Total synthesis and biological evaluation of the tetramic acid based natural product harzianic acid and its stereoisomers

Financial support for this project was provided by Cancer Research UK (Grant No. C21383/A6950)The bioactive natural product harzianic acid was prepared for the first time in just six steps (longest linear sequence) with an overall yield of 22%. The identification of conditions to telescope amide bond formation and a Lacey-Dieckmann reaction into one pot proved important. The three stereoisomers of harzianic acid were also prepared, providing material for comparison of their biological activity. While all of the isomers promoted root growth, improved antifungal activity was unexpectedly associated with isomers in the enantiomeric series opposite that of harzianic acid.Publisher PDFPeer reviewe

First Digit Distribution of Hadron Full Width

A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $1,2,...,9$, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e., the law is scale-invariant, base-invariant, and power-invariant. This means that the lifetimes of hadrons follow also Benford's law.Comment: 8 latex pages, 4 figures, final version in journal publicatio

Investigating timing properties of modern digitizers utilizing interpolating CFD algorithms and the application to digital fast-timing lifetime measurement

The performance of two implementations of digital real-time interpolating constant fraction discriminator algorithms with respect to fast-timing lifetime measurements are investigated. The implementations integrated in two different digitizers were evaluated in terms of the effects of tuning parameters of the digital CFDs and the influence of different input amplitudes on the time resolution and time walk characteristics. Reference is made to the existing analog standard of fast-timing techniques. The study shows, that the timing performance of both modules is comparable to established fast-timing setups using analog constant fraction discriminators, but with the added benefit of digital processing. Both digitizer modules were found to be highly effective and user-friendly instruments for modern fast-timing requirements.Comment: 13 pages, 16 figure

Connection Between Type A and E Factorizations and Construction of Satellite Algebras

Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here the role of the factorization method in the construction of such algebras is investigated. A general procedure for determining an so(2,2) or so(2,1) satellite algebra for all the Hamiltonians that admit a type E factorization is proposed. Such a procedure is based on the known relationship between type A and E factorizations, combined with an algebraization similar to that used in the construction of potential algebras. It is illustrated with the examples of the generalized Morse potential, the Rosen-Morse potential, the Kepler problem in a space of constant negative curvature, and, in each case, the conserved quantity is identified. It should be stressed that the method proposed is fairly general since the other factorization types may be considered as limiting cases of type A or E factorizations.Comment: 20 pages, LaTeX, no figure, to be published in J. Phys.

Generalized Morse Potential: Symmetry and Satellite Potentials

We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace equation on the hyperboloid and the Schr\"odinger equation for the P\"oschl-Teller potential, we explain the exact solvability of the problem by an $so(2,2)$ symmetry algebra, and obtain an explicit realization of the latter as $su(1,1) \oplus su(1,1)$. We prove that some of the $so(2,2)$ generators connect among themselves wave functions belonging to different GMP's (called satellite potentials). The conserved quantity is some combination of the potential parameters instead of the level energy, as for potential algebras. Hence, $so(2,2)$ belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states.Comment: 23 pages, LaTeX, 2 figures (on request). one LaTeX problem settle