The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results.     

Oxygen inhibition in thiol–acrylate photopolymerizations

The overall effects of oxygen on thiol–acrylate photopolymerizations were characterized. Specially, the choice of thiol monomer chemistry, functionality, and concentration on the extent of oxygen inhibition were considered. As thiol concentration was increased, the degree of oxygen inhibition was greatly reduced because of chain transfer from the peroxy radical to the thiol. When comparing the copolymerization of 1,6‐hexanediol diacrylate with the alkane‐based thiol (1,6‐hexane dithiol) to the copolymerization with the propionate thiol (glycol dimercaptopropionate), it was found that the propionate system was much more reactive and polymerized to a greater extent in the presence of oxygen. In addition, the functionality was considered where the glycol dimercaptopropionate was compared to a tetrafunctional propionate of similar chemistry (pentaerythritol tetrakis(mercaptopropionate)). Given the same thiol concentration, the higher functionality thiol imparted a faster polymerization rate, due to the increased polymer system viscosity, which limited oxygen diffusion and decreased the extent of overall oxygen inhibition. Thus, preliminary insight is provided into how thiol monomer choice affects the extent of oxygen inhibition in thiol–acrylate photopolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2007–2014, 2006     

Separation and analysis of radioiodine in nuclear reprocessing solutions of high ionic strength

Ion chromatography (IC) can be used to separate radioiodine from fission products and other ionic species in complex reprocessing solution matrices. A preliminary concentration and separation of the radioiodine is performed using a column filled with a platinum-coated copper bed which converts all forms of iodine to iodide and selectively adsorbs the iodide. The separation is completed by employing an anion chromatographic system. The iodide peak aliquot is collected for subsequent radioanalysis by low energy photon spectroscopy. Results indicate quantitative separation and recovery of iodine. The entire system is automated under computer control and is able to handle small (l) and large (500 ml) sample sizes.     

Photodegradation of poly(methyl methacrylate)

The vacuum photodegradation at 30°C. of poly(methyl methacrylate) and copolymers with acrylaldehyde, methacrylaldehyde, and methyl acrylate has been studied. The polymers were examined in the form of expanded films as produced by a freeze-drying technique. At least one molecule of carbon monoxide is evolved for each chain scission. It is concluded that chain scission in poly(methyl methacrylate) is primarily the result of photoinduced aldehyde groups.     

Additives for the stabilization of double-stranded DNA in UV-MALDI MS

Molecular complexes such as double-stranded oligonucleotides contain non-covalent bonds that are difficult to maintain in the MALDI experiment. Quantifiers are introduced in order to evaluate, summarize, and compare spectra from experiments in which additives are used to stabilize duplex oligonucleotides. Compounds known to complex with and stabilize duplex molecules can be useful as additives in MALDI. Spermine and methylene blue, present at concentrations similar to the matrix, are detected, bound to the duplex. When peptides are used as additives, the duplex is stabilized when the peptide is present at an amount less than that of the duplex.     

The effect of minor-groove hydrogen-bond acceptors and donors on the stability and replication of four unnatural base pairs

The stability and replication of DNA containing self-pairs formed between unnatural nucleotides bearing benzofuran, benzothiophene, indole, and benzotriazole nucleobases are reported. These nucleobase analogues are based on a similar scaffold but have different hydrogen-bond donor/acceptor groups that are expected to be oriented in the duplex minor groove. The unnatural base pairs do not appear to induce major structural distortions and are accommodated within the constraints of a B-form duplex. The differences between these unnatural base pairs are manifest only in the polymerase-mediated extension step, not in base-pair stability or synthesis. The benzotriazole self-pair is extended with an efficiency that is only 200-fold less than a correct natural base pair. The data are discussed in terms of available polymerase crystal structures and imply that further modifications may result in unnatural base pairs that can be both efficiently synthesized and extended, resulting in an expanded genetic alphabet.     

Infrared and Raman spectral interpretations of the ferroelectric phases of NaH3(SeO3)2 and NaD3(SeO3)2

The infrared and Raman spectra of NaH₃(SeO₃)₂ and NaD₃(SeO₃)₂ have been recorded from 24 to 300°K. The interpretation, assignments, and analysis of the spectral studies are presented on the paraelectric α phase (proton disordered), ferroelectric β phase (proton ordered) and ferroelectric γ phase (proton ordered). A discussion of a newly proposed proton-triggered phase transition mechanism and a possible origin of the hydrogen-bonded OH stretching region of KH₂PO₄-type ferroelectrics is given.