Mathematics

  2011 SEP 27 - (VerticalNews.com) -- According to the authors of recent research from Hamilton, Canada, "We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES."

  "These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed," wrote Y.L. Liu and colleagues, McMaster University ...read more

  2011 SEP 27 - (VerticalNews.com) -- According to the authors of a study from Asansol, India, "Given an exact stationary state and its energy-eigenvalue, we devise a simple way of generating new families of exact eigenstates with the same eigenenergy, but for different potentials."

  "While this recipe of designing isoergic states is quite general in the context of arriving at new exact solutions from a known premise, relevance of this route with the scheme of construction of isospectral potentials is noted under specific situations. The idea is extended to finding new exact eigenstates with eigenvalues as the sum of energies of two or more separate but known stationary states in dissimilar potentials," wrote C. Das and colleagues ...read more

  2011 SEP 27 - (VerticalNews.com) -- According to the authors of a study from Catalonia, Spain, "In this paper it is described a new family of homothetic functions, derived from quantum mechanical density functions (DF), which here are called volume functions (VF), appearing with such a sufficient entity level as to merit description."

  "Shape functions become the first term of the VF collection. VFs are elements of the unit shell of the DFs generated collection of tensorial product spaces," wrote R. Carbo-Dorca and colleagues, University of Girona ...read more