to exploit this extraordinary fact without serious artefacting, and in order to be able…
We develop a notion of realizability for Classical Linear Logic based on a concurrent process calculus.
Some explanations to Kaldi's PLDA implementation to make formula derivation easier to catch.
Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim…
We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over a fibred manifold to a convenient Lie algebroid over a…
In this paper, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinct distinguished vertices. Specifically, we introduce a model F on…
A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
In this short note we formalized the definition for the Ducci operator $D$ in the context of the $p$-adic field $\mathbb{Q}_p$ as a natural extension of the classical one. Moreover we will describe the behavior of the operator and will…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
The purpose of this note is to provide exposition for a proof of the statement in the title. This idea, that arbitrary cohomology classes (of high enough degree) of a finite group $G$ can be trivialized in a finite group extension, has been…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…