A survey of acid catalysts for use in two-step, one-flask syntheses of meso-substituted porphyrinic macrocycles

[reaction: see text] Diverse Lewis acids and Bronsted acids were examined in the two-step, one-flask synthesis of meso-tetraphenylporphyrin, N-confused tetraphenylporphyrin, and tetraphenylsapphyrin. The scope of acid catalysis was found to be very broad, with 35 of 45 acids providing TPP in yields ranging from 5% to 58%. NC-TPP was also widely observed in yields of 1-40%, and TPS was infrequently observed in yields of <1%. Additionally, conditions were found for direct preparation of magnesium TPP and copper TPP.     

Wess-Zumino current and the structure of the decay tau- -->K- pi- K+ nu tau

We present the first study of the vector (Wess-Zumino) current in tau(-)-->K-pi-K+nu(tau) decay using data collected with the CLEO III detector at the Cornell Electron Storage Ring. We determine the quantitative contributions to the decay width from the vector and axial vector currents. Within the framework of a model by Kühn and Mirkes, we identify the quantitative contributions to the total decay rate from the intermediate states omegapi, rho(')pi, and K*K.     

Dependence of shell mix on feedthrough in direct drive inertial confinement fusion

The mixing of cold, high-density shell plasma with the low-density, hot spot plasma by the Rayleigh-Taylor instability in inertial confinement fusion is experimentally shown to correlate with the calculated perturbation feedthrough from the ablation surface to the inner shell surface. A fourfold decrease in the density of shell material in the mix region of direct drive implosions of gas filled spherical plastic shells having predicted convergence ratios approximately 15 was observed when laser imprint levels were reduced and the initial shell was thicker, corresponding to a reduction in the feedthrough rms level by a factor of 6. Shell mix is also shown to limit the spherical compression of the implosion.     

Chaotic mixing induced transitions in reaction-diffusion systems

We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the rate of the chemical reaction. When the stirring is fast localized perturbations decay towards a spatially homogeneous state. When the stirring is slow (or fast reaction) localized perturbations propagate by advection in form of a filament with a roughly constant width and exponentially increasing length. The width of the filament depends on the stirring rate and reaction rate but is independent of the initial perturbation. We investigate this problem numerically in both closed and open flow systems and explain the results using a one-dimensional "mean-strain" model for the transverse profile of the filament that captures the interplay between the propagation of the reaction-diffusion front and the stretching due to chaotic advection. (c) 2002 American Institute of Physics.     

Cyanocalix[4]arenes: synthesis,crystal structures and reactivity studies

Abstract

Herein, we describe an improved method to synthesise mono-, di- and tetra-cyanocalix[4]arene and report their crystal structure determinations. We also report our attempts to further functionalise the cyanocalix[4]arenes into dithiadiazolyl-calix[4]arenes, and propose a hypothesis as to why the cyano group on a calix[4]arene is an extremely challenging group to modify.     

A maximum degree theorem for diameter-2-critical graphs

A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ?n ²/4? and that the extremal graphs are the complete bipartite graphs K _?n/2?,?n/2?. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n ₀ where n ₀ is a tower of 2’s of height about 10¹⁴. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true.     

Group automorphisms with prescribed growth of periodic points,and small primes in arithmetic progressions in intervals

We investigate the question of which growth rates are possible for the number of periodic points of a compact group automorphism. Our arguments involve a modification of Linnik?s Theorem, concerning small prime numbers in arithmetic progressions which lie in intervals.     

Experimental investigation of relative timing jitter in passively synchronized Q-switched lasers

Relative timing jitter between synchronized Q-switched lasers, or lack thereof, is important for stable sum-frequency generation. Experimental investigation of two passively synchronized lasers shows that the jitter is minimized when the free-running repetition rates of the two lasers are close to, but not exactly, matching. When the free-running repetition rates are matched, the jitter is significantly large. At the best operating point, the pulse-to-pulse period was 200 μs, while the relative jitter between the two lasers was 9 ns. If the effect of the master laser's pulse-to-pulse jitter is removed, the residual timing jitter between the two lasers was 6 ns, which corresponds to the lower limit set by pump power fluctuations and noise from spontaneous emission.     

Preparation of stable,camphor-derived,optically active allylic sulfoxides

(+)-Camphor has been stereospecifically converted in three steps into a single isoborneol allyl sulfoxide derivative, which upon heating to 145° is quantitatively converted into its sulfoxide epimer; the anions of these compounds undergo stereospecific conjugate addition to cyclopent-2-en-1-one.