Assessing how well a modeling protocol captures a structure-activity landscape

We introduce the notion of structure-activity landscape index (SALI) curves as a way to assess a model and a modeling protocol, applied to structure-activity relationships. We start from our earlier work [ J. Chem. Inf. Model., 2008, 48, 646-658], where we show how to study a structure-activity relationship pairwise, based on the notion of "activity cliffs"-pairs of molecules that are structurally similar but have large differences in activity. There, we also introduced the SALI parameter, which allows one to identify cliffs easily, and which allows one to represent a structure-activity relationship as a graph. This graph orders every pair of molecules by their activity. Here, we introduce the new idea of a SALI curve, which tallies how many of these orderings a model is able to predict. Empirically, testing these SALI curves against a variety of models, ranging over two-dimensional quantitative structure-activity relationship (2D-QSAR), three-dimensional quantitative structure-activity relationship (3D-QSAR), and structure-based design models, the utility of a model seems to correspond to characteristics of these curves. In particular, the integral of these curves, denoted as SCI and being a number ranging from -1.0 to 1.0, approaches a value of 1.0 for two literature models, which are both known to be prospectively useful.     

On generalized Sundman transformation method,first integrals,symmetries and solutions of equations of Painlevé–Gambier type

We employ the generalized Sundman transformation method to obtain certain new first integrals of autonomous second-order ordinary differential equations belonging to the Painlevé–Gambier classification scheme. This method not only yields systematically the known first integrals of a large number of the Painlevé–Gambier equations but also some time dependent ones, which greatly simplify the computation of their corresponding solution. In addition we also compute the Sundman symmetries of these equations.     

Second-degree Painlevé equations and their contiguity relations

We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).     

Effect of transverse static magnetic field on stimulated brillouin scattering of electromagnetic wave

Stimulated Brillouin scattering of a plane polarised electromagnetic wave propagating perpendicular to a static magnetic field has been investigated analytically in ann-type piezoelectric semiconductor-plasma. Using coupled mode theory the dispersion relation is obtained and the threshold value of the amplitude of electromagnetic wave for the onset of instability is studied for both the forward and back-scattered modes. The role of the magnetostatic field on the threshold conditions for the unstable mode has been discussed.     

Pyridinolysis of phenyl-substituted phenyl chlorophosphates in acetonitrile

The kinetics and mechanism of the reactions of phenyl-substituted phenyl chlorophosphates, I, with pyridines in acetonitrile are investigated at 25.0 degrees C. The rates are much faster and the transition state is much earlier on the reaction coordinate with smaller beta(X) (0.16-0.18) and smaller negative beta(XY) (-0.011) values than those for the corresponding reactions with anilines. The vertical approach of the pyridine ring to an apical position of the trigonal bipyramidal transition state enables the p(pi)-d(pi) overlap between the pi orbital of pyridine and an empty d-orbital of phosphorus with less steric hindrance in a concerted process. The activation parameters are in line with the proposed mechanism.     

Kinetics and mechanism of dissociation of copper(II) complexes of biguanide and someN 1-substituted biguanides in aqueous acetate buffer media

The kinetics fo dissociation of thebis complexes [Cu(LH)₂]²⁺ formed by Cu^II with biguanide andN ¹-substituted methyl, phenyl, dimethyl and diethyl biguanides into the mono biguanide complexes in aqueous NaOAc-HOAc buffer media have been studied by stopped-flow spectrophotometry. The results, under pseudo-first-order conditions, indicate k_obs=k_o+k_H[H⁺]. For the different complexes k_o values are comparable, but k_H values differ appreciably; log k_H versus log K _d ^H is linear withca. unit slope K _d ^H being the equilibrium constant for the process: