Polytopes with prescribed contents of (n−1)-facets

If ann-dimensional polytope has facets of areaA ₁,A ₂, …,A _m, then 2A _i <A ₁+…+A _m fori=1,…,m. We show here that conversely these inequalities also ensure the existence of a polytope having these areas.     

Spheres tangent to all the faces of a simplex

There are at most 2ⁿ spheres tangent to all n + 1 faces of an n-simplex. It has been shown that the minimum number of such spheres is $\text{2}{}^{\mathrm{n}}\text{? c(n,}\text{1}\text{2}\text{(n + 1))}$ if n is odd and $\text{2}{}^{\mathrm{n}}\text{? c(n,}\text{1}\text{2}\text{(n + 1))}$ if n is even. The object of this note is to show that this result is a consequence of a theorem in graph theory.     

Reactions of the fluorobromocarbene radical studied by laser-induced fluorescence

CFBr radicals produced by the reaction of atomic oxygen with F₂CCFBr were monitored in a discharge flow system by fluorescence excited at 424 nm. The rate coefficients for reactions of the CFBr radicals were measured between 298 and 358 K, and the following values were obtained in units of cm³/molec·s: O₂ < 2 × 10^?16 at 353 K; NO < 10^?14 at 298 K; F₂CCFBr < 10^?15 at 298 K; Cl₂ (1.9 ± 0.6) × 10^?12 exp(?762 ± 92/T) Br₂ (1.4 ± 0.3) × 10^?12 exp(?533 ± 62/T).     

Structural trends in the dehydrogenation selectivity of palladium alloys

Alloying is well-known to improve the dehydrogenation selectivity of pure metals, but there remains considerable debate about the structural and electronic features of alloy surfaces that give rise to this behavior. To provide molecular-level insights into these effects, a series of Pd intermetallic alloy catalysts with Zn, Ga, In, Fe and Mn promoter elements was synthesized, and the structures were determined using in situ X-ray absorption spectroscopy (XAS) and synchrotron X-ray diffraction (XRD). The alloys all showed propane dehydrogenation turnover rates 5–8 times higher than monometallic Pd and selectivity to propylene of over 90%. Moreover, among the synthesized alloys, Pd₃M alloy structures were less olefin selective than PdM alloys which were, in turn, almost 100% selective to propylene. This selectivity improvement was interpreted by changes in the DFT-calculated binding energies and activation energies for C–C and C–H bond activation, which are ultimately influenced by perturbation of the most stable adsorption site and changes to the d-band density of states. Furthermore, transition state analysis showed that the C–C bond breaking reactions require 4-fold ensemble sites, which are suggested to be required for non-selective, alkane hydrogenolysis reactions. These sites, which are not present on alloys with PdM structures, could be formed in the Pd₃M alloy through substitution of one M atom with Pd, and this effect is suggested to be partially responsible for their slightly lower selectivity.

Alloying is well-known to improve the dehydrogenation selectivity of pure metals, but there remains considerable debate about the structural and electronic features of alloy surfaces that give rise to this behavior.     

Evaluation of high-performance liquid chromatography with a dual working-electrode electrochemical detector for the determination of catecholamines in human cerebrospinal fluid

A procedure is described for quantifying norepinephrine [1(3,4-dihydroxyphenyl)-2-aminoethanol] and dopamine (4-(2-aminoethyl)-1,2-benzenediol] in cerebrospinal fluid by high-performance liquid chromatography (h.p.l.c.) with dual working-electrode electrochemical detection. An ion-pairing reversed-phase h.p.l.c. technique is used after clean-up and preconcentration of the fluid on alumina. The dual working-electrode electrochemical detector used provides amplification in the electrochemical response per unit concentration of material passing through the detector. This is achieved by locating two working electrodes on the opposite walls of a thin-layer cell, holding them close together and at potentials that will induce a sequence of oxidation/reductions. The greater the number of oxidation/reduction cycles, the greater the amplification of the electrochemical response. Peak height ratios are linear over the range expected and detection limits are 3 pg for norepinephrine and 5 pg for dopamine. The concentrations of norepinephrine and dopamine in human cerebrospinal fluid were found to be 141 pg ml^?1 and 262 pg ml^?1 with relative standard deviations of 6.8 and 5.8%, respectively.     

The behaviour of an electrochemical detector used in liquid chromatography and continuous flow voltammetry: Part III. Potential dependent current

The potential dependence of the steady-state current at a channel electrode has been calculated approximately. Six regions of behavior can be described from a consideration of the characteristic times of diffusion, fluid flow and electrochemical reaction. Wave shapes and half-wave potential shifts are as expected for amperometric cells under all values of the heterogeneous reaction rate constant, and for reversible electrochemical reactions in a coulometric cell. The wave adopts a peculiar shape for irreversible reactions at a coulometric electrode. This is caused by the inapplicability of the concept of mass transfer control in these systems.     

A model of the human M2 muscarinic acetylcholine receptor

The M₂ muscarinic acetylcholine receptor belongs to the family of rhodopsin like G-Protein Coupled Receptors. This subtype of muscarinic receptors is of special interest because it bears, aside from an orthosteric binding site, also an allosteric binding site. Based on the X-ray structure of bovine rhodopsin a complete homology model of the human M₂ receptor was developed. For the orthosteric binding site point mutations and binding studies with different agonists and antagonists are available. This knowledge was utilized for an initial verification of the M₂ model. Allosteric modulation of activity is mediated by structurally different ligands such as gallamine, caracurine V salts or W84 (a hexamethonium-derivative). Caracurine V derivatives with different affinities to M₂ were docked using GRID-fields. Subsequent molecular dynamics simulations yielded different binding energies based on diverse electrostatic and lipophilic interactions. The calculated affinities are in good agreement to experimentally determined affinities.     

Density functional theory predicts the barriers for radical fragmentation in solution

[reaction: see text] N-Methoxypyridyl radicals formed by one-electron reduction of the corresponding cationic heterocycles undergo N-O bond cleavage. Experimental activation free energies for a series of these bond fragmentations are compared to corresponding barriers determined from electronic structure calculations. The DFT barriers agree well with those from experiment, being smaller than the latter values by an average value of ca. 1 kcal/mol, for rate constants varying over almost 3 orders of magnitude, or within ca. 3 kcal/mol over 8 orders of magnitude of rate constant. For a model compound, the B3PW91/6-31+G hybrid density functional method is also found to be in good agreement with the MCSCF-MRMP2 method. One of the reactions is found by DFT to have no minimum for the reactant radical, consistent with a truly barrierless reaction.     

Liquid chromatographic retention behavior and separation of chlorophenols on a beta-cyclodextrin bonded-phase column, Part I. Monoaromatic chlorophenols: retention behavior

The liquid chromatographic retention behavior of nineteen monoaromatic chlorophenols on a beta-cyclodextrin bonded-phase column is investigated with respect to mobile phase composition, pH, temperature, and ionic strength. The mechanistic aspects of retention of these compounds on the beta-cyclodextrin column are studied and compared to other reversed-phase columns. Most of the evidence suggests that the unique selectivity of this column is due to inclusion complex formation, which provides the physical basis for the resolution of positional isomers. Under certain chromatographic conditions, however, the more highly chlorinated congeners appear to be excluded from the cyclodextrin cavity; in such cases a normal-phase chromatographic mechanism is postulated, based on the interaction of the substrates with the secondary hydroxyls on the periphery of the cyclodextrin moieties.