Colouring a graph frugally

We prove that any graph with maximum degree sufficiently large, has a proper vertex colouring using +1 colours such that each colour class appears at most log⁸ times in the neighbourhood of any vertex. We also show that for 1, the minimum number of colours required to colour any such graph so that each vertex appears at most times in the neighbourhood of any vertex is (+^1+1//), showing in particular that when =log/loglog, such a colouring cannot always be achieved with O() colours. We also provide a polynomial time algorithm to find such a colouring. This has applications to the total chromatic number of a graph.The second two authors were supported by NATO Collaborative Research Grant #CRG950235.     

All-solid-state generation of 100-kHz tunable mid-infrared 50-fs pulses in type I and type II AgGaS(2)

We report the operation of an all-solid-state system for the generation of tunable mid-infrared sub-50-fs pulses. A Ti:sapphire regenerative amplifier, pumped by 10 W of power from 532-nm, diode-pumped, frequency-doubled Nd:YVO(4) lasers, produced 4-muJ energy, sub-50-fs pulses at 800 nm with a 100-kHz repetition rate. This output was used to drive a beta-BaB(2)O(4) optical parametric amplifier followed by a difference-frequency generator based on a AgGaS(2) crystal. Continuous tuning of ultrafast pulses from 2.4m to longer than 12mum was obtained. A performance comparison of difference-frequency generation in type I and type II phase-matched AgGaS(2) is reported.     

Growth of Ni-doped MgF2 crystals in self-sealing graphite crucibles

Large Ni-doped MgF₂ single crystals of excellent optical quality have been grown in self-sealing graphite crucibles by a vertical gradient freeze technique. This relatively simple technique always yields single crystals having excellent optical quality and should be applicable to the melt growth of other crystals that are too volatile to permit the use of open systems.     

Degree constrained subgraphs

In this paper, we present new structural results about the existence of a subgraph where the degrees of the vertices are pre-specified. Further, we use these results to prove a 16-edge-weighting version of a conjecture by Karoński, ?uczak and Thomason, an asymptotic 2-edge-weighting version of the same conjecture, and a version of Louigi's Conjecture.     

Infrared-vacuum ultraviolet pulsed field ionization-photoelectron study of C2H4(+) using a high-resolution infrared laser

The infrared (IR)-vacuum ultraviolet (VUV)-pulsed field ionization-photoelectron (IR-VUV-PFI-PE) spectrum for C2H4(X1A(g), v11 = 1, N'(Ka'Kc') = 3(03)) in the VUV range of 83,000-84,800 cm(-1) obtained using a single mode infrared laser revealed 24 rotationally resolved vibrational bands for the ion C2H4(+)(X2B(3u)) ground state. The frequencies and symmetry of the vibrational bands thus determined, together with the anharmonic frequency predictions calculated at the CCSD(T)/aug-cc-pVQZ level, have allowed the unambiguous assignment of these vibrational bands. These bands are mostly combination bands. The measured frequencies of these bands yield the fundamental frequencies for v8+ = 1103 +/- 10 cm(-1) and v10+ = 813 +/- 10 cm(-1) of C2H4(+)(X2B(3u)), which have not been determined previously. The present IR-VUV-PFI-PE study also provides truly rovibrationally selected and resolved state-to-state cross sections for the photoionization transitions C2H4(X1A(g); v11, N'(Ka'Kc')) --> C2H4(+)(X2B(3u); vi+, N+(Ka+Kc+)), where N'(Ka'Kc') denotes the rotational level of C2H4(X1A(g); v11), and vi+ and N+(Ka+Kc+) represent the vibrational and rotational states of the cation.     

The basicity of unsaturated hydrocarbons as probed by hydrogen-bond-acceptor ability: bifurcated N-H+ ...pi hydrogen bonding

The competitive substitution of the anion (A(-)) in contact ion pairs of the type [Oct3NH+]B(C6F5)4 (-) by unsaturated hydrocarbons (L) in accordance with the equilibrium Oct3NH+...A(-) + nL right arrow over left arrow [Oct3NH+...Ln]A(-) has been studied in CCl4. On the basis of equilibrium constants, K, and shifts of nuNH to low frequency, it has been established that complexed Oct3NH...+Ln cations with n=1 and 2 are formed and have unidentate and bifurcated N--H+...pi hydrogen bonds, respectively. Bifurcated hydrogen bonds to unsaturated hydrocarbons have not been observed previously. The unsaturated hydrocarbons studied include benzene and methylbenzenes, fused-ring aromatics, alkenes, conjugated dienes, and alkynes. From the magnitude of the redshifts in the N--H stretching frequencies, Delta nuNH, a new scale for ranking the pi basicity of unsaturated hydrocarbons is proposed: fused-ring aromatics相似文献   

Hard and soft acids and bases: atoms and atomic ions

The structural origin of hard-soft behavior in atomic acids and bases has been explored using a simple orbital model. The Pearson principle of hard and soft acids and bases has been taken to be the defining statement about hard-soft behavior and as a definition of chemical hardness. There are a number of conditions that are imposed on any candidate structure and associated property by the Pearson principle, which have been exploited. The Pearson principle itself has been used to generate a thermodynamically based scale of relative hardness and softness for acids and bases (operational chemical hardness), and a modified Slater model has been used to discern the electronic origin of hard-soft behavior. Whereas chemical hardness is a chemical property of an acid or base and the operational chemical hardness is an experimental measure of it, the absolute hardness is a physical property of an atom or molecule. A critical examination of chemical hardness, which has been based on a more rigorous application of the Pearson principle and the availability of quantitative measures of chemical hardness, suggests that the origin of hard-soft behavior for both acids and bases resides in the relaxation of the electrons not undergoing transfer during the acid-base interaction. Furthermore, the results suggest that the absolute hardness should not be taken as synonymous with chemical hardness but that the relationship is somewhat more complex. Finally, this work provides additional groundwork for a better understanding of chemical hardness that will inform the understanding of hardness in molecules.     

The Strongest Acid: Protonation of Carbon Dioxide

The strongest carborane acid, H(CHB₁₁F₁₁), protonates CO₂ while traditional mixed Lewis/Brønsted superacids do not. The product is deduced from IR spectroscopy and calculation to be the proton disolvate, H(CO₂)₂⁺. The carborane acid H(CHB₁₁F₁₁) is therefore the strongest known acid. The failure of traditional mixed superacids to protonate weak bases such as CO₂ can be traced to a competition between the proton and the Lewis acid for the added base. The high protic acidity promised by large absolute values of the Hammett acidity function (H₀) is not realized in practice because the basicity of an added base is suppressed by Lewis acid/base adduct formation.     

High‐Pressure Raman and Calorimetry Studies of Vanadium(III) Alkyl Hydrides for Kubas‐Type Hydrogen Storage

Reversible hydrogen storage under ambient conditions has been identified as a major bottleneck in enabling a future hydrogen economy. Herein, we report an amorphous vanadium(III) alkyl hydride gel that binds hydrogen through the Kubas interaction. The material possesses a gravimetric adsorption capacity of 5.42 wt % H₂ at 120 bar and 298 K reversibly at saturation with no loss of capacity after ten cycles. This corresponds to a volumetric capacity of 75.4 kgH₂ m^?3. Raman experiments at 100 bar confirm that Kubas binding is involved in the adsorption mechanism. The material possesses an enthalpy of H₂ adsorption of +0.52 kJ mol^?1 H₂, as measured directly by calorimetry, and this is practical for use in a vehicles without a complex heat management system.     

Dual aromatase-sulfatase inhibitors based on the anastrozole template: synthesis, in vitro SAR, molecular modelling and in vivo activity

The synthesis and biological evaluation of a series of novel Dual Aromatase-Sulfatase Inhibitors (DASIs) are described. It is postulated that dual inhibition of the aromatase and steroid sulfatase enzymes, both responsible for the biosynthesis of oestrogens, will be beneficial in the treatment of hormone-dependent breast cancer. The compounds are based upon the Anastrozole aromatase inhibitor template which, while maintaining the haem ligating triazole moiety crucial for enzyme inhibition, was modified to include a phenol sulfamate ester motif, the pharmacophore for potent irreversible steroid sulfatase inhibition. Adaption of a synthetic route to Anastrozole was accomplished via selective radical bromination and substitution reactions to furnish a series of aromatase inhibitory pharmacophores. Linking these fragments to the phenol sulfamate ester moiety employed SN2, Heck and Mitsunobu reactions with phenolic precursors, from where the completed DASIs were achieved via sulfamoylation. In vitro, the lead compound, 11, had a high degree of potency against aromatase (IC50 3.5 nM), comparable with that of Anastrozole (IC50 1.5 nM) whereas, only moderate activity against steroid sulfatase was found. However, in vivo, 11 surprisingly exhibited potent dual inhibition.Compound 11 was modelled into the active site of a homology model of human aromatase and the X-ray crystal structure of steroid sulfatase.