We present two purely functional implementations of the computational diierentiation tools { the well known numeric (not symbolic!) techniques which permit to compute point-wise derivatives of functions deened by computer programs economically and exactly. We show how the co-recursive (lazy) algorithm formulation permits to construct in a transparent and elegant manner the entire innnite tower ...

For classical Brownian systems driven out of equilibrium, we derive inhomogeneous two-time correlation functions from functional differentiation of the one-body density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. Th...

The burning rate of the monopropellant nitromethane (NM) has been observed to increase by adding and dispersing small amounts of functionalized graphene sheets (FGSs) in liquid NM. Until now, no plausible mechanisms for FGSs acting as combustion catalysts have been presented. Here, we report ab initio molecular dynamics simulations showing that carbon vacancy defects within the plane of the FGS...

Photoaffinity labeling is a reliable analytical method for biological functional analysis. Three major photophores--aryl azide, benzophenone and trifluoromethyldiazirine--are utilized in analysis. Photophore-bearing L-phenylalanine derivatives, which are used for biological functional analysis, were inoculated into a Klebsiella sp. isolated from the rhizosphere of a wild dipterocarp sapling in ...

This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, can be nested within model includes point-impact effects at the end-points observed functions. Contrasts then employed test specification derivatives. When nonlinear are employed, we apply C dete...

Many crystallographic problems are reduced to the optimization of some functional. In most cases, this functional is expressed in terms of structure factors and depends on a large number of variables; an example is the refinement of atomic models. Calculation of the functional derivatives, necessary for different optimization methods, is a time-consuming procedure. Previously, a technique to ca...

Easy dehalogenation of bromo-, chloro-aryl and alkyl derivatives is performed in the presence a cobalt catalyst, manganese as reductant, alcohol hydrogen donor. This method tolerates variety functional groups with different electronic properties. Noteworthy examples desulfonation are also reported.