The minimum genus of a two-point universal graph

A graph G is two-point universal if, given any two vertices A and B, there is a vertex jointed to both, a vertex joined to neither, a vertex joined to A but not B, and a vertex joined to B but not A. Erdös asked whether there is an infinite family of such graphs of some genus γ. In this note, we show that the number of vertices of a two-point universal graph of genus γ satisfies n ≤ 216(2γ + 1)² so that there are most finitely many of each genus.     

Estimation of slow diffusion rates in confined systems: CCl4 in zeolite NaA

Often the rate of passage of gaseous molecules through model zeolites is too small to be computed directly. An estimate for the rate of passage of CCl₄ through the 8-ring window in a model of zeolite A has been obtained by combining a direct evaluation of the free energy profile and an adaptation of the rare events method. First the free energy profile is found from a direct evaluation of the canonical partition function at high dilution and the transition state theory rate constant obtained. The dynamic correction factor is then estimated from molecular dynamics runs and used to compute the actual rate k_eff. The method is used to estimate the rate of passage through the 8-ring window in a rigid model of zeolite A, and the results are compared with those obtained from rigid models with expanded windows and from the flexible model. Even a small expansion in the 8-ring window diameter increases the rate significantly, but the changes associated with a flexible cage are small.     

Coulometric titration of proteins with silver

The sulfhydryl groups of some proteins were studied by a coulometric argentometric titration; disulfide groups in the presence of sulfite were titrated by the same technique. Direct procedures and a technique utilizing excess coulometrically generated silver(I) were used. The latter method enabled small samples (20–1000 μg of protein) to be titrated with a precision of less than 4%. The proteins were generally titrated in both the native state and the denatured state (8 M urea). Bovine serum albumin, α-chymotrypsin, glutathione reductase, human hemoglobin, insulin, β-lactoglobulin, and ovalbumin were examined and the results compared to those of previous workers.     

The high-performance liquid chromatography and detection of phospholipids and triglycerides: Part 1. Nonpolar stationary phase chromatographic behavior in ultraviolet transparent mobile phases

The liquid chromatographic retention behavior of triglyceride and phospholipid molecular species in the nonpolar stationary (reverse) phase mode is presented for mobile phases compatible with ultraviolet detection. Interpretation of the results by means of the Kovats retention index suggests that correlation of retention to structure requires information on the number of acyl double bonds contained within the lipid molecular species in question. This, in turn, indicates that detection plays a major role in elucidating lipid structure because insufficient information is contained in the chromatographic retention data.     

A differential derivative chronopotentiometric method for evaluating γ

Two-cell differential methods are described for obtaining τ. Results are compared with those obtained from the derivative of the chronopotentiogram, the minimum of which is related to τ. Data are obtained under conditions of low double-layer charging. With the described apparatus cyclic chronopotentiometry does not give the expected values of τ_n/τ_i.     

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).