Alternating-Sign Matrices and Domino Tilings (Part II)

We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.     

Analytical use of the selective extraction of copper as its phenylacetate

Chloroform solution of phenylacetic add has been found very suitable for extraction and colorimetric determination of copper. Iron and uranium are the main interferences, which can be overcome by masking with ammonium fluoridc. Under these conditions, only gold(III), platinum(IV) and palladium(II) are co-extracted, but their colour does not interfere with measurement of the green copper extract at 700 nm. The method has been applied to the determination of copper in iron, steels, uranium, lead concentrates and alloys containing nickel, cobalt, etc. The extraction procedure can also be used to remove interference of iron, copper and uranium in the determination of manganese with formaldoxime.     

Microwave processing for sample preparation to evaluate mitochondrial ultrastructural damage in hemorrhagic shock.

This is a report of the adaptation of microwave processing in the preparation of liver biopsies for transmission electron microscopy (TEM) to examine ultrastructural damage of mitochondria in the setting of metabolic stress. Hemorrhagic shock was induced in pigs via 35% total blood volume bleed and a 90-min period of shock followed by resuscitation. Hepatic biopsies were collected before shock and after resuscitation. Following collection, biopsies were processed for TEM by a rapid method involving microwave irradiation (Giberson, 2001). Samples pre- and postshock of each of two animals were viewed and scored using the mitochondrial ultrastructure scoring system (Crouser et al., 2002), a system used to quantify the severity of ultrastructural damage during shock. Results showed evidence of increased ultrastructural damage in the postshock samples, which scored 4.00 and 3.42, versus their preshock controls, which scored 1.18 and 1.27. The results of this analysis were similar to those obtained in another model of shock (Crouser et al., 2002). However, the amount of time used to process the samples was significantly shortened with methods involving microwave irradiation.     

Analysis of Enzyme Structure and Activity by Protein Engineering

Structure-activity relationships of enzymes can now be analyzed for the first time by the systematic alteration of protein structure. Recent developments in the chemical synthesis of DNA fragments and recombinant DNA technology enable the facile modification of proteins by highly specific mutagenesis of their genes. Kinetic analysis of the mutant enzymes combined with high-resolution structural data from protein X-ray crystallography allow direct measurements on the relationships between structure and function. In particular, the strength and nature of enzyme-substrate interactions and their detailed roles in catalysis and specificity can now be studied. We have developed such analysis of enzyme structure-function by site-directed mutagenesis of the tyrosyl-tRNA synthetase from Bacillus stearothermophilus, concentrating so far on the subtle role of hydrogen bonding in both substrate specificity and catalysis. We find that the energetics of tyrosine and ATP binding must be analyzed in terms of an exchange reaction with solvent water. Based on this idea and structural data, we have engineered an enzyme of improved enzyme-substrate affinity, and there thus appear to be real prospects of engineering proteins of new specificities, activities, and structural properties. We are also using protein engineering to gather direct information on the nature of enzyme catalysis. For example, we find the catalysis of formation of Tyr-AMP from Tyr and ATP is due largely to electrostatic and hydrogen bonding interactions that are stronger in the transition state than in the ground state—a “strain” mechanism rather than acid-base or covalent catalysis.     

Residual smallness in commutative algebra

In Oman and Salminen [19 Oman, G., Salminen, A. Residually small commutative rings. J. Commut. Algebra (17 pages as a preprint, to appear). [Google Scholar]], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R?{0}, there exists an ideal I_r of R such that r?I_r and |R∕I_r|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules.