Subgraphs smaller than the girth

For graphs A, B, let () denote the number of subsets of nodes of A for which the induced subgraph is B. If G and H both have girth > k, and if () = () for every k-node tree T, then for every k-node forest F, () = (). Say the spread of a tree is the number of nodes in a longest path. If G is regular of degree d, on n nodes, with girth > k, and if F is a forest of total spread ≤k, then the value of () depends only on n and d.     

Synthesis of protected L-4-[sulfono(difluoromethyl)phenylalanine and its incorporation into a peptide

[reaction: see text] A protected form of L-4-[sulfono(difluoromethyl)]phenylalanine (F(2)Smp), a novel non-hydrolyzable phospho- and sulfotyrosine mimetic, was synthesized via electrophilic fluorination of a benzylic sulfonate followed by a Pd-catalyzed cross-coupling reaction between the fluorinated sulfonate and the zincate of protected iodoalanine. F(2)Smp was incorporated into a peptide using solid-phase peptide synthesis techniques.     

Analytical scale supercritical fluid fractionation of a low molecular weight,high density polyethylene wax with carbon dioxide

This paper reports on the use of supercritical carbon dioxide to fractionate a low molecular weight, high density polyethylene into very narrow molecular weight distributions (MWDs). A simple extraction system was developed that allowed relatively trouble free extractions of the polyethylene samples. Fractions were collected at successively higher densities of CO₂ at constant temperature and then analyzed by capillary supercritical fluid chromatography (SFC), or high temperature gel permeation chromatography (GPC) and/or differential scanning calorimetry (DSC). Fractionations were performed at three different temperatures (60,80, and 100°C). Higher temperatures were found to yield greater recoveries and higher MWDs at any given density. Reducing the increment between successive extraction steps resulted in polydispersities being reduced to nearly “monodisperse” levels. Total recoveries ranged from 12 to 33% depending on the temperature, and the highest molecular weight fraction extracted by the CO₂ was centered around 1500.     

Polyfluorocyloalkenes Part XI Perfluoro - bicyclo(3,3,0) oct-7(8)-ene, - bicyclo(4,3,0)-non-8(9)-ene and - bicyclo (4,4,0)-dec-9(10)-ene and some derivatives

Tetradecafluorobicyclo (4,3,0) non-8(9)-ene has been prepared by cobaltic fluoride fluorination of decafluoro indane. The reactivities of the double bonds in dodecafluorobicyclo (3,3,0) oct-7(8)-ene and hexadecafluorobicyclo (4,4,0) dec-9(10)-ene have been studied qualitatively by the use of chlorine, methanol, cobaltic fluoride, ammonia and dimethylamine and the derivatives so obtained have been characterised.     

A three-dimensional He-NaH potential energy surface for rovibrational energy transfer studies

A three-dimensional potential energy surface for the He-NaH van der Waals complex is calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triples [CCSD(T)] level of theory. Estimates of CCSD(T) interaction energies for an infinitely large basis set is obtained using a basis set extrapolation scheme. The He-NaH potential energy surface is much different than the He-LiH surface. In particular, the He-NaH system has a binding energy of De=19.73 cm(-1) in comparison to De=176.7 cm(-1) for He-LiH. These minima are at the theta=180 degrees linear geometry where the helium is located at the metal end of the metal hydride. The He-NaH and He-LiH potentials are very similar for the theta=0 degrees linear geometry. The He-NaH potential energy surface supports one vibrational bound state with E=-1.48 cm(-1). Since this energy is smaller than the accuracy of the potential energy surface, the existence of a bound He-NaH complex is questionable.     

Mass spectrometric fragmentations of hexafluoroacetone ketals derived from N-alkenes

The mass spectrometric fragmentation behavior of the cyclic hexafluoroacetone ketals derived from eighteen n-alkenes is discussed with emphasis on locating the original olefinic bond. The major analytically useful fragments result from loss of CF₃, loss of an alkyl side chain or loss of an aldehyde moiety from the ring. Influences of geometric isomerism on the spectra are examined by intensity ratios and ratios of competing fragmentations.     

Enzymatic determination of phosphatidylcholine in human erythrocyte membranes

An enzymatic method for direct colorimetric determination of phosphatidylcholine (lecithin) in solubilized red cell membrane samples has been developed. The method, based on the sequential action of phospholipase D (cabbage), choline oxidase, and peroxidase, is capable of determination of samples under 5 nmol and thus may be used on packed membrane samples as small as 4 μl.     

Meta-conjugation and excited-state coupling in phenylacetylene dendrimers

Traditional pictures of optical properties in phenylacetylene dendrimers view the molecule as a collection of independent chromophores, linked by meta-substitution at the central phenyl ring. While this picture is reasonable for explaining the observed absorption trends, it breaks down in describing the emission behavior. We utilize a combination of ab initio theory and experiment to demonstrate that differences in the absorbing and emitting states can be described using an exciton model with very weak chromophore coupling for the absorption geometry and strong coupling for the emission geometry. This result may have significant implications for the design of energy-funneling dendrimeric molecules.