An optimization algorithm for a penalized knapsack problem

We study a variation of the knapsack problem in which each item has a profit, a weight and a penalty; the sum of profits of the selected items minus the largest penalty associated with the selected items must be maximized. We present an ILP formulation and an exact optimization algorithm.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

On the spectrum of certain noncommutative harmonic oscillators

Abstract Some spectral properties of certain 2×2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator here called noncommutative harmonic oscillators, will be described, with special emphasis on the Poisson relation and clustering properties of the eigenvalues. Keywords: Clustering theorems, Periodic trajectories, Poisson relations, Noncommutative harmonic oscillators     

Online weighted flow time and deadline scheduling

In this paper we study some aspects of weighted flow time. We first show that the online algorithm Highest Density First is an O(1)-speed O(1)-approximation algorithm for P|r_i,pmtn|∑w_iF_i. We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any c-competitive online algorithm for weighted flow time must also be c-competitive for deadline scheduling. We then give an O(1)-competitive algorithm for deadline scheduling.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

Ab initio modelling of crosslinking in polymers. A case of chains with furan rings

A quantum chemical model (Abinitio HF-MO and DFT-B3LYP) of polyfurfuryl alcohol crosslinking is shown. Two pathways were considered: (a) a Diels–Alder (D–A) reaction between a dihydrofuran moiety and a furan ring; (b) the addition reaction of electrophilic specimens on conjugated double bonds. The ability for the formation of D–A adducts (dienes and dienophiles) was investigated by the frontier molecular orbital (FMO) theory. Energy gaps between the FMO's of diene and dienophile structures suggest that the occurrence of the D–A reaction is possible. The results suggest that the carbons of the exo double bonds attached to dihydrofuran rings are the sites most likely to be attacked by electrophilic species, while the C₃ and C₄ atoms display the opposite tendency due to their low HOMO electron densities. Results of a thermochemical approach to these reactions at the MP2 level was in agreement with reactivity modelled by MO predictions.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

An Improved Anharmonic Force Field of Difluoromethanimine, F2C NH

The anharmonic force field of difluoromethanimine, F₂C NH, has been reinvestigated theoretically using a coupled-cluster singles and doubles approach, augmented for structural optimization and harmonic force field by a contribution of connected triple excitations, CCSD(T). The cubic and quartic force constants have been obtained by numerical derivatives computed from analytical quadratic force constants calculated by second-order Møller-Plesset perturbation theory, MP2. The quadratic force constants and the equilibrium structure of F₂C NH have then been scaled by a global least-squares fitting procedure to the spectroscopic data and parameters experimentally determined for this molecule. This force field, obtained in the internal coordinates space and therefore valid for all isotopomers of difluoromethanimine, yields a complete set of spectroscopic molecular constants providing a critical assessment of the experimental rotational and centrifugal distortion constants, fundamentals, overtones, and combination bands determined so far for F₂C NH. In addition, the final force field can be used to make predictions of all important vibrational and rotational parameters which should be accurate and useful for new spectroscopic investigations.