SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Heuristic methods for the single machine scheduling problem with different ready times and a common due date

The single machine scheduling problem with a common due date and non-identical ready times for the jobs is examined in this work. Performance is measured by the minimization of the weighted sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, the application of constructive heuristics that exploit specific characteristics of the problem to improve their performance is investigated. The proposed approaches are examined through a computational comparative study on a set of 280 benchmark test problems with up to 1000 jobs.

Treatment of Domestic Sewage in an Anaerobic-Aerobic Fixed-bed Reactor with Recirculation of the Liquid Phase

This study reports the performance of a combined anaerobic-aerobic packed-bed reactor that can be used to treat domestic sewage. Initially, a bench-scale reactor was operated in three experimental phases. In the first phase, the anaerobic reactor was operated with an average organic matter removal efficiency of 77% for a hydraulic retention time (HRT) of 10 h. In the second phase, the reactor was operated with an anaerobic stage followed by an aerobic zone, resulting in a mean value of 91% efficiency. In the third and final phase, the anaerobic-aerobic reactor was operated with recirculation of the effluent of the reactor through the anaerobic zone. The system yielded mean total nitrogen removal percentages of 65 and 75% for recycle ratios (r) of 0.5 and 1.5, respectively, and the chemical oxygen demand (COD) removal efficiencies were higher than 90%. When the pilot-scale reactor was operated with an HRT of 12 h and r values of 1.5 and 3.0, its performance was similar to that observed in the bench-scale unit (92% COD removal for r = 3.0). However, the nitrogen removal was lower (55% N removal for r = 3.0) due to problems with the hydrodynamics in the aerobic zone. The anaerobic-aerobic fixed-bed reactor with recirculation of the liquid phase allows for concomitant carbon and nitrogen removal without adding an exogenous source of electron donors and without requiring any additional alkalinity supplementation.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

A three-pronged approach to social business: a Brazilian multi-case analysis

Social businesses present a new paradigm to capitalism, in which private companies, non-profit organizations and civil society create a new type of business with the main objective of solving social problems with financial sustainability and efficiency through market mechanisms. As any new phenomenon, different authors conceptualize social businesses with distinct views. This article aims to present and characterize three different perspectives of social business definitions: the European, the American and that of the emerging countries. Each one of these views was illustrated by a different Brazilian case. We conclude with the idea that all the cases have similar characteristics, but also relevant differences that are more than merely geographical. The perspectives analyzed in this paper provide an analytical framework for understanding the field of social businesses. Moreover, the cases demonstrate that in the Brazilian context the field of social business is under construction and that as such it draws on different conceptual influences to deal with a complex and challenging reality.

Models for capacitated lot-sizing problem with backlogging, setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.