On coloring box graphs

We consider the chromatic number of a family of graphs we call box graphs, which arise from a box complex in n$n$-space. It is straightforward to show that any box graph in the plane has an admissible coloring with three colors, and that any box graph in n$n$-space has an admissible coloring with n+1$n+1$ colors. We show that for box graphs in n$n$-space, if the lengths of the boxes in the corresponding box complex take on no more than two values from the set {1,2,3}$\{1,2,3\}$, then the box graph is 3$3$-colorable, and for some graphs three colors are required. We also show that box graphs in 3-space which do not have cycles of length four (which we call “string complexes”) are 3$3$-colorable.     

Annihilation electrogenerated chemiluminescence of mixed metal chelates in solution: modulating emission colour by manipulating the energetics

We demonstrate the mixed annihilation electrogenerated chemiluminescence of tris(2,2′-bipyridine)ruthenium(ii) with various cyclometalated iridium(iii) chelates. Compared to mixed ECL systems comprising organic luminophores, the absence of T-route pathways enables effective predictions of the observed ECL based on simple estimations of the exergonicity of the reactions leading to excited state production. Moreover, the multiple, closely spaced reductions and oxidations of the metal chelates provide the ability to finely tune the energetics and therefore the observed emission colour. Distinct emissions from multiple luminophores in the same solution are observed in numerous systems. The relative intensity of these emissions and the overall emission colour are dependent on the particular oxidized and reduced species selected by the applied electrochemical potentials. Finally, these studies offer insights into the importance of electronic factors in the question of whether the reduced or oxidized partner becomes excited in annihilation ECL.     

A Quadrupole mass spectrometer for resolution of low mass isotopes

The qualitative and quantitative identification of low mass isotopes in the mass range 1–6 u poses certain difficulties when attempting to achieve the required resolution with an instrument suitable for deployment within a process environment. Certain adjacent species present in the process sample (HT and D₂) require a resolution greater than 930 to achieve an accurate measurement. We demonstrate here through simulation techniques that this level of performance required is unachievable using commercially available instruments. Using previously reported simulation techniques, this article demonstrates how the required performance for resolving the low mass isotopes can be achieved by a quadrupole mass spectrometer (QMS), which incorporates a quadrupole mass filter (QMF) constructed from hyperbolic electrodes and operated in zone 3 of the Mathieu stability diagram.     

Observation of dihalide elimination upon electron attachment to oxalyl chloride and oxalyl bromide, 300-550 K

Rate coefficients have been measured for electron attachment to oxalyl chloride [ClC(O)C(O)Cl] and oxalyl bromide [BrC(O)C(O)Br] in He gas at 133 Pa pressure over the temperature range of 300-550 K. With oxalyl chloride, the major ion product of attachment is Cl2(-) at all temperatures (66% at 300 K); its importance increases slightly as temperature increases. Two other product ions formed are Cl- (18% at 300 K) and the phosgene anion CCl2O- (16% at 300 K) and appear to arise from a common mechanism. With oxalyl bromide, the Br2(-) channel represents almost half of the ion product of attachment, independent of temperature. Br- accounts for the remainder. For oxalyl chloride, the attachment rate coefficient is small [(1.8 +/- 0.5) x 10(-8) cm3 s(-1) at 300 K], and increases with temperature. The attachment rate coefficient for oxalyl bromide [(1.3 +/- 0.4) x 10(-7) cm3 s(-1) at 300 K] is nearly collisional and increases only slightly with temperature. Stable parent anions C2Cl2O2(-) and C2Br2O2(-) and adduct anions Cl- (C2Cl2O2) and Br- (C2Br3O2) were observed but are not primary attachment products. G2 and G3 theories were applied to determine geometries of products and energetics of the electron attachment and ion-molecule reactions studied. Electron attachment to both oxalyl halide molecules leads to a shorter C-C bond and longer C-Cl bond in the anions formed. Trans and gauche conformers of the neutral and anionic oxalyl halide species have similar energies and are more stable than the cis conformer, which lies 100-200 meV higher in energy. For C2Cl2O2, C2Cl2O2(-), and C2Br2O2(-), the trans conformer is the most stable conformation. The calculations are ambiguous as to the oxalyl bromide geometry (trans or gauche), the result depending on the theoretical method and basis set. The cis conformers for C2Cl2O2 and C2Br2O2 are transition states. In contrast, the cis conformers of the anionic oxalyl halide molecules are stable, lying 131 meV above trans-C2Cl2O2(-) and 179 meV above trans-C2Br2O2(-). Chien et al. [J. Phys. Chem. A 103, 7918 (1999)] and Kim et al. [J. Chem. Phys. 122, 234313 (2005)] found that the potential energy surface for rotation about the C-C bond in C2Cl2O2 is "extremely flat." Our computational data indicate that the analogous torsional surfaces for C2Br2O2, C2Cl2O2(-), and C2Br2O2(-) are similarly flat. The electron affinity of oxalyl chloride, oxalyl bromide, and phosgene were calculated to be 1.91 eV (G3), and 2.00 eV (G2), and 1.17 eV (G3), respectively.     

Hardy's theorem and rotations

We prove an extension of Hardy's classical characterization of real Gaussians of the form , , to the case of complex Gaussians in which is a complex number with positive real part. Such functions represent rotations in the complex plane of real Gaussians. A condition on the rate of decay of analytic extensions of a function and its Fourier transform along some pair of lines in the complex plane is shown to imply that is a complex Gaussian.

     

Antitumor activity of vanadocene Y and its selenocyanate derivative in xenografted caki-1 tumors in mice

The para-methoxybenzyl-substituted vanadocene dichloride (Vanadocene Y) (1) and its diselenocyanate (Selenocyanato-Vanadocene Y) (2) were tested in vitro in an anti-angiogenesis assay against human umbilical vein endothelial cells (HUVEC) delivering IC50 values of 0.92 ± 0.03 μM (1) and 37 ± 11 μM (2). In a cytotoxicity assay against the human renal cancer cells, CAKI-1, the compounds demonstrated IC50 values of 0.55 ± 0.09 μM (1) and 0.25 ± 0.03 μM (2). Then both compounds were given at their maximum tolerable dose, MTD, of 20 mg/kg/d (1) or 40 mg/kg/d (2) on four consecutive days or at 50% of the MTD on five consecutive days per week for three weeks to overall four cohorts of eight CAKI-1 tumor-bearing female NMRI:nu/nu mice each, while a further cohort was treated with solvent only. Both MTD-treated mouse cohorts showed a statistically significant tumor growth reduction with respect to the solvent-treated control group with an optimal T/C value of 47% on day 39 of the experiment. Immunohistological analysis revealed that the expression of the proliferation marker Ki-67 was reduced due to long-term treatment with 2.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.