A renormalization group proof of perturbative renormalizability

This paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean ₄ ⁴ theory. Its aim is partly pedagogical: by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages. The present version is based on the renormalized tree expansion adapted to the continuous renormalization group: all detailed results are proved by induction on the size of the tree. The continuous RG version presented here has one big advantage over the discrete RG version discussed elsewhere. In the continuous version, a tree has a more restrictive structure: there is a one-to-one correspondence between forks of the tree and lines of Feynman graphs. This extra structure eliminates the need to introduce Feynman graphs in the first place. It also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates.Research supported by the Natural Sciences and Engineering Research Council     

Construction of the two-dimensional sine-Gordon model for β<8π

We present a rigorous renormalization group construction of the two-dimensional massless and massive quantum sine-Gordon models in finite volume for the range 0<<8. We prove analyticity in the coupling constant , which implies the convergence of perturbation theory. The field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory. In the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations.Research supported by NSF Grant PHY-9001178Research supported by the Natural Sciences and Engineering Research Council of Canada     

Synthesis of (+)-casuarine

[formula: see text] The first synthesis of (+)-casuarine, a pentahydroxy pyrrolizidine alkaloid, is described. The key bond-forming events occur in a tandem [4 + 2]/[3 + 2] nitroalkene cycloaddition involving nitroalkene 6, chiral vinyl ether 7b, and vinyl silane 4. This process also creates five of the six stereocenters present in this potent glycosidase inhibitor. Completion of the synthesis required only four additional steps and delivered (+)-casuarine in 20% overall yield.     

Evidence for facile atropisomerism and simple (non-nucleophilic) biradical-forming cycloaromatization within kedarcidin chromophore aglycon

The kinetics and thermodynamics of atropisomerism within the protected kedarcidin chromophore aglycon 8, as well as a series of ansa-bridged synthetic intermediates leading to 8, were determined by 1H NMR spectroscopy. The data show that the ratio of atropisomeric forms of chloropyridine-bridged ansa intermediates is subject to wide variation with seemingly subtle structural variation. The vinyl bromide 4, for example, in the first X-ray structure determination of a kedarcidin ansa-bridged system, was found to exist as a single atropisomer in the solid state, but a nearly equal mixture (K = 0.70) of isomers in solution (t1/2 for isomer interconversion approximately 0.2 s at 20 degrees C). The aglycon 8, a 2.2:1 mixture of atropisomers, was found to undergo direct unimolecular biradical-forming cycloaromatization at ambient temperature in a mixture of 1,4-cyclohexadiene-benzene, without nucleophilic activation. The product 9 was formed as a single atropisomer (k = 2 x 10-4 s-1, t1/2 = 58 min, 81% yield), suggesting that the rate of atropisomerism within 8 is rapid with respect to cycloaromatization. The rate of cycloaromatization of 8 was found to be highly solvent-dependent, being more rapid in the presence of a good hydrogen-atom donor, consistent with the earlier model studies of Hirama et al. that showed that certain nine-membered cyclic (Z)-enediynes may equilibrate with their biradical cycloaromatization products. Incubation of 8 with beta-mercaptoethanol, under conditions mimicking experiments leading to DNA cleavage with kedarcidin, showed no evidence for nucleophilic activation. The product of direct cycloaromatization (9) was isolated instead. The evidence suggests that kedarcidin, like the enediyne agent C-1027, is capable of spontaneous thermal biradical formation without prior chemical activation.     

A comparative study of myo-inositol quantification using LCmodel at 1.5 T and 3.0 T with 3 D 1H proton spectroscopic imaging of the human brain

Myo-inositol is a strongly coupled system and resonates at four chemical shift positions. At 1.5 T, only the singlet component at 3.57 ppm is detected. However, at 3 T this resonance is resolved into its components at 3.55 ppm and 3.61 ppm. Due to the increased spectral resolution and signal-to-noise ratio, it is anticipated that the quantification of myo-inositol should improve at 3 T. Using data from normal controls and the LCmodel quantification procedure, we found that the quantification precision, reproducibility and detection sensitivity of myo-inositol is significantly better at 3 T relative to 1.5 T.     

Effect of Pr-Ca substitution on the transport and magnetic behavior of LaMnO3 perovskite

The effect of simultaneous substitution of a fluctuating cation and a divalent cation in LaMnO₃ perovskite modifies the properties of the material to exhibit large valence colossal magnetoresistance (CMR) effect. A good example of these properties is (La_1−2x Pr _x Ca _x )MnO₃ (LPCMO) type CMR material. In this communication it is reported that, with the increase in x (for x=0.1, 0.15, 0.2), the T _c varies between 100 and 120 K with improvisation in metal-insulator transition. Interestingly, resistance increases with x from few hundred ohms to few kilo ohms with corresponding decrease in the unit cell volume. The results of the studies using X-ray diffraction (XRD), electrical resistivity, magnetoresistance and ac susceptibility measurements on LPCMO samples for understanding the structural, transport and magnetic properties are discussed in detail.     

Dications of fluorenylidenes. The relationship between redox potentials and antiaromaticity for meta- and para-substituted diphenylmethylidenefluorenes

[reaction: see text] Electrochemical oxidation of meta-substituted diphenylmethylidenefluorenes (3a-g) results in the formation of fluorenylidene dications that are shown to be antiaromatic through calculation of the nucleus independent chemical shift (NICS) for the 5- and 6-membered rings of the fluorenyl system. There is a strong linear correlation between the redox potential for the dication and both the calculated NICS and sigma(m). Redox potentials for formation of dications of analogously substituted tetraphenylethylenes shows that, with the exception of the p-methyl derivative, the redox potentials for these dications are less positive than for formation of the dications of 3a-g and for dications of p-substituted diphenylmethylidenefluorenes, 2a-g. The greater instability of dications of 2a-g and 3a-g compared to the reference system implies their antiaromaticity, which is supported by the positive NICS values. The redox potentials for formation of the dications of meta-substituted diphenylmethylidenes (3a-g) are more positive than for the formation of dications of para-substituted diphenylmethylidenes (2a-g), indicating their greater thermodynamic instability. The NICS values for dications of 3a-g are more antiaromatic than for dications of 2a-g, which is consistent with their greater instability of the dications of 3a-g. Although the substituted diphenylmethyl systems are not able to interact with the fluorenyl system through resonance because of their geometry, they are able to moderate the antiaromaticity of the fluorenyl cationic system. Two models have been suggested for this interaction, sigma to p donation and the ability of the charge on the substituted ring system to affect delocalization. Examination of bond lengths shows very limited variation, which argues against sigma to p donation in these systems. A strong correlation between NICS and sigma constants suggests that factors that affect the magnitude of the charge on the benzylic (alpha) carbon of the diphenylmethyl cation affect the antiaromaticity of the fluorenyl cation. Calculated atomic charges on carbons 1-8 and 10-13 show an increase in positive charge, and therefore greater delocalization of charge in the fluorenyl system, with increasing electronegativity of the substituent. The change in the amount of positive charge correlated strongly with NICS, supporting the model in which the amount of delocalization of charge is related to the antiaromaticity of the species. Thus, both aromatic and antiaromatic species are characterized by extensive delocalization of electron density.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.