REAL ROOT ISOLATION OF SPLINE FUNCTIONS

In this paper, we propose an algorithm for isolating real roots of a given univariate spline function, which is based on the use of Descartes＇ rule of signs and de Casteljau algorithm. Numerical examples illustrate the flexibility and effectiveness of the algorithm.     

Rank gain of Jacobians over number field extensions with prescribed Galois groups

We investigate the rank gain of elliptic curves, and more generally, Jacobian varieties, over non-Galois extensions whose Galois closure has a Galois group permutation-isomorphic to a prescribed group G (in short, “G-extensions”). In particular, for alternating groups and (an infinite family of) projective linear groups G, we show that most elliptic curves over (for example) $\mathbb{Q}$ gain rank over infinitely many G-extensions, conditional only on the parity conjecture. More generally, we provide a theoretical criterion, which allows to deduce that “many” elliptic curves gain rank over infinitely many G-extensions, conditional on the parity conjecture and on the existence of geometric Galois realizations with group G and certain local properties.     

A structural approach to investigate halogen substituted MAO-B inhibitors using QSAR modeling,molecular dynamics,and conceptual DFT analysis

Halogenated inhibitors showed robust, reversible, and selective monoamine oxidase-B (MAO-B) inhibitory efficacy in candidates that were derived from them. Our team has previously synthesized and assessed a panel of halogenated chalcones and coumarin for the study on MAO-B inhibition. The aim of this study was to build GA-MLR based QSAR models and predictive 3D Pharmacophore models, as well as to investigate the relationship between halogenated derivatives and MAO-B inhibitory activity. The robust statistical significance in the parameter (R² = 0.78 and Q² = 0.69) was demonstrated. Best Hypo1 contains one hydrophobic and two aromatic rings. The lead molecule for quantum mechanics was performed, and it was revealed that it would bind to proteins and provide stability. To determine the stability of the ligand-enzyme complex, a thorough molecular dynamics analysis of the lead compounds was accomplished.