Reaping Numbers of Boolean Algebras

A subset A of a Boolean algebra B is said to be (n,m)-reapedif there is a partition of unity p B of size n such that |{b p:b a 0}| m for all a A. The reaping number r_n,m (B) ofa Boolean algebra B is the minimum cardinality of a set A B\{0}which cannot be (n,m)-reaped. It is shown that for each n, thereis a Boolean algebra B such that r_n+1,2(B) r_n,2(B). Also, {r_n,m(B):mn } consists of at most two consecutive cardinals. The existenceof a Boolean algebra B such that r_n,m (B) r_n',m' (B) is equivalentto a statement in finite combinatorics which is also discussed.     

Identification and quantitation of phenylalanine, tyrosine and dihydroxyphenylalanine in the thoracic nervous system of the locust, Schistocerca gregaria, by gas chromatography-negative-ion chemical ionisation mass spectrometry

Phenylalanine, tyrosine and dihydroxyphenylalanine (DOPA) were identified unambiguously and quantitatively determined in single ventral thoracic nerve cords from the locust, Schistocerca gregaria, by gas chromatography-negative-ion chemical ionisation mass spectrometry. Deuterium-labelled analogues of each compound were added to a single ventral thoracic nerve cord in hydrochloric acid; the tissue was homogenised and the suspension centrifuged. The remaining hydrochloric acid was eliminated azeotropically by repeated additions of acetonitrile followed by evaporation under a stream of nitrogen and the resultant residue derivatised by reaction with hexafluoroisopropanol and pentafluoropropionic anhydride. Under negative-ion chemical ionisation conditions, the hexafluoroisopropanol-pentafluoropropionyl derivatives produced characteristic ions which were sufficiently abundant to be suitable for selected-ion monitoring. This method is highly specific and gave a limit of detection below the nanogram level. The amounts of phenylalanine, tyrosine and DOPA in a single ventral thoracic nerve cord were, respectively, 194 +/- 81, 347 +/- 88 and 11 +/- 11 ng per tissue.     

Micropolar flow past a stretching sheet

Summary This paper studies the flow of an incompressible, constant density micropolar fluid past a stretching sheet. The governing boundary layer equations of the flow are solved numerically using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newton algorithm. The flow pattern depends on three non-dimensional parameters. Some interesting results are illustrated graphically and discussed.

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Résumé Nous étudions l'écoulement d'un fluid micropolaire et incompressible, de densité constante, le long d'une surface qui l'étend. Les équations de la couche limite qui régissent l'écoulement sont résolues numériquement. On utilise un algorithme quasi-Newtonien de type least change secant update avec une méthode homotopique /`a convergence globale. Certains résultats intéressants sont discutés et illustrés graphiquement.

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This work performed at Sandia National Laboratories supported by the U. S. Department of Energy under contract number DE-AC04-76DP00789.     

Synergism in binary mixtures of Thermobifida fusca cellulases Cel6B,Cel9A,and Cel5A on BMCC and Avicel

In an earlier binding study conducted in our laboratory using Thermobifida fusca cellulases Cel6B, Cel9A, and Cel5A (formally Thermomonospora fusca E₃, E₄, and E₅), it was observed that binding capacities for these three cellulases were 18–30 times higher on BMCC than on Avicel. These results stimulated an interest in how the difference in accessibility between the two cellulosic substrates would affect synergism observed with cellulase mixtures. To explore the impact of substrate, accessibility on the extent of conversion and synergism, three binary T. fusca cellulase mixtures were tested over a range of cellulase ratios and total molar cellulase concentrations on Avicel and BMCC. Higher extents of conversion were observed for BMCC due to the higher enzyme to substrate ratio resulting from the higher binding The processive endoglucanase, Cel9A, had four times the extent of conversion of the end endocellulase Cel5A, while the exocellulase Cel6B had three times the extent of conversion of Cel5A. Approximately 500 nmol/g of the cel9A+Cel6B mixture was needed to obtain 80% conversion, while the Cel6B+Cel5A and Cel9A+Cel5A mixtures required 1500 and 1250 nmol/g, respectively, to obtain 80% conversion. Thus, it appears that the more accessible structure of BMCC, as reflected by its binding capacity, results in relative higher processive activity.     

Matrix effects and selectivity issues in LC-MS-MS

Summary Chlorobenzenes, triazine and phenylurea herbicides were separated by normal micellar electrokinetic chromatography (MEKC) and by micellar electrokinetic chromatography with reversed flow (RF-MEKC) in running buffers containing organic solvents. The relationship between the two techniques is similar to that between reversed-phase and normal-phase HPLC. Using RF-MEKC, the separation of lipophilic compounds is often improved compared to normal MEKC. The migration in MEKC and in RF-MEKC was characterised by lipophilic and polar indices. The experimental values of the lipophilic indices of the compounds tested in the two techniques were close to the indices in reversed-phase HPLC (RP-HPLC). This enables the use of the indices determined in RP-HPLC for predicting the effects of changing composition of the running buffers on migration times in MEKC and in RF-MEKC. Presented at Balaton Symposium '01 on High-Performance Separation Methods, siófok, Hungary, September 2–4, 2001     

Experimental and theoretical studies of Diels-Alder dimerization of 1,2,3,4,5-pentachlorocyclopentadiene and of Diels-Alder cycloaddition of polychlorinated cyclopentadienes to norbornadiene

Diels-Alder cyclodimerization of 1,2,3,4,5-pentachlorocyclopentadiene (1) affords 2a as the exclusive reaction product. Diels-Alder cycloaddition of 1 to norbornadiene also proceeds stereoselectively to produce a single [4+2] cycloadduct, 4c. The structures of 2a and 4c were established unequivocally via application of single crystal X-ray crystallographic techniques. The origins of the observed diastereofacial selectivity in each of these cycloaddition processes have been investigated by application of semiempirical (AM1 Hamiltonian) and ab initio (Hartree-Fock 3-21G*) calculations. The computational results thereby obtained, which are based upon consideration of the kinetically favored transition state for each of the two cycloaddition reactions studied, are consistent with experiment. These semiempirical and ab initio methods also have been used to investigate the mechanisms of the Diels-Alder reactions that have been used to prepare aldrin and isodrin (7 and 8, respectively). The results thereby obtained suggest that isodrin formation via Diels-Alder cycloaddition of cyclopentadiene to 1,2,3,4,7,7-hexachloronorbornadiene proceeds with kinetic control of product stereochemistry.     

Unusual selectivity of unprotected aziridines in palladium-catalyzed allylic amination enables facile preparation of branched aziridines

Functionalized branched aziridines can be prepared in high yields and with high levels of regioselectivity using unprotected aziridines as nitrogen sources in palladium-catalyzed allylic amination. High levels of enantioselectivity can be achieved with BINAP on palladium. This methodology allows for strategic placement of an aziridine-containing fragment within a complex molecule environment for further elaboration.     

Versatile solid-phase synthesis of secondary amines from alcohols. Development of an N-Boc-(o-nitrobenzene)sulfonamide linker

The development of a versatile amine releasing linker based on the modified o-nitrobenzene sulfonamide protective group is described. This new N-Boc-o-nitrobenzenesulfonamide (Boc-ONBS) linker enables the elaboration on resin of primary and secondary amines by sequential substitution of the sulfonamide moiety using the Mitsunobu reaction. A 16-member array of secondary and Boc protected primary amines was then prepared using this linker.