Multiplicity theorems for superlinear elliptic problems

In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions. This paper was completed while the first author was visiting the University of Aveiro as an Invited Scientist. The hospitality and financial support of the host institution are gratefully acknowledged. The second and third authors acknowledge the partial financial support of the Portuguese Foundation for Science and Technology (FCT) under the research project POCI/MAT/55524/2004.     

Psychoacoustics of in-car switch buttons: From feelings to engineering parameters

The car interior is becoming quieter and other sounds are now exposed to user perception, such as the sound produced by interface buttons when actuated. So, the functional role of the button sound on interface operation and its aesthetic and emotional role on the user experience are now more important than before. However, little research and design effort has been paid to understand how to design buttons that produce a pleasant sound. Moreover, the button’s sound requirements received by interface manufacturers are ill-defined, insufficient or even inexistent, and consequently their conversion into specifications for manufacturing is problematic and leads to long and costly development processes. The purpose of this paper is to contribute to identify relevant acoustic parameters that explain the users sound preferences. Data on preference subjective judgments were collected and buttons acoustic signals were measured allowing the development of preference models based on partial least squares regression and neural networks methods. The former was successful in selecting the relevant parameters to describe the preference ratings of the buttons sound. The later, dealing with the non-linear nature of acoustic perception, was able to predict preferences based on the relevant parameters.     

Asymptotic stability and bifurcations of 3D piecewise smooth vector fields

The paper deals with the analysis of the behavior of a nonsmooth three-dimensional vector field around a typal singularity. We focus on a class of generic one-parameter families \({Z_{\lambda}}\) of Filippov systems and address the persistence problem for the asymptotic stability when the parameter varies near the bifurcation value \({\lambda = 0}\).     

Influence of temperature on performance of an anaerobic sequencing biofilm batch reactor with circulation applied to treatment of low-strength wastewater

The effect of temperature on the performance of an anaerobic sequencing biofilm batch reactor (ASBBR) with liquid-phase recirculation was assessed. Assays were performed using a recirculation velocity of 0.20 cm/s, 8-h cycles, and an average treated synthetic wastewater volume of 2 L/cycle with a concentration of 500 mg of Chemical Oxygen Demand (COD)/L. Operation temperatures were 15, 20, 25, 30, and 35°C. At 25, 30, and 35°C, organic matter removal efficiencies for filtered samples ranged from 81 to 83%. At lower temperatures, namely 15 and 20°C, removal efficiency decreased significantly to 61 and 65%, respectively. A first-order model could be fitted to the experimental concentration profile values. The first-order kinetic parameter value of this model varied from 0.46 to 0.81 h¹ considering the lowest and highest temperature studied. Moreover, analysis of the removal profile values allowed fitting of an Arrhenius-type equation with an activation energy of 5715 cal/mol.     

Infrared spectroscopy and outer product analysis for quantification of fat, nitrogen, and moisture of cocoa powder

The combination of the near infrared (NIR) and Fourier-transform infrared (FTIR) absorbance spectra (1100-2500 nm and 4000-600 cm⁻¹) of 100 cocoa powder samples was used to build calibration models for the determination of the content of fat, nitrogen, and moisture. The samples that comprised the dataset had an average composition of 13.51% of fat, 3.77% nitrogen, and 3.98% moisture. The fat content ranged from 2.42 to 22.00%, the nitrogen from 0.88 to 4.48%, and moisture from 1.60 to 7.80%. For NIR, the relative root mean square error of cross-validation (RMSECV) was 7.0% (R² = 0.96) for fat, 1.7% (R² = 0.98) for nitrogen, and 5.2% (R² = 0.94) for moisture. For FTIR, the relative RMSECV was 10.4% (R² = 0.94) for fat and 3.9% (R² = 0.95) for nitrogen. However, for moisture, it was not possible to build a calibration model with suitable predictability. The combination of the NIR and FTIR domains (data fusion) by outer product analysis PLS1 allowed to predict these parameters and to characterise frequencies in one domain based on the information of the other domain. This work allows to conclude that the second derivative of NIR is the recommended procedure to quantify fat, nitrogen, and moisture content in cocoa powders by infrared spectroscopy.     

A multi-commuted flow injection system with a multi-channel propulsion unit placed before detection: Spectrophotometric determination of ammonium

A flow system with a multi-channel peristaltic pump placed before the solenoid valves is proposed to overcome some limitations attributed to multi-commuted flow injection systems: the negative pressure can lead to the formation of unwanted air bubbles and limits the use of devices for separation processes (gas diffusion, dialysis or ion-exchange). The proposed approach was applied to the colorimetric determination of ammonium nitrogen. In alkaline medium, ammonium is converted into ammonia, which diffuses over the membrane, causing a pH change and subsequently a colour change in the acceptor stream (bromothymol blue solution). The system allowed the re-circulation of the acceptor solution and was applied to ammonium determination in surface and tap water, providing relative standard deviations lower than 1.5%. A stopped flow approach in the acceptor stream was adopted to attain a low quantification limit (42 μg L⁻¹) and a linear dynamic range of 50–1000 μg L⁻¹ with a determination rate of 20 h⁻¹.     

Surface tensions of imidazolium based ionic liquids: anion, cation, temperature and water effect

This work addresses the experimental measurements of the surface tension of eight imidazolium based ionic liquids (ILs) and their dependence with the temperature (288-353 K) and water content. The set of selected ionic liquids was chosen to provide a comprehensive study of the influence of the cation alkyl chain length, the number of cation substitutions and the anion on the properties under study. The influence of water content in the surface tension was studied for several ILs as a function of the temperature as well as a function of water mole fraction, for the most hydrophobic IL investigated, [omim][PF(6)], and one of the more hygroscopic IL, [bmim][PF(6)]. The surface thermodynamic functions such as surface entropy and enthalpy were derived from the temperature dependence of the surface tension values.     

Design and Functionalization of a µPAD for the Enzymatic Determination of Nitrate in Urine

In this work, the design of a microfluidic paper-based analytical device (μPAD) for the quantification of nitrate in urine samples was described. Nitrate monitoring is highly relevant due to its association to some diseases and health conditions. The nitrate determination was achieved by combining the selectivity of the nitrate reductase enzymatic reaction with the colorimetric detection of nitrite by the well-known Griess reagent. For the optimization of the nitrate determination μPAD, several variables associated with the design and construction of the device were studied. Furthermore, the interference of the urine matrix was evaluated, and stability studies were performed, under different conditions. The developed μPAD enabled us to obtain a limit of detection of 0.04 mM, a limit of quantification of 0.14 mM and a dynamic concentration range of 0.14–1.0 mM. The designed μPAD proved to be stable for 24 h when stored at room temperature in air or vacuum atmosphere, and 60 days when stored in vacuum at −20 °C. The accuracy of the nitrate μPAD measurements was confirmed by analyzing four certified samples (prepared in synthetic urine) and performing recovery studies using urine samples.     

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 ε‐neighborhood of a portion Γ of the boundary. We assume that this ε‐neighborhood shrinks to Γ as the small parameter ε goes to zero. Also, we suppose the upper boundary of this ε‐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 Γ, which depends on the oscillating neighborhood. Copyright © 2012 John Wiley & Sons, Ltd.