Let $G$ be a simple graph. A function $f$ from the set of orientations of $G$ to the set of non-negative integers is called a continuous function on orientations of $G$ if, for any two orientations $O_1$ and $O_2$ of $G$, $|f(O_1)-f(O_2)|\le 1$ whenever $O_1$ and $O_2$ differ in the orientation of exactly one edge of $G$. We show that any continuous function on orientations of a simple graph $G$ has the interpolation property as follows: If there are two orientations $O_1$ and $O_2$ of $G$ with $f(O_1)=p$ and $f(O_2)=q$, where $p<q$, then for any integer $k$ such that $p<k<q$, there are at least $m$ orientations $O$ of $G$ satisfying $f(O) = k$, where $m$ equals the number of edges of $G$. It follows that some useful invariants of digraphs including the connectivity, the arc-connectivity and the absorption number, etc., have the above interpolation property on the set of all orientations of $G$.
The UV-Vis absorption spectra of detergent-isolated hydrogen-and deuterium-bonded reaction centers (RCs) from Rhodobacter sphaeroides PUC 705Ba were examined as a function of temperature between 20 and 55 °C. The enthalpy and entropy of denaturation for the specimens was determined, revealing that their process of thermal denaturation is significantly different. Deuterium-bonded RCs are most stable at 37 °C, rather than at room temperature, and undergo a "cold denaturation" as the temperature is lowered to room temperature. At room temperature the addition of 1,3,5-heptanetriol brought the deuterium-bonded RC back to its more stable configuration. Hence the hydrogen bonding interactions in the RC do influence its conformation and this is reflected in the microenvironment of its associated pigments. and A. E. Ostafin ... [et al.].