Various methods (Hartree–Fock methods, semi-empirical Density Functional Theory, Molecular Mechanics) used to optimize a molecule structure feature the same basic approach but differ in mathematical approximations used. The geometry optimization procedure calculates energy at an initial of and then proceeds search new with lower energy. Using 3D structures collected from PubChem database, 20 am...

Abstarct In this paper, a new approach to optimize an Autonomous Underwater Vehicle (AUV) hull geometry is presented. Using this methode, the nose and tail of an underwater vehicle are designed, such that their length constraints due to the arrangement of different components in the AUV body are properly addressed. In the current study, an optimal design for the body profile of a torpedo-shaped...

Ab initio calculation at HF/6-31G* level of theory for geometry optimization and MP2/6-31G*//HF/6-31G* for a single point total energy calculation are reported for the important energyminimumconformations and transition-state geometries of of cyclodeca-1,2,3-triene (1). The mostfavorable conformation of 1 is a unsymmetrical twist-chair (1-TC) structure. Degenerateinterconversion of 1-TC with it...

We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc.

background: the aim of this study was to investigate vertebral geometry changes and determine cutoff value of vertebral height to predict fractures. methods: in a cross-sectional study, 280 postmenopausal women recruited .in all subjects bone mineral density and radiog raphy of the lumbar spine performed. lateral radiographs were evaluated for identification of vertebral fractures, using a vali...