Part I: Asymmetric Synthesis of α-Allyl-α-Aryl α-Amino Acids Part II: Asymmetric Spirocyclization of Allenyl Ketones Part III: Chemoselective Activation of C(sp3)−h Bond Over C(sp2)−h Bond With Pd(II)

Part I. The first asymmetric synthesis of a-allyl-a-aryl a-amino acids by means of a three component coupling of a-iminoesters, Grignard reagents, and cinnamyl acetate is reported. Notably, the enolate from the tandem process provides a much higher level of reactivity and selectivity than the same enolate generated via direct deprotonation, presumably due to differences in the solvation/aggregation state. A novel method for removal of a homoallylic amine protecting group delivers the free amine congeners. The a-allyl moiety offers a means to generate further valuable a-amino acid structures. Cross-metathesis of the tandem product provided allylic diversity not afforded in the parent reaction. Cyclic a-amino acid derivatives could be accessed by ring closing metathesis presenting a viable strategy to higher ring homologues of enantioenriched a-substituted proline. The 8-member proline analog was successfully converted to the pyrrolizidine natural product backbone. Part II. The asymmetric spirocyclization of allenyl ketones is reported. High-throughput experimentation by means of a chiral Lewis acid library enabled the determination of a suitable catalyst system. Protecting group manipulation provides an orthogonal route to enantioenriched para-quinone and ortho-quinone spirocycles. This novel technology provides access to the spirocyclic core that is prevalent in many natural products. Part III. Palladium has been identified as a suitable catalyst for the chemoselective activation of C(sp3)-H bond over C(sp2)-H bond of toluene and tolyl analogs. This technology has been combined with the C(sp3)-H activation of acidic C-H bonds to form new C-C bonds. High-throughput experimentation was used for identifying conditions that reduced toluene loading and engendered catalyst turnover via a suitable oxidant. The parent reaction has been extended to include the Pd catalyzed alkylation of phenylglycine azlactones with ethylbenzene, 2-ethylnaphthalene, propylbenzene and butylbenzene. Mechanistic studies were initiated to determine whether the process occurs via free radicals or via Pd mediated C(sp3)-H activation. Our studies support a Pd mediated process in which the C(sp3)-H activation of the tolyl analog is the rate determining step. This finding represents a paradigm shift in our understanding of Pd and its selectivity for arene activation vs benzylic activation

Inequalities for Light Nuclei in the Wigner Symmetry Limit

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three and four-nucleon force terms.Comment: 10 page

The realizability problem as a special case of the infinite-dimensional truncated moment problem

The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated K-moment problem where K is the space of all possible configurations of the components of the considered system. The power of this reformulation has been already exploited by Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253-1281], where necessary and sufficient conditions of Haviland type have been obtained for several instances of the realizability problem. In this article we exploit this same reformulation to apply to the realizability problem the recent advances obtained by Curto, Ghasemi, Infusino, and Kuhlmann [J. Operator Theory 90 (2023), pp. 223-261] for the truncated moment problem for linear functionals on general unital commutative algebras. This provides alternative proofs and sometimes extensions of several results of Kuna, Lebowitz, and Speer [Ann. Appl. Probab. 21 (2011), pp. 1253-1281], allowing to finally embed them in the above-mentioned unified framework for the infinite-dimensional truncated moment problem

Convolutional Goppa Codes

We define Convolutional Goppa Codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some Maximum-Distance Separable (MDS) convolutional codes.Comment: 8 pages, submitted to IEEE Trans. Inform. Theor

Isotope Spectroscopy

The measurement of isotopic ratios provides a privileged insight both into nucleosynthesis and into the mechanisms operating in stellar envelopes, such as gravitational settling. In this article, we give a few examples of how isotopic ratios can be determined from high-resolution, high-quality stellar spectra. We consider examples of the lightest elements, H and He, for which the isotopic shifts are very large and easily measurable, and examples of heavier elements for which the determination of isotopic ratios is more difficult. The presence of 6Li in the stellar atmospheres causes a subtle extra depression in the red wing of the 7Li 670.7 nm doublet which can only be detected in spectra of the highest quality. But even with the best spectra, the derived $^6$Li abundance can only be as good as the synthetic spectra used for their interpretation. It is now known that 3D non-LTE modelling of the lithium spectral line profiles is necessary to account properly for the intrinsic line asymmetry, which is produced by convective flows in the atmospheres of cool stars, and can mimic the presence of 6Li. We also discuss briefly the case of the carbon isotopic ratio in metal-poor stars, and provide a new determination of the nickel isotopic ratios in the solar atmosphere.Comment: AIP Thinkshop 10 "High resolution optical spectroscopy", invited talk, AN in pres

The planet search programme at the ESO CES and HARPS. IV. The search for Jupiter analogues around solar-like stars

In 1992 we began a precision radial velocity (RV) survey for planets around solar-like stars with the Coude Echelle Spectrograph and the Long Camera (CES LC) at the 1.4 m telescope in La Silla (Chile). We have continued the survey with the upgraded CES Very Long Camera (VLC) and HARPS, both at the 3.6 m telescope, until 2007. The observations for 31 stars cover a time span of up to 15 years and the RV precision permit a search for Jupiter analogues. We perform a joint analysis for variability, trends, periodicities, and Keplerian orbits and compute detection limits. Moreover, the HARPS RVs are analysed for correlations with activity indicators (CaII H&K and CCF shape). We achieve a long-term RV precision of 15 m/s (CES+LC, 1992-1998), 9 m/s (CES+VLC, 1999-2006), and 2.8 m/s (HARPS, 2003-2009, including archive data), resp. This enables us to confirm the known planets around Iota Hor, HR 506, and HR 3259. A steady RV trend for Eps Ind A can be explained by a planetary companion. On the other hand, we find previously reported trends to be smaller for Beta Hyi and not present for Alp Men. The candidate planet Eps Eri b was not detected despite our better precision. Also the planet announced for HR 4523 cannot be confirmed. Long-term trends in several of our stars are compatible with known stellar companions. We provide a spectroscopic orbital solution for the binary HR 2400 and refined solutions for the planets around HR 506 and Iota Hor. For some other stars the variations could be attributed to stellar activity. The occurrence of two Jupiter-mass planets in our sample is in line with the estimate of 10% for the frequency of giant planets with periods smaller than 10 yr around solar-like stars. We have not detected a Jupiter analogue, while the detections limits for circular orbits indicate at 5 AU a sensitivity for minimum mass of at least 1 M_Jup (2 M_Jup) for 13% (61%) of the stars.Comment: 63 pages, 24 figures (+33 online figures), 13 Tables, accepted for publication in A&A (2012-11-13