Single Quality Factor for Enthalpy-Entropy Compensation,Isoequilibrium and Isokinetic Relationships

Enthalpy-entropy compensation (EEC) is very often encountered in chemistry, biology and physics. Its origin is widely discussed since it would allow, for example, a very accurate tuning of the thermodynamic properties as a function of the reactants. However, EEC is often discarded as a statistical artefact, especially when only a limited temperature range is considered. We show that the likeliness of a statistical origin of an EEC can be established with a compensation quality factor (CQF) that depends only on the measured enthalpies and entropies and the experimental temperature range. This is directly derived from a comparison of the CQF with threshold values obtained from a large number of simulations with randomly generated Van ‘t Hoff plots. The value of CQF is furthermore a direct measure of the existence of a genuine isoequilibrium or isokinetic relationship.     

Quark loop model of vector meson mixing and radiative meson decays

We consider the one quark loop contributions to ω-φ mixing and radiative meson decays. With three triplets of colored quarks, we obtain a number of relations (some old and some new) which are in excellent accord with experiment.     

Largeness of the set of finite products in a semigroup

We investigate when the set of finite products of distinct terms of a sequence 〈x _n 〉 _n=1^∞ in a semigroup (S,⋅) is large in any of several standard notions of largeness. These include piecewise syndetic, central, syndetic, central*, and IP*. In the case of a “nice” sequence in (S,⋅)=(ℕ,+) one has that FS(〈x _n 〉 _n=1^∞) has any or all of the first three properties if and only if {x _n+1−∑ _t=1 ⁿ x _t :n∈ℕ} is bounded from above. N. Hindman acknowledges support received from the National Science Foundation via Grant DMS-0554803.     

Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields

We present new explicit volume-preserving methods based on splitting for polynomial divergence-free vector fields. The methods can be divided in two classes: methods that distinguish between the diagonal part and the off-diagonal part and methods that do not. For the methods in the first class it is possible to combine different treatments of the diagonal and off-diagonal parts, giving rise to a number of possible combinations. This paper is dedicated to Arieh Iserles on the occasion of his 60th anniversary.     

Flashlamp-pumped laser performance of LiCaAIF6:Cr3+

The results of flashlamp pumping of the LiCaAIF₆:Cr³⁺ (Cr:LiCAF) laser crystal are reported. We have so far obtained slope efficiencies as high as 1.55% in a close-coupled, diffusely reflecting cavity. Based on the measured insertion loss of the presently available material, we predict that an efficiency of about 4% will be obtained when low-loss material becomes available. This extrapolated efficiency is comparable with the performance of a high-quality alexandrite laser rod in the same apparatus.