First total syntheses of aeruginosin 298-A and aeruginosin 298-B, based on a stereocontrolled route to the new amino acid 6-hydroxyoctahydroindole-2-carboxylic acid

The first total syntheses of aeruginosin 298-A (1) and aeruginosin 298-B (3) are described. The syntheses of the alternative putative structures 2 and 4 were also accomplished. The key common strategic element is the stereo-controlled synthesis of (2S,3aS,6R,7aS)-6-hydroxyoctahydroindole-2-carboxylic acid (L-Choi, 5) from L-tyrosine. The synthesis of this new bicyclic alpha-amino acid, which is the core of aeruginosins, involves Birch reduction of O-methyl-L-tyrosine (6) and aminocyclization of the resulting dihydroanisole 7 in acid medium, followed by N-benzylation to give the diastereoisomers 12 and 13. Upon acid treatment with HCl-MeOH, the last two produce an equilibrium mixture in which the endo isomer 13 significantly predominates. Hydrogenation of 13 in the presence of (Boc)2O gives 16, which on reduction with LS-Selectride furnishes the alcohol 22, a protected L-Choi. Successive couplings of 22 with D-leucine, protected (R)-(4-hydroxyphenyl)lactic acid, and L-arginine fragments, followed by reduction to the argininol level and a deprotection end step complete the synthetic sequence to produce aeruginosin 298-A (1). Spectral comparison showed that peptide 2, with the structure previously proposed for aeruginosin 298-A, was different from the natural product. However, synthetic 1 was found to be identical to the isolated natural sample of aeruginosin 298-A. These results unequivocally establish that the absolute stereochemistry of aeruginosin 298-A, formerly assigned incorrectly, is D-Hpla-D-Leu-L-Choi-L-Argol, as shown by structure 1. Aeruginosin 298-B was also synthesized and shown to be a mixture of rotamers of D-Hpla-D-Leu-L-ChoiNH2 (3), rather than an epimeric mixture of 3 and the L-Leu-incorporating 4.     

A Grobman-Hartman theorem for nonuniformly hyperbolic dynamics

We establish a version of the Grobman-Hartman theorem in Banach spaces for nonuniformly hyperbolic dynamics. We also consider the case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. More precisely, we consider sequences of Lipschitz maps Am+fm such that the linear parts Am admit a nonuniform exponential dichotomy, and we establish the existence of a unique sequence of topological conjugacies between the maps Am+fm and Am. Furthermore, we show that the conjugacies are Hölder continuous, with Hölder exponent determined by the ratios of Lyapunov exponents with the same sign. To the best of our knowledge this statement appeared nowhere before in the published literature, even in the particular case of uniform exponential dichotomies, although some experts claim that it is well known in this case. We are also interested in the dependence of the conjugacies on the perturbations fm: we show that it is Hölder continuous, with the same Hölder exponent as the one for the conjugacies. We emphasize that the additional work required to consider the case of nonuniform exponential dichotomies is substantial. In particular, we need to consider several additional Lyapunov norms.     

Nonuniform Exponential Dichotomies and Lyapunov Regularity

The notion of exponential dichotomy plays a central role in the Hadamard–Perron theory of invariant manifolds for dynamical systems. The more general notion of nonuniform exponential dichotomy plays a similar role under much weaker assumptions. On the other hand, for nonautonomous linear equations v′ = A(t)v with global solutions, we show here that this more general notion is in fact as weak as possible: namely, any such equation possesses a nonuniform exponential dichotomy. It turns out that the construction of invariant manifolds under the existence of a nonuniform exponential dichotomy requires the nonuniformity to be sufficiently small when compared to the Lyapunov exponents. Thus, it is crucial to estimate the deviation from the uniform exponential behavior. This deviation can be measured by the so-called regularity coefficient, in the context of the classical Lyapunov–Perron regularity theory. We obtain here lower and upper sharp estimates for the regularity coefficient, expressed solely in terms of the matrices A(t).     

Conjugacies for linear and nonlinear perturbations of nonuniform behavior

We construct topological conjugacies between linear and nonlinear evolution operators that admit either a nonuniform exponential contraction or a nonuniform exponential dichotomy. We consider evolution operators defined by nonautonomous differential equations x^′=A(t)x+f(t,x) in a Banach space. The conjugacies are obtained by first considering sufficiently small linear and nonlinear perturbations of linear equations x^′=A(t)x. In the case of linear perturbations, we construct in a more or less explicit manner topological conjugacies between the two linear flows. In the case of nonlinear perturbations, we obtain a version of the Grobman-Hartman theorem for nonuniformly hyperbolic dynamics. Furthermore, all the conjugacies that we construct are locally Hölder continuous provided that the vectors fields are of class C¹. As a byproduct of our approach, we give conditions for the robustness of strong nonuniform exponential behavior, in the sense that under sufficiently small perturbations the structure determined by the stable and unstable bundles persists up to small variations. We also show that the constants determining the nonuniform exponential contraction or nonuniform exponential dichotomy vary continuously with the perturbation. All the results are obtained in Banach spaces.     

Two-step melting of the vortex solid in layered superconductors with random columnar pins

We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.     

Cryopreservation of Arachis species by vitrification of in vitro-grown shoot apices and genetic stability of recovered plants

A storage protocol at cryogenic temperature was established for shoot apices from in vitro plants of the cultivated groundnut (Arachis hypogaea) and wild Arachis species (A. retusa and A. burchellii) using a basic vitrification protocol with direct immersion in liquid nitrogen (LN). The effect of pre-treatments of donor-plants with ABA as well as of different supplements in the post-thaw culture medium was studied. After rapid warming at 40 C, the explants were cultured on MS medium devoid of growth regulators (MS0) or MS supplemented with 4.4(M benzylaminopurine (BAP) and 0.5(M naphthalene acetic acid (NAA) plus 5(M silver nitrate (AgNO3), 0.25% polyvinylpyrrolidone (PVP) or 0.2% activated charcoal. Non-frozen explants from the three species formed one shoot through meristematic amplification when cultured on MS0 medium. These explants also developed callus on MS supplemented with growth regulators (4.4(M BAP and 0.5(M NAA) alone or plus PVP or AgNO3. Callus formation was suppressed in the presence of activated charcoal. Post-thaw regeneration ocurred only through indirect organogenesis on media containing AgNO3 or PVP. Preculturing on medium supplemented with abscisic acid (ABA) improved regrowth rate in these media. Recovery failed to occur in the presence of activated charcoal. The genetic stability of shoots of A. burchellii originated from shoot apices was analyzed through Random Amplified Polymorphic DNA (RAPD) markers.     

Measurement of the decay amplitudes of B0 --> J/psiK*0 and B(s)(0) --> J/psistraight phi decays

An angular analysis of B0-->J/psiK(*0) and B(0)(s)-->J/psistraight phi has been used to determine the decay amplitudes with parity-even longitudinal ( A0) and transverse ( A( parallel)) polarization and parity-odd transverse ( A( perpendicular)) polarization. The measurements are based on 190 B0 and 40 B(0)(s) candidates obtained from 89 pb(-1) of &pmacr;p collisions at the Fermilab Tevatron. The longitudinal decay amplitude dominates with |A0|(2) = 0.59+/-0. 06+/-0.01 for B0 and |A0|(2) = 0.61+/-0.14+/-0.02 for B(0)(s) decays. The parity-odd amplitude is found to be small with |A( perpendicular)|(2) = 0.13(+0.12)(-0.09)+/-0.06 for B0 and |A( perpendicular)|(2) = 0.23+/-0.19+/-0.04 for B(0)(s) decays.     

Measurement of b-quark fragmentation fractions in p&pmacr; collisions at sqrt

We have studied the production of B hadrons in 1.8-TeV pp[over ˉ] collisions. We present measurements of the fragmentation fractions, f_{u}, f_{d}, f_{s}, and f_{baryon}, of produced b quarks that yield B^{+}, B^{0}, B_{s}^{0}, and Λ[over ˉ]_{b}^{0} hadrons. Reconstruction of five electron-charm final states yields f_{s}/( f_{u}+f_{d})=0.213±0.068 and f_{baryon}/( f_{u}+f_{d})=0.118±0.042, assuming f_{u}=f_{d}. If all B hadrons produced in pp[over ˉ] collisions cascade to one of these four hadrons, we determine f_{u}=f_{d}=0.375±0.023, f_{s}=0.160±0.044, and f_{baryon}=0.090±0.029. If we do not assume f_{u}=f_{d}, we find f_{d}/f_{u}=0.84±0.16.     

Search for new particles decaying to t&tmacr; in p&pmacr; collisions at radicals = 1.8 TeV

We use 106 pb (-1) of data collected with the Collider Detector at Fermilab to search for narrow-width, vector particles decaying to a top and an antitop quark. Model independent upper limits on the cross section for narrow, vector resonances decaying to t&tmacr; are presented. At the 95% confidence level, we exclude the existence of a leptophobic Z' boson in a model of top-color-assisted technicolor with mass M(Z')<480 GeV/c(2) for natural width gamma = 0.012M(Z'), and M(Z')<780 GeV/c(2) for gamma = 0.04M(Z').