Improved state space relaxation for constrained two-dimensional guillotine cutting problems

Christofides and Hadjiconstantinou (1995) introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably obtains the optimal weights. In order to obtain even better upper bounds, that algorithm is generalized into Algorithm X2 for obtaining optimal two-dimensional item weights. We also present a full hybrid method, called Algorithm X2D, that computes those strong upper bounds but also provides feasible solutions obtained by: (1) exploring the suboptimal solutions hidden in the dynamic programming matrices; (2) performing a number of iterations of a GRASP based primal heuristic; and (3) executing X2H, an adaptation of Algorithm X2 to transform it into a primal heuristic. Extensive experiments with instances from the literature and on newly proposed instances, for both variants with and without item rotation, show that X2D can consistently deliver high-quality solutions and sharp upper bounds. In many cases the provided solutions are certified to be optimal.     

Properties of abelian categories via recollements

A recollement is a decomposition of a given category (abelian or triangulated) into two subcategories with functorial data that enables the glueing of structural information. This paper is dedicated to investigating the behaviour under glueing of some basic properties of abelian categories (well-poweredness, Grothendieck's axioms AB3, AB4 and AB5, existence of a generator) in the presence of a recollement. In particular, we observe that in a recollement of a Grothendieck abelian category the other two categories involved are also Grothendieck abelian and, more significantly, we provide an example where the converse does not hold and explore multiple sufficient conditions for it to hold.     

Information-theoretical complexity for the hydrogenic abstraction reaction

In this work, we have investigated the complexity of the hydrogenic abstraction reaction by means of information functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e. the I–D, D–L and I–J planes and the Fisher–Shannon and López–Mancini–Calbet (LMC) shape complexities. The analysis of the information-theoretical functionals of the one-particle density was computed in position (r) and momentum (p) space. The analysis revealed that all of the chemically significant regions can be identified from the information functionals and most of the information-theoretical planes, i.e. the reactant/product regions (R/P), the transition state (TS), including those that are not present in the energy profile such as the bond cleavage energy region (BCER), and the bond breaking/forming regions (B–B/F). The analysis of the complexities shows that, in position as well as in the joint space, the energy profile of the abstraction reaction bears the same information-theoretical features as the LMC and FS measures. We discuss why most of the chemical features of interest, namely the BCER and B–B/F, are lost in the energy profile and that they are only revealed when particular information-theoretical aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.     

NMR Analysis of a Complex Spin System from a Siruo-Chamigrene

The compound 2,10-dibromo-3-chloro-8-hydroxy-β-chamigrene was analysed in detail by NMR Spectroscopy. the complete assignment of the signals in the ¹H and ¹³C NMR spectra and the determination of the relative configurations were achieved by 2D NMR techniques, AM1 data and ¹H spectrum simulation. Comparisons of the results with related spiro chamigrene systems are also presented.     

Asymptotic convergence of a simulated annealing algorithm for multiobjective optimization problems

In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, the Markov chain that describes the algorithm converges with probability one to the Pareto optimal set.     

A Note on Boundary Unique Contination for Harmonic Functions in Non-Smooth Domains

In this note, we prove the boundary unique continuation property for harmonic function dfined on convex domain     

Automated parallel anionic polymerizations: Enhancing the possibilities of a widely used technique in polymer synthesis

Anionic polymerization techniques have been implemented successfully in a commercial automated synthesizer. The main problems for a successful adaptation of the experimental technique in the automated synthesizer are addressed, as well as some simple potential applications, such as the anionic polymerization of styrene, isoprene, and methyl methacrylate. The obtained results were reproducible and in concordance with literature knowledge. The apparent rate constant of the anionic polymerization of styrene in cyclohexane initiated by sec‐butyllithium could be determined at two different concentrations of the monomer and initiator in a temperature range of 10–60 °C. All the synthesis and characterization experiments of the polymers were performed within a short time period. Moreover, the syntheses of poly(styrene‐b‐isoprene) and poly(styrene‐b‐methyl methacrylate) block copolymers were also successfully carried out within the automated synthesizer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4151–4160, 2005     

Homogeneity and Curvatures of Geodesic Spheres

We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces.     

Synthesis and spectra of 12-(o- and p-R-phenyl)-9,9-dimethyl-7,8,9,10,11,12-hexahydro and 8,9,10,11-tetrahydrobenz[a]acridin-11-ones. Structure correction of 1,2,3,4,5,6-hexahydro and 1,2,3,4-tetrahydro-2,2-dimethyl-5-aryl-6-aza-9,10-benzophenanthren-4-ones. II

It has been reported that the reaction of β-naphthylamine, dimedone and the appropriate aromatic aldehyde in ethanol gave 1,2,3,4,5,6-hexahydro-2,2-dimethyl-5-aryl-6-aza-9,10-benzophenanthren-4-ones, III , which upon treatment with chromic anhydride, yielded the corresponding tetrahydro derivatives, IV . However, the attempted preparation of these compounds resulted instead of the formation of isomeric acridin-11-ones, V and VI . Structures were confirmed by ir, ¹H nmr, ms and X-ray spectroscopy.