Related papers: An extension of the classical derivative

We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.

Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from…

We define the eigenderivatives of a linear operator on any real or complex Banach space, and give a sufficient condition for their existence.

This paper presents a generalization for Differential and Integral Calculus. Just as the derivative is the instantaneous angular coefficient of the tangent line to a function, the generalized derivative is the instantaneous parameter value…

A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.

The goal of this paper is to construct a multivariate generalisation of the Grunwald-Letnikov derivative, a classical fractional derivative operator. To do so, we first produce a formalism of fractional derivatives in terms of infinitesimal…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…

One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…

Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…

We present a generalization of a formula of higher order derivatives and give a short proof.

The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…

A generalization of L{\"u}roth's theorem expresses that every transcendence degree 1 subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this…

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…

A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…

The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.