Related papers: A note on Leibniz rule for difference quotient
We summarize results concerning the Bernstein property of differential equations.
The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.
In \cite{Nam} Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with…
In this article, we describe the construction of graded $q$-differential algebra with ternary differential satisfying the property $d^3=0$ and the $q$-Leibniz rule. Our starting point is coordinate first order differential calculus on some…
In this Note, we start off with the primary representation of e and from there present an elementary short proof for the Wallis formula for $\pi$.
We use a Leibnitz rule type inequality for fractional derivatives to prove conditions under which a solution $u(x,t)$ of the k-generalized KdV equation is in the space $L^2(|x|^{2s}\,dx)$ for $s \in \mathbb R_{+}$.
In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local…
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
We give a new proof of Chen-Lin result with Li-Zhang method.
The arithmetic partial derivative (with respect to a prime $p$) is a function from the set of integers that sends $p$ to 1 and satisfies the Leibniz rule. In this paper, we prove that the $p$-adic valuation of the sequence of higher order…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.
Derivations of Borns Rule are of interest because they tell us what's connected to what in quantum mechanics if we ever need to change or modify it.
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
The Demazure operator associated to a simple reflection satisfies the twisted Leibniz rule. In this paper we introduce a generalization of the twisted Leibniz rule for the Demazure operator associated to any atomic double coset. We prove…
We prove a version of Dedekind's Transposition Principle that holds in lattices of equivalence relations.
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…