Circles through two points that always enclose many points

This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.     

An experimental investigation of high permittivity dielectric resonators for millimeter-wave microstrip components

This paper proposes a new type of high permittivity whispering gallery mode cylindrical dielectric resonators with a geometry which is very suitable for use in microstrip type integrated circuits. These oversized resonators, together with high Q factors and ease of fabrication, are potentially interesting for millimeter wave integrated filters and oscillators. In this paper, we report an experimental investigation of such resonators carried out in Ka band (26.5–40 GHz). Measured results including resonant frequencies and loaded quality factors will be presented. Application to millimeter wave filters will also be demonstrated.     

Electronic properties of polyoxometalates: a DFT study of alpha/beta-[XM(12)O(40)](n-) relative stability (M=W, Mo and X a main group element)

Keggin heteropolyanions [XM(12)O(40)](n-) have various isomeric structures, alpha and beta being the most common. Conventionally, the alpha structure appears to be the most stable, but calculations carried out at the DFT level for X = P(V), Si(IV), Al(III), As(V), Ge(IV), and Ga(III) and M = W(VI) and Mo(VI) show that this stability depends on several factors, particularly on the nature of the heteroatom (X) and the total charge of the cluster. In this paper, we apply the clathrate model to the Keggin molecule to carry out a fragment-interaction study to elucidate when and why the traditional relative stability of various isomers can be inverted. The fully oxidized anions that have inverted the traditional stability trend in this series are [AlW(12)O(40)](5-) and [GaW(12)O(40)](5-), both of which contain a third-group heteroatom and an overall charge of -5. beta-isomers are always more easily reduced than alpha-isomers. This experimental observation suggests that reduction favors the stability of beta-isomers and one of the most important results of this study is that the alpha/beta inversion is achieved in most cases after the second reduction. The alpha- and beta-isomers may have different properties because the energy of the LUMO, a symmetry-adapted d(xy)-metal orbital, is different.     

Absolute rate constants for the quenching of reactive excited states by melanin and related 5,6-dihydroxyindole metabolites: implications for their antioxidant activity

The triplet-excited state of benzophenone and the singlet-excited state of 2,3-diazabicyclo[2.2.2]oct-2-ene (Fluorazophore-P) have been employed as kinetic probes to obtain information on the antioxidant activity of the skin and eye pigment melanin and its biogenetic precursors 5,6-dihydroxyindole (DHI) and 5,6-dihydroxyindole-2-carboxylic acid (DHICA). The excited states were generated by the laser-flash photolysis technique and their reaction kinetics was examined by time-resolved transient absorption or fluorescence spectroscopy, respectively. The reaction between triplet benzophenone and DHI produced with unit efficiency the corresponding 6O-centered semiquinone radical, which was characterized by its characteristic transient absorption. The quenching rate constants for DHI (3.1-8.4 x 10(9) M-1 s-1) and DHICA (3.3-5.5 x 10(9) M-1 s-1) were near the diffusion-controlled limit, indicating excellent antioxidant properties. Kinetic solvent effects were observed. The reactivity of synthetic melanin, assessed through the quenching rate constant of Fluorazophore-P and normalized to the number of monomer units, was more than one order of magnitude lower (2.7 x 10(8) M-1 s-1) than that of its precursors. The trend of the quenching rate constants, i.e. DHI > DHICA approximately alpha-tocopherol > melanin, along with the preferential solubility of DHICA in aqueous environments, serves to account for several experimental results from biochemical studies on the inhibition of lipid peroxidation by these natural antioxidants.