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.     

Development and certification of reference materials for residues of organochlorine and organophosphorus pesticides in beef fat ACSL CRM 1 and 2

Beef fat samples were prepared and tested as candidate reference materials for organochlorine and organophosphorus pesticides. The CRMs consisted of beef fat spiked with pesticide solutions. One sample (ACSL CRM 1) was prepared containing close to 0.2 mg/kg of each of the organochlorine pesticides dieldrin and heptachlor epoxide. A second sample (ACSL CRM 2) was prepared containing close to 0.8 mg/kg of each of the organophosphorus pesticides diazinon, chlorpyrifos and ethion. The spiking levels and homogeneity of the materials were verified. The coefficients of variation of 5 analyses carried out to test between-jar homogeneity for each reference material were dieldrin, 3.5%; heptachlor epoxide, 1.1%; diazinon, 2.1%; chlorpyrifos, 1.2% and ethion, 3.1%. No instability in any of these compounds was detected over a twelve month period. The candidate reference materials were found to be suitable for certification by interlaboratory testing. The certification process was based on a two-stage nested design described in ISO Guide 35. Analysis of results reported by collaborating laboratories provided an assessment of the homogeneity of the reference materials. The certified values together with their upper and lower 95% confidence limits are: ACSL CRM 1*Dieldrin*0.199 mg/kg **(0.188, **0.210 mg/kg) *Heptachlor epoxide*0.194 mg/kg **(0.176, **0.212 mg/kg) ACSL CRM 2*Diazinon*0.805 mg/kg **(0.755, **0.855 mg/kg) *Chlorpyrifos*0.790 mg/kg **(0.728, **0.852 mg/kg) *Ethion*0.813 mg/kg **(0.746, **0.879 mg/kg). A certificate for each material was prepared according to the guidelines set out in ISO Guide 31.     

Reactions of dicobalt octacarbonyl and related compounds with gem-dihalides

Dicobalt octacarbonyl and some of its derivatives (NaCo(CO)₄, Co₄(CO)₁₂, Hg[Co(CO)₄]₂, [Co(CO)₃PPh₃]₂, NaCo(CO)₃PPh₃) react with activated gem-dihalides, R₂CX₂, such as dichlorodiphenylmethane, 9,9-dihalofluorenes and dimethyl dibromomalonate, to give the ‘dimer’ olefin, R₂CCR₂. The course of this conversion involves formation of the coupling product, R₂XCCXR₂, followed by dehalogenation of the latter. These separate steps have been confirmed for activated monohalides (bromodiphenylmethane, 9-bromofluorene, dimethyl bromomalonate) which were readily coupled by cobalt carbonyls, and for activated vicinal dihalides (D,L and meso-dibromostilbene, 9,9′-dichlorobisfluorenyl) which cobalt carbonyls readily dehalogenated. A radical mechanism is favored for these processes, and indirect evidence in its favor is presented.     

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.     

Determination of phenylalanine isotope ratio enrichment by liquid chromatography/time- of-flight mass spectrometry

The application of time-of-flight mass spectrometry to isotope ratio measurements has been limited by the relatively low dynamic range of the time-to-digital converter detectors available on commercial LC/ToF-MS systems. Here we report the measurement of phenylalanine isotope ratio enrichment by using a new LC/ToF-MS system with wide dynamic range. Underivatized phenylalanine was injected onto a C18 column directly with 0.1% formic acid/acetonitrile as the mobile phase. The optimal instrument parameters for the time-of-flight mass spectrometer were determined by tuning the instrument with a phenylalanine standard. The accuracy of the isotope enrichment measurement was determined by the injection of standard solutions with known isotope ratios ranging from 0.02% to 9.2%. A plot of the results against the theoretical values gave a linear curve with R2 of 0.9999. The coefficient of variation for the isotope ratio measurement was below 2%. The method is simple, rapid, and accurate and presents an attractive alternative to traditional GC/MS applications.     

Oxygen atom transfer in models for molybdenum enzymes: isolation and structural, spectroscopic, and computational studies of intermediates in oxygen atom transfer from molybdenum(VI) to phosphorus(III)

Intermediates in the oxygen atom transfer from Mo(VI) to P(III), [Tp(iPr)MoOX(OPR3)] (Tp(iPr) = hydrotris(3-isopropylpyrazol-1-yl)borate; X = Cl-, phenolates, thiolates), have been isolated from the reactions of [Tp(iPr)MoO2X] with phosphines (PEt3, PMePh2, PPh3). The green, diamagnetic oxomolybdenum(IV) complexes possess local C(1) symmetry (by NMR spectroscopy) and exhibit IR bands assigned to nu(Mo==O) (approximately 950 cm(-1)) and nu(P==O) (1140-1083 cm(-1)) vibrations. The X-ray crystal structures of [Tp(iPr)MoOX(OPEt3)] (X = OC6H4-2-sBu, SnBu), [Tp(iPr)MoO(OPh)(OPMePh2)], and [Tp(iPr)MoOCl(OPPh3)] have been determined. The monomeric complexes exhibit distorted octahedral geometries, with coordination spheres composed of tridentate fac-Tp(iPr) and mutually cis monodentate terminal oxo, phosphoryl (phosphine oxide), and monoanionic X ligands. The electronic structures and stabilities of the complexes have been probed by computational methods, with the three-dimensional energy surfaces confirming the existence of a low-energy steric pocket that restricts the conformational freedom of the phosphoryl ligand and inhibits complete oxygen atom transfer. The reactivity of the complexes is also briefly described.