We consider the effect of phase shifts in the context of second-order recoupling techniques in solid-state NMR. Notably we highlight conditions leading to significant improvements for the Third Spin Assisted Recoupling (TSAR) mechanism and demonstrate the benefits of resulting techniques for detecting long-distance transfer in biomolecular systems. The modified pulse sequences of PAR and PAIN-C...

In this note we announce preliminary results obtained by applying the methodology of Sussmann [4, 5, 6, 7, 8] to the problem studied by Ledzewicz and Schättler (cf. [1, 2]), of deriving high-order necessssary conditions for a minimum in optimal control theory, extending the classical Pontryagin Maximum Principle (abbr. MP) of [3]. The work of [1, 2] uses high-order generalizations of the theore...

Using the representation theory of groups, we are able to give simple necessary and suucient conditions regarding the structure of the galois groups of second and third order linear diierential equations. These allow us to give simple necessary and suucient conditions for a second order linear diierential equation to have liouvillian solutions and for a third order linear diierential equation t...

Data envelopment analysis (DEA) is a widely used benchmarking technique. Its strength stems from the fact that it can include several inputs and outputs of not necessarily same type to evaluate efficiency scores. Indeed, aforesaid method based on mathematical optimization. This paper constructs second-order conic optimization problem unifying DEA models. Moreover, presents an algorithm solves f...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...