Synthesis of (±)-1-(2,6,6-trimethyl-4-hydroxycyclohexenyl)-1,3-butanedione (1), a marine natural product

A short synthesis of racemic natural product (1) from the known compound (7) is described. A model study, using cyclochexanone as starting material, is also reported.     

On the origin of self-replicating information-containing polymers from oligomeric mixtures

Within the renormalization group formalism we study condensation reactions between oligomeric molecules catalysed by residues complementary to the growing ones. By assuming that the substrate-catalyst binding constatnt is the relevant parameter, we show that the transition to an information-containing self-replicating polymer is a critical phenomenon.     

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps

Ensemble averages of the sensitivity to initial conditions xi(t) and the entropy production per unit of time of a new family of one-dimensional dissipative maps, x(t+1)=1-ae(-1/|x(t)|(z))(z>0), and of the known logisticlike maps, x(t+1)=1-a|x(t)|(z)(z>1), are numerically studied, both for strong (Lyapunov exponent lambda(1)>0) and weak (chaos threshold, i.e., lambda(1)=0) chaotic cases. In all cases we verify the following: (i) both [ln((q)x triple bond (x(1-q)-1)/(1-q); ln((1)x=ln(x] and [S(q) triple bond (1- sigma p(q)(i))/(q-1); S(1)=- sigma p(i)ln(p(i)] linearly increase with time for (and only for) a special value of q, q(av)(sen), and (ii) the slope of and that of coincide, thus interestingly extending the well known Pesin theorem. For strong chaos, q(av)(sen)=1, whereas at the edge of chaos q(av)(sen)(z)<1.     

Simple approach to the mesoscopic open electron resonator: quantum current oscillations

The open electron resonator, described by Duncan et al. [D.S. Duncan, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Phys. Rev. B 64 (2001) 033310. [1]], is a mesoscopic device that has attracted considerable attention due to its remarkable behaviour (conductance oscillations), which has been explained by detailed theories based on the behaviour of electrons at the top of the Fermi sea. In this work, we study the resonator using the simple quantum quantum electrical circuit approach, developed recently by Li and Chen [Y.Q. Li, B. Chen, Phys. Rev. B 53 (1996) 4027. [2]]. With this approach, and considering a very simple capacitor-like model of the system, we are able to theoretically reproduce the observed conductance oscillations. A very remarkable feature of the simple theory developed here is the fact that the predictions depend mostly on very general facts, namely, the discrete nature of electric charge and quantum mechanics; other detailed features of the systems described enter as parameters of the system, such as capacities and inductances.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

An efficient synthesis of 3‐hydroxychromone using niobium pentachloride

A new and efficient 2‐step synthesis of 3‐hydroxychromone is described. Commercially available chromone is converted to the corresponding epoxide which is rearranged with niobium pentachloride to 3‐hydroxychromone in 61% overall yield.     

Erratum: Long‐range JCH heteronuclear coupling constants in cyclopentane derivatives. Part II

The original article to which this Erratum refers was published in Magnetic Resonance in volume 45 issue 1.     

Description of 2-integer continuous knapsack polyhedra

In this paper we discuss the polyhedral structure of several mixed integer sets involving two integer variables. We show that the number of the corresponding facet-defining inequalities is polynomial on the size of the input data and their coefficients can also be computed in polynomial time using a known algorithm [D. Hirschberg, C. Wong, A polynomial-time algorithm for the knapsack problem with two variables, Journal of the Association for Computing Machinery 23 (1) (1976) 147–154] for the two integer knapsack problem. These mixed integer sets may arise as substructures of more complex mixed integer sets that model the feasible solutions of real application problems.     

Ferromagnetic phase breakdown of a quenched bond-mixed Ising model

Within the framework of an effective field theory beyond Mean Field Approximation, we discuss the ferromagnetic phase stability limit in the temperature-concentration space of a quenched bond-mixed spin-$\text{1}\text{2}$ Ising model in square lattice for both competing and noncompeting interactions J₁ and J₂. Quite reasonable results are obtained in both situations. In particular for the case of competing interactions, numerical estimates of the vanishing temperature critical bond concentrations are predicted for particular values of the ratio $\text{J}{}_1\text{J}{}_2$.