Enumerating maximal independent sets with applications to graph colouring

We give tight upper bounds on the number of maximal independent sets of size k (and at least k and at most k) in graphs with n vertices. As an application of the proof, we construct improved algorithms for graph colouring and computing the chromatic number of a graph.     

Dual‐Function Cobalt–Nickel Nanoparticles Tailored for High‐Temperature Induction‐Heated Steam Methane Reforming

The tailored chemical synthesis of binary and ternary alloy nanoparticles with a uniform elemental composition is presented. Their dual use as magnetic susceptors for induction heating and catalytic agent for steam reforming of methane to produce hydrogen at temperatures near and above 800 °C is demonstrated. The heating and catalytic performance of two chemically synthesized samples of CoNi and Cu ? CoNi are compared and held against a traditional Ni‐based reforming catalyst. The structural, magnetic, and catalytic properties of the samples were characterized by X‐ray diffraction, elemental analysis, magnetometry, and reactivity measurements. For induction‐heated catalysts, the conversion rate of methane is limited by chemical reactivity, as opposed to the case of traditional externally heated reformers where heat transport limitations are the limiting factor. Catalyst production by the synthetic route allows controlled doping with miniscule concentrations of auxiliary metals.     

Pre-equilibrium capillary zone electrophoresis or frontal analysis: advantages of plateau peak conditions in affinity capillary electrophoresis

The feasibility of using the affinity CE methodologies pre-equilibrium CZE and CE frontal analysis was tested on interaction systems exhibiting rapid on-and-off kinetics. Experimentally, the methodologies differ only with respect to the volume of sample introduced into the capillary. Pre-equilibrium CZE has been considered amendable to interactions with slow on-and-off kinetics only; however, it has recently been applied in studies of interactions with fast on-and-off kinetics. The effect of varying the sample volume introduced hydrodynamically into the capillary on the apparent degree of complexation was studied. For two different binding systems, the fraction of free analyte was found to be overestimated using pre-equilibrium CZE as compared to volumes providing plateau peak conditions as used with frontal analysis. Results indicate that frontal analysis conditions lead to more robust binding assays and thus more reliable data. The validity of data obtained by pre-equilibrium CZE may be low, thus the use of an experimental setup providing plateau peaks is highly recommended. It is suggested that the effect of altering the sample volume on the degree of binding should be investigated as part of method development and validation.     

Determination of octanol-water partition coefficients for carbonate esters and other small organic molecules by microemulsion electrokinetic chromatography

Microemulsion electrokinetic chromatography (MEEKC) was assessed as a tool for determination of octanol-water partition coefficients using 34 solutes encompassing 8 carbonate esters. It was confirmed that microemulsions containing 1.44-2.88% w/w SDS, 6.49% w/w 1-butanol, and 0.82% w/w n-heptane constitute a good model of octanol-water partitioning in the pH range of 1.4-7.4. Use of the migration index concept led to improved repeatability of the MEEKC method compared to the use of retention factors. Using a dynamical coating, a high electroosmotic flow at pH 1.4 and 4.75 was achieved expanding the practical pH working range of the MEEKC system. The correlation obtained between the migration index and log P was unaffected by pH indicating that the properties of the microemulsion droplets and, thus, partitioning are independent of pH. No evidence for congeneric behavior was found for the sample set comprising solutes with different hydrogen bonding properties suggesting that simple reference compounds can be used as calibrators. Lipophilicity estimates for the series of carbonate esters were obtained. The increase in lipophilicity with chain length was smaller than expected from the Hansch substituent constant, pi.     

Electron delocalization in the radical cation of 1,3,6,8-tetraazatricyclo[4.4.1.1(3,8)]dodecane, a 4-nitrogen-7-electron system.

The radical cation of 1,3,6,8-tetraazatricyclo [4.4.1.1(3,8)]dodecane (TTD) has been studied using magnetic resonance and optical spectroscopic methods and computational techniques. With the help of deuterated isotopomers, assignments of EPR and resonance Raman spectra could be unequivocally established. The results demonstrate that the radical cation has D(2d) symmetry, and instantaneous electron delocalization over the four equivalent nitrogen atoms occurs. This extensive delocalization in a completely saturated system is a unique feature of the TTD radical cation. The spectroscopy of TTD, in contrast to that of simpler diamines such as 1,4-diaza[2.2.2]bicyclooctane, simultaneously reveals the consequences of orbital interactions through space and through bonds. The relationship between nitrogen pyramidalization and hyperfine coupling constants in nitrogen-centered radical cations with a number of different bonding arrangements is reviewed.     

Density of configurational states from first-principles calculations: the phase diagram of Al-Na surface alloys.

The structural phases of Al(x)Na(1-x) surface alloys have been investigated theoretically and experimentally. We describe the system using a lattice-gas Hamiltonian, determined from density functional theory, together with Monte Carlo (MC) calculations. The obtained phase diagram reproduces the experiment on a quantitative level. From calculation of the (configurational) density of states by the recently introduced Wang-Landau MC algorithm, we derive thermodynamic quantities, such as the free energy and entropy, which are not directly accessible from conventional MC simulations. We accurately reproduce the stoichiometry, as well as the temperature at which an order-disorder phase transition occurs, and demonstrate the crucial role, and magnitude, of the configurational entropy.     

Novel optical and statistical methods reveal colloid-wall interactions inconsistent with DLVO and Lifshitz theories

We present an experimental method based on video microscopy to perform nanometer scale position detection of a micrometer bead in the direction along the propagation of the detection light. Using the same bead for calibration and detection significantly improves the in depth resolution in comparison to video microscopy methods from literature. This method is used together with an optical trap to measure interaction potentials between a glass surface and colloids made of polystyrene or silica at different electrolyte concentrations. The results are confirmed by an independent method where the optical trap is used in connection with a quadrant photodiode. Also, we present a maximum likelihood analysis method which considerably improves the spatial resolution of interaction potentials by optimizing the underlying potential function to fit all observed position distributions. The measured interaction potentials agree well with DLVO theory for small electrolyte concentrations; however, for larger electrolyte concentrations the potentials differ qualitatively from both DLVO and Lifshitz theory.     

Oligodeoxynucleotides containing amide-linked LNA-type dinucleotides: synthesis and high-affinity nucleic acid hybridization

Synthesis of three different amide-linked LNA-type dinucleotides and their incorporation into 9-mer and 17-mer oligodeoxynucleotides is described; compared to the reference DNA-RNA duplex, incorporation of one of the three dimers (5'-DNA*LNA dimer) induced significantly increased duplex thermostabilities.