Gauging the conformal group

It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

1-D hydrogen-bonded organization of hexanuclear {3d-4f-5d} complexes: evidence for slow relaxation of the magnetization for [{LMe2Ni(H2O)Ln(H2O)4.5}2{W(CN)8}2] with Ln = Tb and Dy

Heterometallic {3d-4f-5d} aggregates with formula [{LMe2Ni(H2O)Ln(H2O)4.5}2{W(CN)8}2]·15H2O, (LMe2 stands for N,N-2,2-dimethylpropylenedi(3-methoxysalicylideneiminato) Schiff-base ligand) with Ln = Gd, Tb, Dy, have been obtained by reacting bimetallic [LMe2Ni(H2O)2Ln(NO3)3] and Cs3{W(CN)8} in H2O. The hexanuclear complexes are organized in 1-D arrays by means of hydrogen bonds established between the solvent molecules coordinated to Ln and the CN ligands of an octacyanometallate moiety. The X-ray structure was solved for the Tb derivative. Magnetic behavior indicates ferromagnetic {W–Ni} and {Ni–Ln} interactions (JNiW = 18.5 cm-1, JNiGd = 1.85 cm-1) as well as ferromagnetic intermolecular interactions mediated by the H-bonds. Dynamic magnetic susceptibility studies reveal slow magnetic relaxation processes for the Tb and Dy derivatives, suggesting SMM type behavior for these compounds.

The mechanism of intestinal absorption of phosphatidylcholine in rats

1. The mechanism of absorption of phosphatidylcholine was studied in rats by injecting into the intestine phosphatidylcholine specifically labelled either in the fatty acid or in the glycerol moiety or with 32P, when considerable amounts of 1-acyl-lysophosphatidylcholine were found in the intestinal lumen. 2-([14C]Acyl)phosphatidylcholine gave markedly more radioactive unesterified fatty acids in the lumen, compared with the 1-([14C]acyl) derivative. Some of the radioactivity from either the fatty acid or the glycerol moiety of the injected phosphatidylcholine appeared in the mucosal triacylglycerols. 2. Injection of 32P-labelled phosphatidylcholine or 32P-labelled lysophosphatidylcholine led to the appearance of radioactive glycerylphosphorylcholine, glycerophosphate and Pi in the mucosa. 3. Rat mucosa was found to contain a highly active glycerylphosphorylcholine diesterase. 4. It was concluded that the dietary phosphatidylcholine is hydrolysed in the intestinal lumen by the pancreatic phospholipase A to 1-acylglycerylphosphorylcholine, which on entering the mucosal cell is partly reacylated to phosphatidylcholine, and the rest is further hydrolysed to glycerylphosphorylcholine, glycerophosphate, glycerol and Pi. The fatty acids and glycerophosphate are then reassembled to give triacylglycerols via the Kennedy (1961) pathway.

Ultrasonic velocities and thermal expansion coefficients of amorphous Se80Te20 and Se90Te10 alloys near glass transitions

Precise measurements of the ultrasonic velocities and thermal expansivities of amorphous Se80Te20 and Se90Te10 alloys are reported near the glass transition. The samples are produced by liquid quenching. The longitudinal and transverse velocities are measured at 10 MHz frequency using the McSkimin pulse superposition technique. The thermal expansivities,agr, are measured using a three-terminal capacitance bridge. Theagr-values show a sharp maximum near the glass transition temperature,T g. The ultrasonic velocities also show a large temperature derivative, dV/dT nearT g. The data are discussed in terms of existing theories of the glass transition. The continuous change inagr shows that the glass transition is not a first-order transition, as suggested by some theories. The samples are found to be deformed by small loads nearT g. The ultrasonic velocities and dV/dT have contributions arising from this deformation.

Studies of phosphazenes. 12. Reactions of N4P4Cl8 with dibenzylamine- isolation of an unusual "bicyclic" phosphazene, N4P4[N(CH2Ph)2]6(NCH2Ph)

Octachlorocyclotetraphosphazene, N4P4CIa, reacts with dibenzylamine to give the chloro(dibenzy1amino) derivatives, N4P,C18,[N(CH2Ph)2],,, n = 1, 2 (two isomers), and 4 (three isomers). Nongeminal structures have been assigned to these compounds on the basis of ‘H and jlP NMR spectra. The presence of at least two tris(dibenzylamin0) derivatives in some reaction mixtures is also inferred from NMR spectra. Steric effects become important at the tetrakis stage of chlorine replacement, and further substitution by dibenzylamine to give monocyclic tetrameric derivatives does not occur. A “bicyclic” phosphazene, N4P4[N(CH2Ph)2]6(NCHzPh)is, obtained from the reaction of N4P4Claw ith an excess of dibenzylamine in boiling methyl cyanide. The formation of this derivative and its spectroscopic data are discussed.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Ambidentate coordination of isonitrosoacetylacetone imines in their nickel(II) and palladium(II) complexes

Nickel(I1) and palladium(I1) complexes of the types Ni(R-IAI)(IAI'), Pd(IAI)(IAI'), and Pd(R-IAI), , where IAI and IAI' represent isonitrosoacetylacetone imine and R-IAI represents its Aralkyl derivative, have been prepared. The molar conductance, molecular weight, magnetic moment, and ir, pmr, and electronic spectra of these com- plexes have been studied. It is suggested that the isonitroso group of R-IAI coordinates through the nitrogen and that of IAI' thiough the oxygen in Ni(R-IAI)(IAI'). In Pd(R-IAI), the isonitroso groups of both ligands coordinate through nitrogen while Pd(IAI)(IAI') has a structure similar to that of Ni(R-IAI)(IAI'). The amine- exchange reactions of nickel(I1) and palladium(I1) complexes are discussed and compared on the basis of their structures.

Change to costs and lengths of stay in the emergency department and the Brisbane protocol: An observational study

- Objective To compare health service cost and length of stay between a traditional and an accelerated diagnostic approach to assess acute coronary syndromes (ACS) among patients who presented to the emergency department (ED) of a large tertiary hospital in Australia. - Design, setting and participants This historically controlled study analysed data collected from two independent patient cohorts presenting to the ED with potential ACS. The first cohort of 938 patients was recruited in 2008–2010, and these patients were assessed using the traditional diagnostic approach detailed in the national guideline. The second cohort of 921 patients was recruited in 2011–2013 and was assessed with the accelerated diagnostic approach named the Brisbane protocol. The Brisbane protocol applied early serial troponin testing for patients at 0 and 2 h after presentation to ED, in comparison with 0 and 6 h testing in traditional assessment process. The Brisbane protocol also defined a low-risk group of patients in whom no objective testing was performed. A decision tree model was used to compare the expected cost and length of stay in hospital between two approaches. Probabilistic sensitivity analysis was used to account for model uncertainty. - Results Compared with the traditional diagnostic approach, the Brisbane protocol was associated with reduced expected cost of $1229 (95% CI −$1266 to $5122) and reduced expected length of stay of 26 h (95% CI −14 to 136 h). The Brisbane protocol allowed physicians to discharge a higher proportion of low-risk and intermediate-risk patients from ED within 4 h (72% vs 51%). Results from sensitivity analysis suggested the Brisbane protocol had a high chance of being cost-saving and time-saving. - Conclusions This study provides some evidence of cost savings from a decision to adopt the Brisbane protocol. Benefits would arise for the hospital and for patients and their families.

Knoevenagel condensation of 2-carbethoxycyclohexanone and malononitrile: Synthesis of 4-cyano-3-ethoxy-1-hydroxy-5,6,7,8-tetrahydroisoquinoline, an isomer of the abnormal product

The structure of the abnormal product 1a formed in the Knoevenagel condensation of 2-carbethoxycyclohexanone and malononitrile has been further confirmed. Oxidation of the tetrahydroisoquinoline 3b using Na2Cr2O-AcOH-H2SO4 gave the keto isoquinoline 3d and the isoquinoline-1-carboxylic acid 5a. The acid chloride of 5a was condensed with diethyl ethoxymagnesiomalonate to afford after decarbethoxylation the methyl ketone 5d which on Baeyer-Villiger oxidation gave a mixture of the acetate 1g and the title compound 1b. The unambiguous synthesis of 1b confirms the structure assigned earlier to the title compound also formed during the partial hydrolysis of the diethoxy compound 1c. Condensation of 2-acetylcyclohexane-1,3-dione with malononitrile gave the quinoline derivative 4c which on ethylation yielded the ketoquinoline 4d. The present studies have confirmed that the quinoline compound 4a is also formed in the condensation of 2-acetylcyclohexanone and cyanoacetamide.

Facile Entry into Triazole Fused Heterocycles via Sulfamidate Derived Azido-alkynes

Direct synthesis of condensed triazoles from diverse sulfamidates by ring opening of sulfamidates with sodium azide followed by one-pot propargylation and cycloaddition furnished title compounds. The methodology in general has been demonstrated on diverse sulfamidates derived from amino acids, amino acid derivatives, and carbohydrates to obtain diverse triazole fused scaffolds. In one example, a condensed triazole containing amino acid has been synthesized by ring opening of a sulfamidate derivative with propargyl amine.

Sequence of reactions leading to cytochrome-p-450 synthesis-effect of drugs

The effect of phenobarbital on the rates of the synthesis of the protein and heme moieties of cytochrome P-450 has been studied. For this purpose, cytochrome P-450 has been partially purified as its P-420 derivative and the labeled amino acid incorporation into the protein has been studied after subjecting a partially purified preparation to sodium dodecyl sulfate gel electrophoresis. The incorporation studies into the protein species after sodium dodecyl sulfate gel electrophoresis reveal that the drug primarily accelerates the rate of apoprotein synthesis followed by an increase in the rate of heme synthesis. The messenger for apocytochrome P-450 appears to be fairly stable.

Structural studies of analgesics and their interactions. III. The crystal and molecular structure of amidopyrine

Amidopyrine (1-phenyl-2,3-dimethyl-4-dimethylaminopyrazolone), C13HzvN30, a dimethylamino derivative of antipyrine and an important analgesic and antipyretic agent, crystallizes in the triclinic space group P1 with four molecules in a unit cell of dimensions a= 7.458 (5), b = 10.744 (5), c= 17.486 (15)/~,, e=98.6 (2),/~= 85.6 (3), y= 108-6 (2) . The structure was solved by direct methods and refined to an R value of 0.055 for 3706 photographically observed reflexions. The dimensions of the two crystallographically independent molecules are very nearly the same. The pyrazolone moiety in the molecule has dimensions comparable to those in antipyrine. Unlike antipyrine, the molecular dimensions of amidopyrine in the free state (the present structure) are close to those found in some of its hydrogenbonded complexes. Thus it appears that the presence of the dimethylamino group makes the molecule more resistant to changes in its dimensions resulting from molecular association. An attempt has also been made to correlate the polar nature of the pyrazolone moiety and the hybridization state of the hetero nitrogen atoms in antipyrine, amidopyrine and their complexes.

Studies of phosphazenes. Part I. Reactions of octachlorocyclotetraphosphazatetraene with ethylamine

The reaction of octachlorocyclotetraphosphazatetraene, N4P4Cl8, with ethylamine has been investigated. Seven derivatives, N4P4Cl8–n(NHEt)n[n= 1, 2 (two isomers), 3, 4 (two isomers), and 8] have been isolated and their structures established by 1H and 31P n.m.r. spectroscopy. A non-geminal chlorine atom replacement scheme is observed. Attempts to prepare penta- or hexa-ethylamino derivatives were unsuccessful: only sticky, non-crystalline resins were obtained from 1 : 10 or 1 : 12 reactions. The preparation and n.m.r. spectroscopic data of mixed ethylamino(methoxy)-derivatives. N4P4(NHEt)–8-n(OMe)n[n= 6, 4 (two isomers)], and an ethylamino-(dimethylamino)-derivative, N4P4(NHEt)2(NMe2)6, are generally consistent with the proposed structures. The reaction pattern is discussed.

Effect of temperature and precipitation on salmonellosis cases in South-East Queensland, Australia: An observational study

Objective Foodborne illnesses in Australia, including salmonellosis, are estimated to cost over $A1.25 billion annually. The weather has been identified as being influential on salmonellosis incidence, as cases increase during summer, however time series modelling of salmonellosis is challenging because outbreaks cause strong autocorrelation. This study assesses whether switching models is an improved method of estimating weather–salmonellosis associations. Design We analysed weather and salmonellosis in South-East Queensland between 2004 and 2013 using 2 common regression models and a switching model, each with 21-day lags for temperature and precipitation. Results The switching model best fit the data, as judged by its substantial improvement in deviance information criterion over the regression models, less autocorrelated residuals and control of seasonality. The switching model estimated a 5°C increase in mean temperature and 10 mm precipitation were associated with increases in salmonellosis cases of 45.4% (95% CrI 40.4%, 50.5%) and 24.1% (95% CrI 17.0%, 31.6%), respectively. Conclusions Switching models improve on traditional time series models in quantifying weather–salmonellosis associations. A better understanding of how temperature and precipitation influence salmonellosis may identify where interventions can be made to lower the health and economic costs of salmonellosis.