Related papers: A note on Leibniz rule for difference quotient
This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.
The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.
In this note we give a detailed proof of a theorem of Aubin.
We study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the…
This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.
We obtain simple proofs of certain inequalites for bivariate means.
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
In this note, we describe a method to construct the Picard-Vessiot ring of a given linear differential equation.
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
In this article we develop a simplistic approach to revisit the classical Kato-Ponce inequality, which is also known as 'fractional Leibniz rule.' As a consequence, we derive the validity of this inequality even in quasi-Banach spaces $L^p$…
In this note we prove a weighted version of the Khintchine inequalities.
Starting from the Riemann-Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated…
This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.
The paper presents a counterexample to the Hodge conjecture.
New recursive estimators for computing higher-order derivatives of mean queueing time from a single sample path of a first-come, first-served single-server queue are presented, derived using the well-known Lindley equation and applying the…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved…
The natural forms of the Leibniz rule for the $k$th derivative of a product and of Fa\`a di Bruno's formula for the $k$th derivative of a composition involve the differential operator $\partial^k/\partial x_1 ... \partial x_k$ rather than…