Ring Contraction Through Epoxide Rearrangement: A Formal Synthesis of Capsorubin

An eight-step synthesis of the cyclopentane keto-alcohol 2, which has previously been converted in one step into the carotenoid pigment capsorubin (1), is described. The key step in our synthesis is a stereospecific epoxide rearrangement with ring contraction, thus producing the cyclopentane ring from an epoxide of a cyclohexene.     

(1)H and (13)C NMR spectral data for a tricyclic derivative of a Diels-Alder adduct

A complete NMR analysis with full assignment for (1)H and (13)C NMR spectral data for 5-(acetyloxy)-3-hydroxy-9,10-dimethoxy-6-oxo-11-oxatricyclo[6.2.1.0(2,7)]undec-2-yl acetate is described. This compound was prepared by rapid hydrogenation of the unstable Diels-Alder adduct obtained from the reaction between 3,4-dimethoxyfuran and 2,5-diacetoxy-1,4-benzoquinone. Full homonuclear hydrogen coupling constants measurements and molecular mechanics calculations were performed for the determination of the relative stereochemistry.     

Spin anisotropy effects on the dimerization of the magnetostrictive quasi-one-dimensional XY model

The one-dimensional first-neighbour spin - $\text{1}\text{2}$ magnetostrictive XY model (with crystalline degrees of freedom assumed three- dimensional) with $\text{different}$ X and Y spin coupling constants presents a quite rich spin-Peierls dimerization phase diagram. In the (low anisotropy) - (low temperature) region we recover previous results (in particular the possibility for a first-order phase transition in the absence of external magnetic field); in the other three regions of the temperature-anisotropy space interesting branches of the phase diagram (including the tricritical line) are exhibited (for the first time as far as we know).     

Lifting two-integer knapsack inequalities

In this paper we discuss the derivation of strong valid inequalities for (mixed) integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables (and one continuous variable). The basic polyhedra can be described in polynomial time. We use superadditive valid lifting functions in order to obtain sequence independent lifting. Most of these superadditive functions and valid inequalities are not obtained in polynomial time.     

Silver sorption isotherms onto bentonites: Comparing mathematical models

Herein is reported the application of models on sorption isotherms for removal of silver ions from aqueous solution using 2 bentonites: SWy‐2 and BaVC‐1, low‐cost sorbents. Physicochemical attributes were determined for both materials, and sorption experiments were carried out in batch system. The pH before and after sorption decreased from 7.8 to 6.1 and 8.4 to 6.7 for SWy‐2 and BaVC‐1, respectively. Langmuir, Freundlich, Sips, Toth, Kolbe‐Corrigan, Khan, and Radke‐Prausnitiz models were applied to the data. The models showed good fit with R² above 0.999 and RMSE < 2%. The adjustable parameters indicated high affinity of silver ions to BaVC‐1 sorption sites, demonstrating high sorption capacity and thermodynamic feasibility. In general, SWy‐2 showed most heterogeneous sorption sites, while BaVC‐1 showed most homogeneous sites. Moreover, BaVC‐1 has shown larger surface area and smaller particle size, which can explain its better sorption performance as compared with SWy‐2.     

On the universality classes of the Henon map

Within an appropriate renormalization framework, we discuss a¹(b) and δ associated with the bifurcation road to chaos of a Hénon-like map generalized as follows: (x_t+1, y_t+1) = (1?a|x_t|^z + y_t, ?bx_t); (b?0, z?1). For fixed z, we obtained (i) only two universality classes, namely the conservative (b = 1) and non-conservative (b≠1) ones and (ii) $\text{a}{}^1\text{(}\text{1}\text{b}\text{) =}\text{a}{}^1\text{(b)}\text{b}{}^{\mathrm{z}}$. For b = 1, δ(z) presents a minimum, and diverges for z → 1 and z → ∞ (this contrasts with the b≠1 case).     

A cutting plane approach to capacitated lot-sizing with start-up costs

We consider a mixed integer model for multi-item single machine production planning, incorporating both start-up costs and machine capacity. The single-item version of this model is studied from the polyhedral point of view and several families of valid inequalities are derived. For some of these inequalities, we give necessary and sufficient facet inducing conditions, and efficient separation algorithms. We use these inequalities in a cutting plane/branch and bound procedure. A set of real life based problems with 5 items and up to 36 periods is solved to optimality.     

Do the simple and 2/3 majority models belong to the same universality class?: A monte carlo approach

We extend the majority model (introduced by Tsallis in 1982) in the sense that the required majority might be different from the simple majority. We simulate these models for typical cases which include simple and 2/3 majorities. We exhibit the average cluster size as well as the order parameter as functions ofp, the concentration of one of the two possible constituents. No crossover exists between the simple- and non-simple-majority models.     

One-step biomimetic conversion of a furanoheliangolide into an eremantholide using Stryker’s reagent

The conversion of a furanoheliangolide structure (15-deoxygoyazensolide) into an eremantholide one (eremantholide C) was achieved by tandem hydride conjugate addition–intramolecular carbanion addition using Stryker’s reagent.     

Roundoff-induced attractors and reversibility in conservative two-dimensional maps

We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys. Rev. Lett. 64 (1990) 2354] in the context of undecidability. We calculate the time evolution of the entropy (). We exhibit the dramatic effect introduced by numerical precision. Indeed, in spite of being area-preserving maps, they present, well after the initially concentrated ensemble has spread virtually all over the phase space, unexpected pseudo-attractors (fixed-point like for the baker map, and more complex structures for the Moore map). These pseudo-attractors, and the apparent time (partial) reversibility they provoke, gradually disappear for increasingly large precision. In the case of the Moore map, they are related to zero Lebesgue-measure effects associated with the frontiers existing in the definition of the map. In addition to the above, and consistent with the results by V. Latora and M. Baranger [Phys. Rev. Lett. 82 (1999) 520], we find that the rate of the far-from-equilibrium entropy production of baker map numerically coincides with the standard Kolmogorov-Sinai entropy of this strongly chaotic system.