Difference Sets and Recursion Theory

There is a recursive set of natural numbers which is the difference set of some recursively enumerable set but which is not the difference set of any recursive set.     

Induced smectic C* phases

Induced ferroelectric S*_C phases are formed by non-chiral S_C host phases doped with chiral dipolar guest molecules. In those mixtures the spontaneous polarization P_s and the tilt angle Θ has been investigated as a function of the mole fraction x_G of the chiral dopant. In most cases the reduced polarization P₀ = P_S/ sin Θ has been found to depend linearly on x_G. The polarization power which is defined by δ_P=(∂P₀/∂x_G)ΔT is discussed in terms of the molecular structure of the chiral dopants. There are systems in which P₀(x_G) deviates positively from linearity. This behaviour can be understood by considering a local field correction to P₀. By assuming a local field of Lorentz type a theoretical relation for P₀(x_G) has been derived which explains the experimental results. The effect of a local field is considerable if the transverse dipole moment and the polarizability of the chiral dopant are large.     

Microdetermination of hyaluronic acid in human urine by high performance liquid chromatography.

A high performance liquid chromatographic (HPLC) system is described for determination of the unsaturated disaccharide (delta Di-HA) derived from hyaluronic acid (HA) in human urine by digestion with hyaluronidase SD. The effects of eluents on the separation of delta Di-HA and delta Di-0S, which is derived from the reaction of chondroitin with the enzyme, have been studied. The established chromatographic conditions were as follows--column: a stainless steel tube (4 mm i.d. x 250 mm) packed with TSKgel NH2-60; eluent: a mixture of acetonitrile and 0.1 M Tris-HCl buffer containing 0.1 M boric acid and 10 mM sodium sulphate, pH 7.0 (64:36, v/v). The strong fluorescence of unsaturated disaccharide after the reaction with 2-cyanoacetamide in alkaline medium was used for post-column detection. The calibration curve for delta Di-HA was linear in the range 5 pmol-5nmol with a practical detection limit of 2 pmol. The assay coefficients of variation (n = 5) at 200 pmol for delta Di-HA and delta Di-0S were 1.7 and 1.5%, respectively. This HPLC system has been applied to the determination of HA in human urine.     

Isolation of acetic acid-tolerant Baker’s yeast variants in a turbidostat

A commercial baker’s yeast was subjected to selection in a continuous turbidostat cultivation with increasing concentration of acetic acid. The final acetic acid content in fresh medium was 0.6% or 0.8% v/v. Two of seven selected variants were stable over 15 sequential shake flask cultivations without selection pressure. After laboratory scale production of baker’s yeast, one of the variants also showed increased acetic acid tolerance in sour dough. The overall raising power (mL CO₂/h) in sour dough was improved 36%.     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).