The first total synthesis of (-)-tamandarin A

[formula: see text] Tamandarin A (1), a newly isolated natural product similar in structure to didemnin B (2), was shown to be somewhat more active in vitro than 2 against pancreatic carcinoma with an ED50 value 1.5 to 2 ng/mL. We report here the first total synthesis of 1. The key steps include a practical stereoselective synthesis of the Hiv-isostatine unit, high-yielding linear precursor formation, a successful macrocyclization, and coupling of the macrocycle with the side chain to afford tamandarin A (1).     

The existence of ferrous ferricyanide

Evidence in the literature on the synthesis of ferrous ferricyanide is critically discussed. Pyrolysis and pressure effects on Prussian Blue lead to ferrous ferrocyanide together with decomposition by-products, and not to ferrous ferricyanide. The latter compound could be a precursor in the formation of Turnbull's Blue or an excited state of Prussian Blue, but it is not a stable chemical species.     

Determination of propazine by differential pulse polarography in micellar and emulsified media

An electroanalytical study of the herbicide propazine's reduction process in micellar solutions and oil-in-water emulsions is reported. The anionic surfactant sodium pentanesulphonate was chosen as the most suitable. The differential pulse polarograms of micellar solutions had two reduction peaks below pH 2.0, whereas only one peak was obtained above pH 2.O. Ethyl acetate was chosen as the organic solvent to form propazine emulsions. Unlike in micellar solutions, the DPP polarograms of propazine emulsions showed only one peak even at pH < 2.0, suggesting that propazine hydrolysis was hindered in the emulsified medium. The limiting current is diffusion-controlled and the electrode process is irreversible. Propazine can be determined by differential pulse polarography over the 1.0 × 10^–1 – 1.0 × 10^–1moll^–1 and 1.0 × 10^–15 – 4.0 × 10^–1 moll^–1 concentration ranges and the limit of detection was 2.8 × 10^–1 moll^–1. Of the potential interferents simazine, methoprotryne and terbutryn (alls-triazines), thiram (a dithiocarbamate), dinoseb (nitrophenolic), and heptachlor (chlorinated cyclo-diene herbicide), only the first two were significant (10% error for equimolar concentrations). The method was applied to the determination of propazine in spiked drinking water. At a concentration level of 2.0 × 10^–1 moll^–1 a recovery of 94 ± 6% was obtained, after tenfold concentration on Sep-Pak.     

Kinematical and gravitational analysis of the rocket-borne clock experiment by Vessot and Levine using the revised Robertson's test theory of special relativity

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of spherically symmetric line elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the real coordinate transformations from the Lorentz transformations.This work was started while the author was at Departamento de Fisica, Facultad Experimental de Ciencias, Universidad del Zulia, Maracaibo, Venezuela. It was completed at the Department of Physics, Utah State University, Logan, Utah 83422.     

Integrable non-linear σ models with fermions

The two-dimensional non-linear model on a Riemannian symmetric spaceM=G/H is coupled to fermions with quartic self-interactions. The resulting hybrid model is presented in a gauge-dependent formulation, with a bosonic field taking values inG and a fermionic field transforming under a given representation of the gauge groupH. General criteria for classical integrability are presented: they essentially fix the Lagrangian of the model but leave the fermion representation completely arbitrary. It is shown that by a special choice for the fermion representation (derived from the adjoint representation ofG by an appropriate reduction) one arrives naturally at the supersymmetric non-linear model onM=G/H. The issue of quantum integrability is also discussed, though with less stringent results.Work partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, and KFA Jülich, Federal Republic of GermanyOn leave of absence from Fakultät für Physik der Universität Freiburg, Federal Republic of Germany     

Intersections of random hypersurfaces and visibility

Summary For a wide class of stationary random hypersurfaces in ^d the notion of the projection body is introduced. It turns out that this convex body, a very special case of which is Matheron's Steiner compact associated with a Poisson process of hyperplanes, contains most of the information concerning certain intersection properties of the random hypersurface, while its polar reciprocal set is closely connected with the behaviour of the random hypersurface in visibility problems. This enables one to give a unified treatment of several intersection and visibility problems for random hypersurfaces. A detailed investigation of the case where the random hypersurface is generated by a Poisson process is given separately.     

Revised Robertson's test theory of special relativity: Space-time structure and dynamics

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant Robertson's subfamilies. It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory.Part of this work was done at the Department of Physics, Utah State University, Logan, Utah 84322.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.