A Characterization of the degree sequences of 2‐trees

A graph G is a 2‐tree if G = K₃, or G has a vertex v of degree 2, whose neighbors are adjacent, and G/ v is a 2‐ tree. A characterization of the degree sequences of 2‐trees is given. This characterization yields a linear‐time algorithm for recognizing and realizing degree sequences of 2‐trees. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:191‐209, 2008     

Synthesis of the 7-deaza and 5-aza-7-deaza purine analogs of the antiherpes agent 9-[(1,3-dihydroxy-2-propoxy)methyl]guanine (DHPG)

Synthesis of 2-amino-7-[(1,3-dihydroxy-2-propoxy)methyl]pyrrolo[2,3-d]pyrimidin-4-one (3) a 7-deaza purine analogue and 2-amino-8-[(1,3-dihydroxy-2-propoxy)methyl]imidazo[1,2-a]-s-triazin-4-one (4) a 5-aza-7-deaza purine analogue of DHPG (2) are reported.     

Immunofiltration as sample cleanup for the immunochemical detection of beta-agonists in urine

Despite the ban of the European Union on use of drugs to improve animal growth, occasionally beta-agonist drugs are still found in samples from cattle. Over time, the specified limits for the detection of these illegal drugs have been lowered. To improve the immunochemical screening of urine samples to detect lower levels of several beta-agonists, immunofiltration (IF) was applied for sample cleanup in combination with a beta-agonist-ELISA. In the applied IF format, free (non-immobilised) anti-salbutamol polyclonal antibodies were mixed with the urine sample in an ultra-filtration device (cut off 30 kDa) and the sample was removed by centrifugation. The antibody bound beta-agonists were freed from the antibodies by the addition of a mixture of methanol and 0.1 M acetic acid (1:1; v/v) and centrifugation. The filtrate, containing the free beta-agonists, was evaporated to dryness and the residue dissolved in buffer, an aliquot of which was analysed with the beta-agonist ELISA. Compared with the direct beta-agonist ELISA, this IF cleanup procedure resulted in a 30-times lower limit of detection (LOD) of 0.14 ng ml(-1) (salbutamol equivalents). The anti-salbutamol antibodies recognised several beta-agonists and the combination of IF with the beta-agonist ELISA was found suitable for the detection of at least ten beta-agonists in urine with comparable LODs.     

Discontinuum between a thiolate and a thiol ligand

The effect of H-bond donation to the thiolate ligand of (eta(5)-C(5)H(5))Fe(CO)(2)SR (1) to give H-bond adducts (1 small middle dotHX) and eventually protonation to give [(eta(5)-C(5)H(5))Fe(CO)(2)(HSR)](+) (1H(+)()) has been investigated experimentally and computationally. The electronic structures of 1(R = Me), several derivatives of 1(R = Me) small middle dotHX, and 1(R = Me)H(+)() have been investigated using DFT (density functional theory) computational methods. As previously suggested, these calculations indicate the HOMO of 1 is Fedpi-Sppi antibonding and largely sulfur in character. The calculations indicate the electronic structure of 1 is not altered markedly by H-bond donation to the S center, but protonation results in a reorganization of the electronic structure of 1H(+)() and a HOMO that is largely metal in character. The reduction of Fe-S distances upon protonation of 1(R = Ph) to give 1(R = Ph)H(+)() small middle dotBF(4)()(-)() (2.282(2) and 2.258(2) A, respectively), as determined by single-crystal X-ray crystallography, also indicates diminished Fedpi-Sppi antibonding. Using the carbonyl stretching frequencies as a gauge of the donor ability of the thiolate ligand, we conclude that H-bonding has a continuous effect on the donor properties of the thiolate ligand of 1 (i.e., is a function of the pK(a) of the H-bond donor). A discontinuous effect results when the pK(b) of 1 is reached and the complex is protonated. For our study of 1, the maximal effect of H-bonding is about 30% of protonation. Because the position of acid-base equilibrium depends on the relative basicities of the thiolate ligand and the conjugate base of the H-bond donor (and the relative heats of solvation of the acids and their conjugate bases), a true continuum of effects can be anticipated only for systems that are pK-matched in their given environments. Thus, when the conjugate base of the H-bond donor is a stronger base than the thiolate ligand (as in the present case), H-bond donation has a relatively small effect, but protonation triggers a large, discontinuous effect on the electronic structure of 1.     

The multiconfigurational spin tensor electron propagator method (MCSTEP): Comparison with extended Koopmans' theorem results

Summary We applied the multiconfigurational spin tensor electron propagator method (MCSTEP) for determining the lowest few (in energy) vertical ionization potentials (IPs) of HF, H₂O, NH₃, CH₄, N₂, CO, HNC, HCN, C₂H₂, H₂CO, and B₂H₆. We chose these molecules so that we could compare MCSTEP IPs with recently reported extended Koopmans' theorem (EKT) IPs on the same molecules. Using standard Dunning core-valence basis sets with relatively small complete active spaces, MCSTEP results are in very good to excellent agreement with experiment. These MCSTEP IPs are obtained using matrices no larger than 400 × 400. EKT matrices are even smaller; however, to obtain similar but generally slightly worse agreement with experiment, fairly large active spaces are required with EKT.     

Improved model for improving the inter-instrument agreement of spectrocolorimeters

A proposal by Robertson slightly modified by Berns and Petersen, to use spectral differences to predict systematic errors in spectrophotometers has found limited success in practical application. Porter suggested a way to improve the level of agreement between standardizing laboratories based on the Berns and Petersen method but suggested using derivatives calculated from piecewise polynomial splines. He did not know it at the time, but such a model was already in use. That model now has over five years of successful field testing and this paper discloses how the model was developed, the efficiency with which it can reduce systematic errors and the kinds of errors that cannot presently be corrected by computational comparison of reflectance or transmittance factor readings. For instruments of the same basic design, this model will produce a reduction of the systematic errors in colorimetric coordinates on the order of factors of 2–3. The magnitude of the initial color differences appears to be irrelevant. The corrective power of the model is limited by the numerical noise generated by the process of simulating analytical derivatives. We show that instruments with average color differences of 1.0 CIELAB unit can be reduced to a level of 0.5–0.3 units. Our testing has included a large variety of material samples including textiles, plastics, inks, paints and ceramics. Over 400 samples have been measured in proving this method. In addition, the model has been in place in industrial environments where multiple instruments of different manufacturer have been made to operate successfully from the same set of laboratory standards at reproducibility levels that rival those of national standards laboratories.     

Engineering reactions in crystals: suppression of photodecarbonylation by intramolecular β-phenyl quenching

The photochemical reactivity of cis- and trans-2-(p-carboxybenzyl)-2,6-diphenyl-6-vinylcyclohexanone, cis-1 and trans-1, was investigated in solution and in the crystalline solid state. Photochemical decarbonylation in solution proceeded in excellent yields to give cis- and trans-1-(p-carboxybenzyl)-1,2-diphenyl-2-vinylcyclopentanes cis-2 and trans-2 along with 3-(p-carboxybenzyl)-1,3-diphenylcycloheptene 3. Reactions in crystals were suppressed by a stereospecific quenching interaction between the benzyl substituent and the carbonyl oxygen in the crystalline ketone.     

Length and Stable Length

This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive ϵ there is a positive δ depending only on n and on ϵ such that an element of π₁(M) with stable commutator length less than δ is represented by a geodesic with length less than ϵ. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12. Conversely, “most” short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of homological Margulis constant. Received: June 2006 Revision: May 2007 Accepted: June 2007