Related papers: A note on Leibniz rule for difference quotient

A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation.

We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…

In fractional calculus there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…

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An observation on Hall-Littlewood polynomials.

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We use GL(2) delta method to establish the Burgess bound.

Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule.…

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A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite…

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

A formula for the difference of Vassiliev invariants of degree k+1 of two knots all of whose Vassiliev invariants of degree k agree is proven. The proof uses K. Habiro's C-moves and his theorem which relates them to Vassiliev invariants.

We establish a sequential Hopf's Lemma for higher order differential inequalities in one variable and give some applications of this result.

We derive a closed form solution for the Kullback-Leibler divergence between two Weibull distributions. These notes are meant as reference material and intended to provide a guided tour towards a result that is often mentioned but seldom…

The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.

In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties…