Proposed substitution of apolane-87 for squalane as a nonpolar reference phase in gas chromatography

Squalane is the standard, nonpolar reference phase used in schemes to characterize the solvent strength and selectivity of stationary phases in gas-liquid chromatography. A commentary, supported by additional experimental evidence, is provided to indicate a lack of suitability for this purpose. Primary objections to its use as a reference phase are its high volatility, compositional variations due to the presence of impurities, susceptibility to oxidative degradation, poor film forming and stabilizing properties, and retention properties that are strongly influenced by the character and treatment of the support used to prepare column packings. Because similar problems were not observed, or were much less significant, for the synthetic hydrocarbon Apolane-87, its use as a reference phase is to be preferred. Reference values for retention indexes, gas—liquid partition coefficients, and partial molal Gibbs free energies of solution for a series of solvent-selectivity test solutes are provided for both phases.     

L 1 ergodic behavior of non-negative kernels

Some results that have been obtained in the study of strongly and weakly ergodic behavior of non-homogeneous stochastic kernels are generalized to the case of non-negative kernels. The first generalization simply involves extending the definitions of weakly and strongly ergiodic behavior to the case of non-negative kernels and using the ergodic coefficient which was first defined for stochastic kernels by Dobrushin and extended to non-negative kernels by Blum and Reichaw. It happens that this straightforward extension excludes many cases of non-negative kernels which do exhibit a types of ergodic behavior. In order to study these cases a definition ofL ₁ weakly and strongly ergodic behavior is given in which normalizing by constants is allowed. Sufficient conditions for these types of ergodic behavior are given.     

On normal characterizations by the distribution of linear forms,assuming finite variance

If X₁ and X₂ are independent and identically distributed (i. i. d.) with finite variance, then $\text{(X}{}_1\text{+X}{}_2\text{)}\text{√2}$ has the same distribution as X₁ if and only if X₁ is normal with mean zero (Pólya [9]). The idea of using linear combinations of i. i. d. random variables to characterize the normal has since been extended to the case where σ^∞_i=1a_iX_i has the same distribution as X₁. In particular if at least two of the a_i's are non-zero and X₁ has finite variance, then Laha and Lukacs [8] showed that X₁ is normal. They also [7] established the same result without the assumption of finite variance. The purpose of this note is to present a different and easier proof of the characterization under the assumption of finite variance. The idea of the proof follows closely the approach used by Pólya in [9]. The same technique is also used to give a characterization of the exponential distribution.     

Classical trajectory calculations of the dissociation of hydrogen on copper: III. The effect of surface roughness

Further calculations have been performed for the dissociation of H₂ on copper in which the empirical potential surface has been increased in roughness as suggested by our previous studies. This change is effected through an increase in the barriers to adatom surface diffusion, keeping the minimum energy requirements for dissociation about the same. The result is to bring the calculation into satisfactory agreement with molecular beam experiments. We examine the effect of changing the internal energy (vibration and rotation), mass, (D₂), the adatom binding site, and evaluate the validity of the correlating parameter E⊥ = Ecos²θ.     

The convergence of Cesaro averages for certain nonstationary Markov chains

If P is a stochastic matrix corresponding to a stationary, irreducible, positive persistent Markov chain of period d>1, the powers Pⁿ will not converge as n → ∞. However, the subsequences P^nd+k for k=0,1,...d-1, and hence Cesaro averages Σⁿ_k-1 P^k/n, will converge. In this paper we determine classes of nonstationary Markov chains for which the analogous subsequences and/or Cesaro averages converge and consider the rates of convergence. The results obtained are then applied to the analysis of expected average cost.     

Longest cycles in 3-connected graphs contain three contractible edges

We show that if G is a 3-connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges.