The Encyclopedia of Integer Sequences includes some sequences that are connected with the Bell numbers and that have a particular combinatorial meaning. In this article, we find a general meaning for framing sequences, including the above mentioned ones. Furthermore, by using Laguerre-type derivatives, we derive the Laguerre-type Bell numbers of higher order, showing, as a by-product, that it i...

Transient precursor states are often experimentally observed for molecules adsorbing on surfaces. However, such precursor states are typically rather short-lived, quickly yielding to more stable adsorption configurations. Here we employ first-principles calculations to systematically explore the interaction mechanism for benzene derivatives on metal surfaces, enabling us to selectively tune the...

We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we rewrite the fractional problem into a classical optimal control problem. The latter problem is then solved by application of standard numerical techniques. We i...

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where RiemannLiouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions ...

In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer kH , the covariant derivatives of the curvature tensor up to order kH + 2 and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to...

An< accurate, stable and very fast corner finder (for feature based vision) has been developed', based on a novel definition of corners, using:no image derivatives. This note describes the algorithm and the results obtained from its use.

The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology experimental constraints are summarized the application paradigm to quantum discussed. We also clarify issue unitarity in with integer-order derivatives.

The multistep differential transform method is first employed to solve a time-fractional enzyme kinetics. This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of...

Fractional centred differences and derivatives definitions are proposed generalising to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalisations of the Cauchy integral derivative. To compute this integral, a special two straight line path was use...