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 nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

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.

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.

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.

Carbon monoxide and related trace gases and aerosols over the Amazon Basin during the wet and dry seasons

We present the results of airborne measurements of carbon monoxide (CO) and aerosol particle number concentration (CN) made during the Balan double dagger o Atmosf,rico Regional de Carbono na Amazonia (BARCA) program. The primary goal of BARCA is to address the question of basin-scale sources and sinks of CO2 and other atmospheric carbon species, a central issue of the Large-scale Biosphere-Atmosphere (LBA) program. The experiment consisted of two aircraft campaigns during November-December 2008 (BARCA-A) and May-June 2009 (BARCA-B), which covered the altitude range from the surface up to about 4500 m, and spanned most of the Amazon Basin. Based on meteorological analysis and measurements of the tracer, SF6, we found that airmasses over the Amazon Basin during the late dry season (BARCA-A, November 2008) originated predominantly from the Southern Hemisphere, while during the late wet season (BARCA-B, May 2009) low-level airmasses were dominated by northern-hemispheric inflow and mid-tropospheric airmasses were of mixed origin. In BARCA-A we found strong influence of biomass burning emissions on the composition of the atmosphere over much of the Amazon Basin, with CO enhancements up to 300 ppb and CN concentrations approaching 10 000 cm(-3); the highest values were in the southern part of the Basin at altitudes of 1-3 km. The Delta CN/Delta CO ratios were diagnostic for biomass burning emissions, and were lower in aged than in fresh smoke. Fresh emissions indicated CO/CO2 and CN/CO emission ratios in good agreement with previous work, but our results also highlight the need to consider the residual smoldering combustion that takes place after the active flaming phase of deforestation fires. During the late wet season, in contrast, there was little evidence for a significant presence of biomass smoke. Low CN concentrations (300-500 cm(-3)) prevailed basinwide, and CO mixing ratios were enhanced by only similar to 10 ppb above the mixing line between Northern and Southern Hemisphere air. There was no detectable trend in CO with distance from the coast, but there was a small enhancement of CO in the boundary layer suggesting diffuse biogenic sources from photochemical degradation of biogenic volatile organic compounds or direct biological emission. Simulations of CO distributions during BARCA-A using a range of models yielded general agreement in spatial distribution and confirm the important contribution from biomass burning emissions, but the models evidence some systematic quantitative differences compared to observed CO concentrations. These mismatches appear to be related to problems with the accuracy of the global background fields, the role of vertical transport and biomass smoke injection height, the choice of model resolution, and reliability and temporal resolution of the emissions data base.

Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control

A new methodology for the synthesis of tunable patch filters is presented. The methodology helps the designer to perform a theoretical analysis of the filter through a coupling matrix that includes the effect of the tuning elements used to tune the filter. This general methodology accounts for any tuning parameter desired and was applied to the design of a tunable dual-mode patch filter with independent control of center frequency and bandwidth (BW). The bandpass filter uses a single triangular resonator with two etched slots that split the fundamental degenerate modes and form the filter passband. Varactor diodes assembled across the slots are used to vary the frequency of each degenerate fundamental mode independently, which is feasible due to the nature of the coupling scheme of the filter. The varactor diode model used in simulations, their assembling, the dc bias configuration, and measured results are presented. The theory results are compared to the simulations and to measurements showing a very good agreement and validating the proposed methodology. The fabricated filter presents an elliptic response with 20% of center frequency tuning range around 3.2 GHz and a fractional BW variation from 4% to 12% with low insertion loss and high power handling with a 1-dB compression point higher than +14.5 dB.

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.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

Two sequential PCR amplifications for detection of Schistosoma mansoni in stool samples with low parasite load

Schistosomiasis constitutes a major public health problem, with an estimated 200 million individuals infected worldwide and 700 million people living in risk areas. In Brazil there are areas of high, medium and low endemicity. Studies have shown that in endemic areas with a low prevalence of Schistosoma infection the sensitivity of parasitological methods is clearly reduced. Consequently diagnosis is often impeded due to the presence of false-negative results. The aim of this study is to present the PCR reamplification (Re-PCR) protocol for the detection of Schistosoma mansoni in samples with low parasite load (with less than 100 eggs per gram (epg) of feces). Three methods were used for the lysis of the envelopes of the S. mansoni eggs and two techniques of DNA extraction were carried out. Extracted DNA was quantified, and the results suggested that the extraction technique, which mixed glass beads with a guanidine isothiocyanate/phenol/chloroform (GT) solution, produced good results. PCR reamplification was conducted and detection sensitivity was found to be five eggs per 500 mg of artificially marked feces. The results achieved using these methods suggest that they are potentially viable for the detection of Schistosoma infection with low parasite load.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.