Rational Points on the Sphere

Using only basic tools from the theory of modular forms, the rational points of bounded height on the sphere are counted and shown to be uniformly distributed. The more difficult case of points with a given height is also treated.     

The simulated ab-initio molecular orbital (SAMO) method for polymers. Polyethylene and polyene

The application of the simulated ab-initio molecular orbital (SAMO) method — a new non-empirical technique — to the band structure of polymers is reported. The method uses full ab-initio results on small molecules to construct for polymers molecular orbitals which simulate those obtained from full ab-initio treatments. Results are compared with those obtained from published ab-initio and semi-empirical calculations.     

A study of radionuclides in vegetation on abandoned uranium tailings

A study has been carried out of the uptake of uranium and other radionuclides by plants growing on abandoned tailings from an uranium mining operation. Assay methods included instrumental neutron activation analysis, delayed neutron counting, fission track imaging, and counting of natural radioactivity. Care was taken to avoid contamination of the plant material and a number of methods are described to identify such contamination. All plants observed showed high uptake of radionuclides, compared to plants studied from naturally uraniferous and control areas. Graminoid (grass-like) plants showed significant uptake in the above-ground parts while woody plants showed exceedingly high uranium accumulation in the root portions. These results have significance in determination of the spread of radioactive material from such sites.     

Fission track mapping of uranium in black spruce (Picea Mariana) twigs

Fission track analysis (FTA) has been used to investigate the biological uptake of uranium. Examination of fission track maps of black spruce twigs (from areas of uranium mineralization and mill tailings) shows uranium to be concentrated in the inner bark while decreasing in the outer bark of the twigs. Track clusters in the bark, too large to be uraniferous airborne particulate matter, are identified as being associated with resin canals in the twigs. The results of this work help clarify the mechanisms by which uranium is incorporated in black spruce twigs. The observation of decreasing uranium content with the increasing age of black spruce twigs by an earlier worker, can now be explained by the relative reduction in volume of the uranium enriched inner bark with age.     

The ab initio neglect of differential diatomic overlap method

The ab initio Neglect of Differential Diatomic Overlap (N.D.D.O.) method of Roby is tested numerically for an extensive series of molecules. Agreement with the full ab initio molecular orbital method is poor. Total energies are more negative and dipole moments are overestimated. The failings of the N.D.D.O. method are accounted for using multipole-multipole expansions.     

endo-1,4,5,6,7,7-hexachlorobicyclo[2.2.1]hept-5-ene-2-carboxylic acid, a superior resolving agent for the high-performance liquid chromatographic separation of enantiomers of hydroxylated derivatives of two azaaromatic hydrocarbons

The high-performance liquid chromatographic (HPLC) separation of enantiomers of oxide and hydroxy derivatives of dibenz[a,j]acridine and 7-methylbenz[c]acridine was investigated on a chiral stationary phase chromatography column using commercially available columns. In most cases either poor or no separation of enantiomers was achieved. Normal-phase separation of diastereoisomeric ester derivatives of the hydroxy compounds, prepared from commercially available (-)-menthoxyacetic acid or (+)-alpha-methoxy-alpha-(trifluoromethyl)phenylacetic acid, was investigated. No separation of the diastereoisomeric esters of trans-3,4-dihydroxy-3,4-dihydrodibenz[a,j]acridine was observed. However, diastereoisomeric esters prepared from (+)-endo-1,4,5,6,7,7-hexachlorobicyclo[2.2.1]hept-5-ene-2-carboxyl ic acid [(+)-HCA] were easily separated. Using the three chiral acids, diastereoisomers were prepared from sixteen hydroxy derivatives of dibenz[a,j]acridine and 7-methylbenz[c]acridine. (+)-HCA esters gave good to excellent HPLC separations which were superior to those achieved using other chiral acids in most cases. The enantiomeric composition of trans-3,4-dihydroxy-3,4-dihydrodibenz[a,j]acridine formed as a major rodent liver microsomal metabolite of dibenz[a,j]acridine was determined using (+)-HCA.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].