Klein–Gordon equation from the path integral formalism

By using Feynman's path integral formalism in the second order for the relativistic Lagrangian for a spinless particle in a gauge field and applying the covariant derivative instead of the commonly used derivative, but without knowing the operator expressions for the momentum and energy, one can obtain the Klein–Gordon equation. Received: 9 March 2001 / Published online: 13 June 2001     

The relationship between the models of perturbed Newton iterations,with applications

The quasi-Newton method and the inexact Newton method are classical models of Newton iterates which take into account certain error terms. We have recently introduced the inexact perturbed Newton method, which takes into account all the possible sources of perturbations. We show that these models are in fact equivalent, in the sense that each one may be used to characterize the high convergence orders of the other two. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exploring the Research Progress about the Applications of Cyclodextrins and Nanomaterials in Electroanalysis

Cyclodextrins and nanomaterials are widely used in the achievement of powerful platforms in supramolecular chemistry and nanotechnology. The relatively hydrophobic internal cavity of the CDs selectively retains molecules having the proper geometry, while the hydrophilic exterior allows CDs to improve the dispersibility and molecular recognition. The nanomaterials provide higher surface area, good conductivity, and electrocatalytic effect. The use of nanomaterials and CDs in electrochemical sensors’ design allows the development of a large variety of devices, explaining the increasing number of papers in the last years that are discussed in this review.