Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density f...

We took a collection of 100 drum beats from popular music tracks and estimated the measure length and downbeat position of each one. Using these values, we normalized each pattern to form an ensemble of aligned drum patterns. Principal Component Analysis on this data set results in a set of basis ‘patterns’ that can be combined to give approximations and interpolations of all the examples. We u...

Exposure to radiation from different types of television sets was measured to ascertain the levels of hazards posed to the human biological system. Measurement of the annual radiation dose hazards was performed using a halogen-quenched GM tube with thin mica end window having a density of 1.5 mg/cm2, effective window diameter of 0.360 inch and side wall of 0.012 inch thick. The GM tube was plac...

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energi...

We state new results concerning the zero sets of polynomials belonging to the dual canonical basis of C[x1,1, . . . , xn,n]. As an application, we show that this basis is related by a unitriangular transition matrix to the simpler bitableau basis popularized by Désarménien-Kung-Rota. It follows that spaces spanned by certain subsets of the dual canonical basis can be characterized in terms of p...