On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

A high-speed high-sensitivity acoustic cell for in-line continuous monitoring of MOCVD precursor gases

We describe a continuous wave resonant acoustic sensor that has been optimized as a very sensitive in-line monitor for measuring the composition of precursor gases used in MOCVD processes. The precursor/carrier gas mixtures flow through a compact stainless steel acoustic chamber that is isolated from the acoustic transducers by a set of metallic diaphragms. The sensor has been successfully operated at supply line pressures from atmosphere down to 50 Torr with gas flow rates of up to 1600 sccm. The accuracy of the speed of sound measurement for hydrogen gas is better than 0.005%, even in a high noise and low pressure environment. Hydrogen, as well as nitrogen or argon carrier gases, are accommodated within the instrument's 1–5 kHz working frequency range. The instrument's sensitivity and stability are demonstrated with the laboratory data. Measurements of the dynamic response characteristics of the metalorganic bubbler lines at low pressure are also be presented. Application of the cell is general, encompassing any of the metalorganic and hydride materials typically used in MOCVD processes.     

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     

Autocorrelated 13c-13c double quantum coherence two-dimensional nmr spectroscopy: Utilization of a modified version of the technique as an adjunct in the total assignment of the 1h- and 13c-nmr spectra of the mutagen phenanthro[3,4-b]thiophene

Development of successively higher field nmr spectrometers has facilitated the study of increasingly more complex molecules, although smaller molecules such as phenanthro[3,4-b]thiophene still offer very substantial assignment problems because of the highly congested nature of their ¹H- and ¹³C-nmr spectra. Assignments of such spectra, if they are to be unequivocal, frequently require the utilization of two-dimensional nmr spectroscopic techniques. Total assignments of the ¹H- and ¹³C-nmr spectra of phenanthro[3,4-b]thiophene are reported. Assignments were based on a conventional high resolution 500 MHz ¹H-nmr spectrum, autocorrelated two-dimensional ¹H-nmr spectra (COSY), two-dimensional ¹H-¹³C chemical shift correlation spectra and a modified version of autocorrelated ¹³C-¹³C double quantum coherence two-dimensional nmr spectroscopy. From NOE measurements, a separation of 1.99 Å between H1 and H11 was computed, suggesting that phenanthro[3,4-b]thiophene has a pronounced helical conformation in solution.     

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     

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.     

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.