Conformable Fractional Nikiforov-Uvarov Method

We introduce conformable fractional Nikiforov-Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods-Saxon potential, and Hulthen potential.     

Synthesis of an L-proline modified mimetic of the A83586C antitumour cyclodepsipeptide

A mimetic of the A83586C cyclodepsipeptide has been synthesised via a three-segment coupling protocol involving dipeptides 9, 8 and 7; in contrast to our previous synthesis of A83586C, where the HATU-mediated macrolactamisation proceeded in 25% yield, the corresponding macro-lactamisation of seco-amino acid 18 occurred in ca. 78% yield.     

Electronic and structural properties of borazine and related molecules

Ab initio SCF MO calculations are reported for benzene, s-triazine, borazine and boroxine. The Laplacian of the charge density and the Mulliken population analysis procedure demonstrate that the delocalization of the π electrons decreases and the polarity of the ring bonds increases substantially as the atoms in the ring become more dissimilar. Several other properties, including distortion of the ring angles, puckering of the ring and nuclear quadrupolar coupling constants, emphasize the different chemical properties within the isoelectronic series.     

Convergence in gradient-like systems with applications to PDE

In gradient-like systems, the limit set of an orbit belongs to the set of equilibrium points. We give easily applied conditions to determine when this limit set is a single point. Applications are given to parabolic equations, linearly damped hyperbolic equations as well as their discretizations.Dedicated to Klaus Kirchgässner on his 60th birthday