Generalized quadrangles in finite projective spaces

If a pointset of the projective spacePG(d,q), together with a lineset ofPG(d,q) form a generalized quadrangleS, thenS is of classical type. This beautiful theorem was proved by F. Buekenhout and C. Lefèvre. In this paper we give a simple proof of this theorem in the cased 4 (we suppose that the result is established ford = 3). We remark that in our proof a central role is played by the theory of subquadrangles.     

The cluster expansion for potentials with exponential fall-off

Continuing the work of a previous paper, the Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by potentials that fall off exponentially at large distance. The HamiltonianH ₀+V need be stable in the extended sense thatH ₀+4V+BN0 for someB. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infinite volume limit of the correlation functions exists, at low enough density. These infinite volume correlation functions cluster exponentially. A natural system included in the present treatment is that of matter with ther ^–1 potential replaced bye ^–ar/r. The Hamiltonian is stable, but the system would collapse in the absence of the exclusion principle—the potential is unstable. Therefore this system cannot be handled by the classic work of Ginibre, which requires stable potentials.This work was supported in part by NSF Grant MPS 75-10751Michigan Junior Fellow     

Estimating measurement uncertainty in an afternoon. A case study in the practical application of measurement uncertainty

The ISO/IEC 17025:1999 standard requires chemical testing laboratories to have an estimate of the uncertainty of their measurements. This is a new requirement for many laboratories and there is confusion as to how to estimate uncertainty. Concerns have been raised about the time and effort required to obtain uncertainty estimates.Uncertainty budgets were prepared for the measurement of benzene, toluene, ethyl benzene and xylenes (BTEX) in water using purge and trap coupled with GC/MS. A time limit of one working afternoon (2 pm–5.30 pm) was imposed for preparing the uncertainty estimate. Details of the uncertainty estimate for toluene are described.The method in question had been in routine use for several years and the laboratory held third party (NATA) accreditation for the test. Consequently a considerable amount of performance data was readily available. Relevant information was extracted from the documented test method, validation data, instrument calibration and from routine quality control. This data was combined according to the principles of the ISO Guide to the Expression of Uncertainty, as promulgated in the Eurachem document "Quantifying Uncertainty in Analytical Measurement."The uncertainty estimates were compared to estimates obtained from generalised empirical models (the Horwitz and Lowthian equations), and from interlaboratory studies of this analysis.A traceability chain from routine measurements to the SI units of metre, kilogram and mole is described.Realistic and useful uncertainty estimates were obtained with a few hours work using data extant in the laboratory.     

A SIFT ion-molecule study of some reactions in Titan's atmosphere. reactions of N(+), N(2)(+), and HCN(+) with CH(4), C(2)H(2), and C(2)H(4)

The results of a study of the ion-molecule reactions of N(+), N(2)(+), and HCN(+) with methane, acetylene, and ethylene are reported. These studies were performed using the FA-SIFT at the University of Canterbury. The reactions studied here are important to understanding the ion chemistry in Titan's atmosphere. N(+) and N(2)(+) are the primary ions formed by photo-ionization and electron impact in Titan's ionosphere and drive Titan's ion chemistry. It is therefore very important to know how these ions react with the principal trace neutral species in Titan's atmosphere: Methane, acetylene, and ethylene. While these reactions have been studied before the product channels have been difficult to define as several potential isobaric products make a definitive answer difficult. Mass overlap causes difficulties in making unambiguous species assignments in these systems. Two discriminators have been used in this study to resolve the mass overlap problem. They are deuterium labeling and also the differences in reactivities of each isobar with various neutral reactants. Several differences have been found from the products in previous work. The HCN(+) ion is important in both Titan's atmosphere and in the laboratory.     

Structures and anion-binding properties of M4L6 tetrahedral cage complexes with large central cavities

Reaction of the bis-bidentate bridging ligand L(3), in which two bidentate chelating 3(2-pyridyl)pyrazole units are separated by a 3,3'-biphenyl spacer, with Co(II) salts affords tetranuclear cage complexes of composition [Co(4)(L(3))(6)]X(8)(X =[BF(4)](-), [ClO(4)](-), [PF(6)](-) or I(-)) in which four 6-coordinate Co(II) ions in an approximately tetrahedral array are connected by six bis-bidentate bridging ligands, one spanning each of the six edges of the Co(4) tetrahedron. In every case, X-ray crystallography reveals that the 'apical' Co(II) ion has a fac tris-chelate geometry, whereas the other three Co(II) ions have mer tris-chelate geometries, resulting in (non-crystallographic)C(3) symmetry for the cages; that this structure is retained in solution is confirmed by (1)H NMR spectroscopy of the paramagnetic cages. In every case one of the anions is located inside the central cavity of the cage, with the remaining seven outside. We found no clear evidence for an anion-based templating effect. The cage superstructure is sufficiently large to leave gaps in the centres of the faces through which the internal and external anions can exchange. Variable-temperature (19)F NMR spectroscopy was used to investigate the dynamic behaviour of the cages with X =[BF(4)](-) and [PF(6)](-) in MeCN solution: in both cases two separate signals, corresponding to external and internal anions, are clear at 233 K which have coalesced to a single signal at room temperature. Analysis of the linewidth of the minor signal (for the internal anion) at various temperatures below coalescence gave an activation energy for anion exchange of ca. 50 kJ mol(-1) in each case, a figure which suggests that anion exchange can occur via a conformational rearrangement of the cage superstructure in solution rather than opening of the cavity by cleavage of metal-ligand bonds.     

Role of the A-ring of bryostatin analogues in PKC binding: synthesis and initial biological evaluation of new A-ring-modified bryologs

The syntheses of three newly designed bryostatin analogues are reported. These simplified analogues, which lack the A-ring present in the natural product but possess differing groups at C9, were obtained using a divergent approach from a common intermediate. All three analogues exhibit potent, single-digit nanomolar affinity to protein kinase C.     

Dynamic chirality: keen selection in the face of stereochemical diversity in mechanically bonded compounds

The template-directed syntheses, employing bisparaphenylene-[34]crown-10 (BPP34C10), 1,5-dinaphthoparaphenylene-[36]crown-10 (1/5NPPP36C10), and 1,5-dinaphtho-[38]crown-10 (1/5DNP38C10) as templates, of three [2]catenanes, whereby one of the two bipyridinium units in cyclobis(paraquat-p-phenylene) is replaced by a bipicolinium unit, are described. The crude reaction mixtures comprising the [2]catenanes all contain slightly more of the homologous [3]catenanes, wherein a "dimeric" octacationic cyclophane has the crown ether macrocycles encircling the alternating bipyridinium units with the bipicolinium units completely unfettered. X-ray crystallography, performed on all three [2]catenanes and two of the three [3]catenanes reveals co-conformational and stereochemical preferences that are stark and pronounced. Both the [3]catenanes crystallize as mixtures of diastereoisomers on account of the axial chirality associated with the picolinium units in the solid state. Dynamic (1)H NMR spectroscopy is employed to probe in solution the relative energy barriers for rotations by the phenylene and pyridinium rings in the tetracationic cyclophane component of the [2]catenanes. Where there are co-conformational changes that are stereochemically "allowed", crown ether circumrotation and rocking processes are also investigated for the relative rates of their occurrence. The outcome is one whereby the three [2]catenanes containing BPP34C10, 1/5NPPP36C10, and 1/5DNP38C10 exist as one major enantiomeric pair of diastereoisomers amongst two, four, and eight diastereoisomeric pairs of enantiomers, respectively. The diastereoisomerism is a consequence of the presence of axial chirality together with helical and/or planar chirality in the same interlocked molecule. These [2]catenanes constitute a rich reserve of new stereochemical types that might be tapped for their switching and mechanical properties.     

Capture-ROMP-release: application to the synthesis of amines and alkyl hydrazines

Application of a capture-ROMP-release strategy for the chromatography-free purification of Mitsunobu reaction products is described. Norbornenyl-tagged reagents are utilized for standard solution phase Mitsunobu chemistry. Post-reaction phase-switching is accomplished via in situ ring-opening metathesis polymerization (ROMP) followed by precipitation of the polymer with methanol. Release of the product from the polymer affords amines and alkyl hydrazine derivatives with good yields and purities.     

Etude de la structure K2NiF4 par la méthode des invariants,I. Cas des oxydes A2BO4

The study of the K₂NiF₄ structure by the “method of invariants” leads to the relationship

$\text{0.99615 V}\text{1}\text{3}\text{=β}{}_{\mathrm{B}}\text{+ψ}{}_{\mathrm{A}}\text{2}\text{1}\text{2}$

with V = a²c (β_B and ψ_A are invariant values associated with cations B and A) in compounds with K₂NiF₄ structures. Some values of ψ_A and examples are proposed.     

The synthesis and spectroscopic properties of some but-2-yne tungsten complexes of the type [WIX(CO){Ph2P(CH2)PPh2}(η-MeC2Me)] (X = Cl, Br, I, NO2, NO3, NCS or OH)

Reaction of the cationic complex [WI(CO)(NCMe){Ph₂P(CH₂)PPh₂}(η²-MeC₂ME)][BF₄] with an equimolar amount of MX (MX = NaCl, NaBr, NaI, KNO₂, KNO₃, NaNCS or KOH) in acetone at room temperature gave the neutral complex [WIX(CO){Ph₂P(CH₂)PPh₂}(η²-MeC₂Me)] (1–7) in good yield. Complexes 1–7 have been characterized by elemental analysis (C, H and N), IR and ¹H NMR spectroscopy.