New caulerpenyne-derived metabolites of an Elysia sacoglossan from the South Indian coast

Chemical analysis of the secondary metabolite pattern of the sacoglossan mollusc Elysia cf. expansa, collected along South Indian coasts, showed the presence of the typical Caulerpa-derived sesquiterpene caulerpenyne (1) and two new minor co- occurring metabolites, the compounds dihydrocaulerpenyne (4) and expansinol (5). The chemical characterization of these molecules, structurally related to 1, is reported.     

Parallel protocol for the selective methylation and alkylation of primary amines

One of the still unresolved problems in parallel synthesis is the availability of a general and rapid method for the transformation of a primary amine into the corresponding secondary amine without the issue of polyalkylation. Following the Fukuyama method, which is based on the alkylation of o-nitrobenzenesulfonamides, followed by removal of the sulfonyl group, we have developed a simple protocol which can be easily applied to parallel synthesis making use of supported reagents and scavengers. To verify the robustness of the method, a small representative array of secondary amines have been prepared. Moreover, taking advantage of the possibility to use different supported reagents in the same pot, we also prepared, starting from primary amines, a series of differently substituted tertiary amines.     

The first organocatalytic addition of 2-trimethylsilyloxyfuran to carbonyl compounds: hydrogen-bond catalysis in γ-butenolides synthesis

This letter describes the first example of diastereoselective ‘organocatalyzed’ synthesis of the butenolide products substituted at the γ-position by a chain bearing hydroxyl groups. The urea-derivative 4 has proved to be an efficient catalyst for the addition of the commercial TMSOF to carbonyl compounds under solvent-free conditions. The reaction conditions and generality of the procedure have been examined.     

Interior‐point methods and preconditioning for PDE‐constrained optimization problems involving sparsity terms

Partial differential equation (PDE)–constrained optimization problems with control or state constraints are challenging from an analytical and numerical perspective. The combination of these constraints with a sparsity‐promoting L¹ term within the objective function requires sophisticated optimization methods. We propose the use of an interior‐point scheme applied to a smoothed reformulation of the discretized problem and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method, we introduce fast and efficient preconditioners that enable us to solve problems from a number of PDE applications in low iteration numbers and CPU times, even when the parameters involved are altered dramatically.     

Double vortex condensates in the Chern-Simons-Higgs theory

For a selfdual model introduced by Hong-Kim-Pac [18] and Jackiw-Weinberg [19] we study the existence of double vortex-condensates“bifurcating” from the symmetric vacuum state as the Chern-Simons coupling parameter k tends to zero. Surprisingly, we show a connection between the asymptotic behavior of the given double vortex as with the existence of extremal functions for a Sobolev inequality of the Moser-Trudinger's type on the flat 2-torus ([22], [1] and [15]). In fact, our construction yields to a “best” minimizing sequence for the (non-coercive) associated extremal problem, in the sense that, the infimum is attained if and only if the given minimizing sequence admits a convergent subsequence. Received: March 3, 1998 / Accepted October 23, 1998     

Functional equations onA-orthogonal vectors

Summary LetH be a real (complex) Hilbert space with dimH 3,A:H H a continuous selfadjoint operator with dimA(H) > 2; we introduce onH a suitableA-orthogonality relation and study, in the class of the real (complex) functionals defined onH, two conditional functional equations — the Cauchy and the quadratic one — on the restricted domain of theA-orthogonal vectors.In this paper we determine the general solutions of these equations by theorems in which we establish the equivalence between each equation postulated on the whole space and the respective conditional equation.Our investigations have been motivated by incomplete studies on these conditional functional equations made in 1986 and 1966 by H. Drljevié and F. Vajzovié, respectively.     

Structural and thermal investigation of gadolinium gallium mixed oxides obtained by coprecipitation: Observation of a new metastable phase

Polycrystalline gadolinium gallium mixed oxides were prepared by coprecipitation and annealing at various temperatures below 1000 °C. The oxide materials appear to be X-ray amorphous after a heat treatment at 500 °C for 30 h, but after 30 h at 800 and 900 °C a major, unreported, hexagonal phase, isostructural with TAlO₃ compounds (where T=Y, Eu, Gd, Tb, Dy, Ho, Er) appears to crystallize. On the other hand, a highly energetic mechanical treatment of the amorphous powder previously annealed at 500 °C changes considerably the shape and position of exothermal events occurring in the range from 700 up to 900 °C. Subsequent annealing at 900 °C of the mechanically treated powder gives rise to the complete formation of the Gd₃Ga₅O₁₂ garnet structure at the expense of the hexagonal phase and of the minor Gd₄Ga₂O₉ oxide phase. However, a 7.0 wt% contamination is found to be due to tetragonal zirconia coming from vials and balls colliding media. The garnet phase may have strong deviations from the nominal stoichiometry of the garnet, as suggested by the refined lattice parameter obtained from the powder diffraction patterns and by the remarkable absence of intensity relative to the (220) Bragg peak position.     

Mo(CO)6-Catalyzed oxidation of furan derivatives to E- and Z-enediones by cumyl hydroperoxide

E- and Z-Enediones are easily accessible by controlled oxidation of 2,5-disubstituted furans with Mo(CO)₆/cumyl hydroperoxide system. The use of t-butyl hydroperoxide, as oxygen donor, leads to the formation of 2H-pyran-3(6H)-one derivatives.