A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.     

Relationship between cohesive energy density and hydrophobicity

It has been recently claimed that the large cohesive energy density of water is the ultimate cause of the poor solubility of nonpolar compounds in water. In order to test the validity of this idea, we analyze the difference in solubility between light water and heavy water of several nonpolar compounds. Even though the cohesive energy density of D(2)O is larger than that of H(2)O, nonpolar compounds are slightly more soluble in D(2)O than H(2)O. In such case experimental data do not support the correctness of the large cohesive energy density as the ultimate cause of hydrophobicity. We show that D(2)O is a slightly better solvent than H(2)O for nonpolar compounds because it is slightly less costly to create a cavity in the former liquid. This is because there is slightly more void volume in heavy water than in light water.     

The temperature-induced denaturation of small globular proteins as a first-order phase transition of ‘crystal molecules’

A general feature of temperature-induced reversible denaturation of small globular proteins is its all-or-none character. This strong cooperativity leads to think that protein molecules, possessing only two accessible thermodynamic states, the native and the denatured one, resemble ‘crystal molecules’ that melt at raising temperature. An analysis, grounded on mean field theory, allows to conclude that the two-state transition is a first-order phase transition. The implication of this conclusion are briefly discussed.