Spreadsheets and Bulgarian goats

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a successful and lucid spreadsheet implementation.     

A reversal index for tournament matrices *

Given a tournament matrix T, its reversal indexi_R (T), is the minimum k such that the reversal of the orientation of k arcs in the directed graph associated with T results in a reducible matrix. We give a formula for i_R (T) in terms of the score vector of T which generalizes a simple criterion for a tournament matrix to be irreducible. We show that i_R (T)≤[(n?1)/2] for any tournament matrix T of order n, with equality holding if and only if T is regular or almost regular, according as n is odd or even. We construct, for each k between 1 and [(n?1)/2], a tournament matrix of order n whose reversal index is k. Finally, we suggest a few problems.     

The heat capacities and standard entropies of corresponding potassium and ammonium ion species: is there a constant difference?

It is found that there is a nearly constant difference between the normalized values of the heat capacities and standard entropies of potassium and ammonium ion salts in the condensed phase, both solid salts and their aqueous solutions. Extension to the free gaseous ions remains moot.     

Allergen immunoassays—considerations for use of naturally incurred standards

The enzyme-linked immunosorbent assay (ELISA) offers many advantages for the detection of potentially hazardous allergenic food residues that might become adventitious components of other foods during the course of food production and processing. ELISAs detect proteins, and food allergens are proteins. ELISAs are sufficiently sensitive and specific for detection of food allergen residues. ELISAs can also be produced in formats that are compatible with the industrial food processing environment. However, ELISAs also have disadvantages that should be carefully evaluated and widely recognized. Various food-processing operations can have profound effects on the detectability of allergenic food residues. ELISAs detect intact proteins but protein hydrolysates evade detection in some ELISA formats. The residual proteins present in some ingredients derived from commonly allergenic sources may also not be easily detected with ELISAs because of the nature of the protein residues remaining, e.g. lipophilic. Processing operations can dramatically lower the solubility of proteins. In some food formulations, heat processing, in particular, induces chemical modifications that can affect antibody binding to epitopes in the ELISA. The use of naturally incurred standards where allergenic food residues are incorporated into various representative food matrices and then processed in a manner similar to “real-world” food processing can reveal some of the limitations of allergen ELISAs. Methods for the preparation of naturally incurred standards in chocolate, cookie, muffin, ice cream, pasta, frankfurter, and cream of potato soup are provided as examples.     

Cover Picture: Highly Water‐Soluble,Fluorescent, Conjugated Fluorene‐Based Glycopolymers with Poly(ethylene glycol)‐Tethered Spacers for Sensitive Detection of Escherichia coli (Chem. Eur. J. 10/2009)

Detection of pathogenic Escherichia coli is of the utmost importance in the food industry, water and environmental quality control, and clinical diagnosis for health and safety reasons. In their Full Paper on page 2289 ff., H. Liu et al. describe glycopolymers, with the use of poly(ethylene glycol), as glycoside‐tethered spacers that offer the sensitive detection of E. coli, as a result of the significantly reduced steric binding hindrance of the polymeric carbohydrates to the bacterial pili.

     

HPLC coupled with ICPMS for the determination of metalloporphyrins in coal extracts

The HPLC-ICPMS determination of gallium porphyrins in various coal extracts is described. The HPLC-ICPMS results are compared with results obtained by HPLC-UV/VIS. The presence of gallium has been confirmed in all the porphyrin macrocycles.     

Theory of DNA electrophoresis (approximately 1999-2002(1/2))

Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.     

Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein

Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation . This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions of with certain real values of . As a consequence, a result first stated by Krein is proven.

     

Sorptive reconstruction of the CuAlCl(4) framework upon reversible ethylene binding

Three ethylene adducts to CuAlCl(4) have been characterized by single crystal and/or powder X-ray diffraction, (13)C, (27)Al and (63)Cu MAS NMR and diffuse reflectance UV-vis spectroscopy. (C(2)H(4))(2)CuAlCl(4), a = 7.1274(5) b = 12.509(1) c = 11.997(3) beta = 91.19 degrees, Pc, Z = 4; alpha-(C(2)H(4))CuAlCl(4), a =7.041(3) b = 10.754(8) c =11.742(9) beta = 102.48(6), P2(1), Z = 4 and beta-(C(2)H(4))CuAlCl(4), a = 7.306(2), b = 16.133(3), c = 7.094(1), Pna2(1), Z = 4. Up to 2 equiv of ethylene ( approximately 200 cm(3)/g relative to stp) are sorbed at room temperatures and pressures as low as 300 Torr. The ethylene ligands are bound to copper (I) primarily through a sigma-interaction, because the AlCl(4)(-) groups also bound to copper prevent any significant pi-back-bonding. The olefin binding is reversible and has been characterized by gravimetric and volumetric adsorption analysis and by time and pressure resolved synchrotron powder X-ray diffraction. Comparison of the parent crystal structure to those of the adduct phases provide an atomistic picture of the sorptive reconstruction reactions. These are proposed to proceed by a classic substitution mechanism that is directed by the van der Waals channels of the parent crystalline lattice.