On theT-ideal generated by a standard identity

We determine the structure of the ideal of identities of degreen +1 in theT-ideals T_o(s_n(x₁,…,x_n)) and T_o(u_n(x₁,…,x_n)), wheres _n is the standard identity and u_n the unitary identity of degreen.     

On the codimensions of the verbally prime P.I. algebras

Razmyslov’s theory of trace identities for the prime P.I. algebrasM _{k, l} is applied to give bounds for the cocharacters and the codimensions of these algebrasM _{k, l}, as well as for the matrix algebrasM _k(E) over the Grassmann algebraE. These bounds are easier to obtain and are better (tighter) than earlier obtained bounds. Work supported by NSF grant DMS 9100258. Work supported by NSF grant DMS 9101488.     

A library of spirooxindoles based on a stereoselective three-component coupling reaction

A collection of structurally complex and chemically diverse small molecules is a useful tool to explore cell circuitry. In this article, we report the split-pool synthesis of more than 3000 spirooxindoles on high capacity macrobeads. The key reaction to assemble the spirooxindole core stereoselectively is a Lewis acid variant of the Williams' three-component coupling. After formation, the skeleton was elaborated using Sonogashira couplings, amide forming reactions, and N-acylations of gamma-lactams. The final library was analyzed by sampling individual macrobeads and by using binomial confidence limits. It was determined that at least 82% of the library compounds should have better than 80% purity. To demonstrate the utility of our discovery process, a high-throughput chemical genetic modifier screen was performed using stock solutions of the resultant products. A number of positives were identified as enhancers of the cellular actions of latrunculin B, an actin polymerization inhibitor. Through resynthesis, we confirmed one of the positives and demonstrated that, in yeast cells, it has an EC50 in the sub-micromolar range.     

Correction for relative interferences in a cholesterol determination

The detrimental influences of thiouracil, propylthiouracil, and bromide on the ferric perchlorate reaction for cholesterol have been previously reported (2, 3). On the basis of recovery studies it can be shown that their role in the reaction results in a relative rather than an absolute error of cholesterol measurement. Because a relative error causes a linear fanning effect on increasing concentrations of analyte which depends for its slope on both the concentration of the interference as well as on the concentration of constituent being measured, the method of standard additions can be used to correct a matrix effect on the reaction. A system in which the standard is used internally can eliminate the need to pretreat the sample in order to separate the interfering compound from the analyte. Therefore, both the interference and its obviation by this method of internal standardization are discussed here in a procedure which results in a means for simpler rescue of a contaminated sample than is afforded by the more laborious and time consuming pretreatment of previous workers.     

Bilirubin and hemoglobin interferences in direct colorimetric cholesterol reactions using enzyme reagents

The interferences of bilirubin and hemoglobin were tested in two cholesterol procedures in which enzymes were used as chemical reagents. Both procedures used similar approaches with cholesterol esterase to free cholesterol from its esters and cholesterol oxidase to generate hydrogen peroxide from the total free cholesterol resulting. From that common start, one procedure then used catalase to generate formaldehyde from methanol and the peroxide produced from cholesterol, and the formaldehyde was then reacted with acetylacetone to produce a yellow chromogen, while the other procedure used peroxidase to catalyze a reaction directly between peroxide and 4-aminoantipyrine plus phenol to generate a pink chromogen. Bilirubin and hemoglobin were shown to produce some interference by reacting competitively with peroxide in both systems and by contributing residual absorbance at the wavelengths of measurement of each of the chromogens. Since bilirubin showed a spectral change, static blanking with sample blanks caused overcorrections. However, the elimination of a sample blank for either procedure could result in a favorable compensating error because the residual color of bilirubin could substitute in part at least for the lost reactivity of the peroxide used up in reaction with the bilirubin of the sample.     

Pulsed ELDOR spectroscopy measures the distance between the two tyrosyl dadicals in the R2 subunit of the E. coli ribonucleotide reductase

Escherichia coli ribonucleotide reductase (RNR) catalyzes the conversion of nucleoside diphosphates (NDPs) to deoxynucleoside diphosphates (dNDPs). This RNR is composed of two homodimeric subunits: R1 and R2. R1 binds the NDPs in the active site, and R2 harbors the essential di-iron tyrosyl radical (Y*) cofactor. In this paper, we used PELDOR, a method that detects weak electron-electron dipolar coupling, to make the first direct measurement of the distance between the two Y*'s on each monomer of R2. In the crystal structure of R2, the Y*'s are reduced to tyrosines, and consequently R2 is inactive. In R2, where the Y*'s assume a well-defined geometry with respect to the protein backbone, the PELDOR method allows measurement of a distance of 33.1 +/- 0.2 A that compares favorably to the distance (32.4 A) between the center of mass of the spin density distribution of each Y* on each R2 monomer from the structure. The experiments provide the first direct experimental evidence for two Y*'s in a single R2 in solution.     

On the Codimension Growth of Finite-Dimensional Lie Algebras

We study the exponential growth of the codimensions c_n(L) of a finite-dimensional Lie algebra L over a field of characteristic zero. We show that if the solvable radical of L is nilpotent then exists and is an integer.     

Open conformal cobordisms

Conformal field theories were first axiomatized by Segal (2004) as symmetric monoidal functors from a topological category of conformal cobordisms between compact oriented 1-dimensional manifolds to vector spaces. Costello (2007) later expanded the definition of the category to allow for cobordisms between manifolds with boundaries, and was able to use representations of this category to give a mirror partner for Gromov-Witten invariants. The main goal of this paper is to provide a rigorous definition of the category of open conformal cobordisms. To the best of our knowledge, such a definition does not appear in the literature. Although most results here are probably known to the experts, the proofs are, as far as we can tell, new, and require only elementary results about quasiconformal mappings.     

“Organic Metals”—The Intermolecular Migration of Aromaticity

The electrical conductivity of a wide variety of organic materials is reviewed and a comparison made between those materials which transport charge efficiently and those that do not. This comparison reveals that the most efficient conductors contain molecules (a) whose radical ions form a new aromatic sextet upon one-electron oxidation or reduction and (b) whose aromaticity can migrate by mixed-valence interaction. The electrical data are presented in light of the chemistry of these materials and the importance of chemical bonding interactions in the electron transport process. Several new examples are discussed and directions for further research explored.