Generalized sum graphs

Harary [8] calls a finite, simple graphG asum graph if one can assign to eachv _i V(G) a labelx _i so that{v _i ,v _j }E(G) iffx _i +x _j =x _k for somek. We generalize this notion by replacing x _i +x _j with an arbitrary symmetric polynomialf(x _i ,x _j ). We show that for eachf, not all graphs are f-graphs. Furthermore, we prove that for everyf and every graphG we can transformG into anf-graph via the addition of |E(G)| isolated vertices. This result is nearly best possible in the sense that for allf and for , there is a graphG withn vertices andm edges which, even after the addition ofm-O(n logn) isolated vetices, is not andf-graph.Research supported in part by a U.S.A.-Israel Binational Science Foundation and by a Bergmann Memorial Grant.Research supported in part by the Office of Naval Research contract number N00014-85-K0622.     

Synthesis and antimalarial effects of 2-(3,4-dichloroanilino)-7-[[[(dialkylamino)alkyl]amino]]-5-methyl-s-triazolo[1,5-a]pyrimidines

3,4-Dichlorophenylisothioeyanate ( 10 ) was allowed to react with 2-methy1-2-thiopseudourea to give methyl 4-(3,4-dichlorophenyl)(dithioaltophanimidate ( 11 ) (41%), which upon treatment with hydrazine afforded 3-amino-5-(3,4-dichloroanilino)-s-triazole ( 12 ) (54-91%). Ring-closure with ethyl acetoacetale in acetic acid afforded 2-(3,4-dichloroanilino)-5-methyl-s-triazolo[ 1,5-α ]-pyrimidin-7-ol ( 13 ) (81%). Chlorination with phosphorus oxychloride gave 7-chloro-2-(3,4-dichloroanilino)-5-methyl-s-triazolo[1,5-α ]pyrimidine ( 14 ) (98%), which was condensed with various amines to yield the desired 2-(3,4-diehloroanilino)-7-¶[(dialkylamino)alkyl]arnino¶-5-methyl-s-triazolo[ 1,5-α]pyrimidines ( 6 a-d). The structures of the s-triazolo[ 1,5-α ]pyrimidines were based on nmr spectroscopy and ring stability considerations. Several of the amino-s-triazolo[ 1,5-α ]pyrimidines possessed antimalarial activity against P. berghei in mice.     

A theoretical interpretation of isotope effects in mixtures of light and heavy water—II

Solvent isotope effects for H₂O---D₂O mixtures and for ionic hydration equilibria in such mixtures can be calculated from the structure difference between D₂O and H₂O and that between HDO and H₂O and the relative amounts of the three waters. The behavior of acids in H₂O---D₂O mixtures is considered in detail. Dissociation constants of acetic acid are calculated over the complete range of deuterium concentrations and found to agree with the experimentally determined ones. The Gross equation for the dependence of isotope effect on mole fraction of deuterium for acid-catalyzed reaction of substrates S proceeding via SL⁺ transition states (L=H or D) is derived from first principles.     

Folate antagonists. 6. Synthesis and antimalarial effects of fused 2,4-diaminothieno[2,3-d]pyrimidines

2,4-Diamino-5,7-dihydro-6H-thiopyrano[4′,3′:4,5]thieno[2,3-d]pyrirnidine, 2,4-diamino-9H-mdeno[1′,2′:4,5]thieno[2,3-d]pyrimidine, 2,4-diamino-5H-indeno[2′,1′:4,5]thieno[2,3-d]pyrimidine, 9,11-diamino-5,6-dihydronaphtho[1′,2′:4,5]thieno[2,3-d]pyrimidine, 7,9-diamino-5,6-dihydronaphtho[2′,1′:4,5]thieno[2,3-d]pyrimidine, 2,4-diamino-7-benzy]-5,6,7,8-tetrahydropyrido[4′,3′:4,5]thieno[2,3-d]pyrimidine, and various 2,4-diamino-5,6,7,8-tetrahydro-[1]benzothieno[2,3-d]pyrimidines were synthesized by cyclization of the requisite fused 2-aminothio-phenene-3-carbonitriles utilizing chloroformamidine hydrochloride in diglyme. Several compounds exhibited strong inhibitory effects against Streptococcus faecalis (MGH-2), Staphylococcus aureus (UC-76), Streptococcus faecium (ATCC 8043), Lactobacillus casei (ATCC 7469), and Pediococcus cerevisiae (ATCC 8081) in vitro, and three compounds displayed antimalarial activity against Plasmodium berghei in mice and P. falciparum (Uganda I) in vitro.     

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

Analysis of Plant–Plant Interactions Reveals the Presence of Potent Antileukemic Compounds

A method to identify anticancer compounds in plants was proposed based on the hypothesis that these compounds are primarily present in plants to provide them with an ecological advantage over neighboring plants and other competitors. According to this view, identifying plants that contain compounds that inhibit or interfere with the development of other plant species may facilitate the discovery of novel anticancer agents. The method was developed and tested using Magnolia grandiflora, Gynoxys verrucosa, Picradeniopsis oppositifolia, and Hedyosmum racemosum, which are plant species known to possess compounds with cytotoxic activities. Plant extracts were screened for growth inhibitory activity, and then a thin-layer chromatography bioautography assay was conducted. This located the major antileukemic compounds 1, 2, 4, and 5 in the extracts. Once the active compounds were located, they were extracted and purified, and their structures were determined. The growth inhibitory activity of the purified compounds showed a significant correlation with their antileukemic activity. The proposed approach is rapid, inexpensive, and can easily be implemented in areas of the world with high biodiversity but with less access to advanced facilities and biological assays.     

Model correction for the formation of amorphous silicon by ion implantation

The critical dose at which an implanted amorphous layer in silicon is formed cannot be explained by a previous energy independent model. An energy dependent correction to this model can explain our ESR data as well as other data. The correction is most important for light ions.