Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Maximum diameter of regular digraphs

We prove that every r-biregular digraph with n vertices has its directed diamter bounded by (3n - r - 3)/(r +1). We show that this bound is tight for directed as well as for undirected graphs. The upper bound remains valid for Eulerian digraphs with minimum outdegree r. © 1929 John Wiley & Sons, Inc.     

Scaling probability, key to the equilibrium statistical volume distribution in foams

The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam.     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx     

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.