Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in 2 and 3 dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative).Comment: 26 pages, 20 figure

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian

We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimisers do not depend on $\alpha$, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on $\alpha$. We derive a Wolf-Keller type result for this problem and show that optimal eigenvalues grow at most with $n^{1/N}$, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further show that the gap between consecutive eigenvalues does go to zero as $n$ goes to infinity. Numerical results then support the conjecture that for each $n$ there exists a positive value of $\alpha_{n}$ such that the $n^{\rm th}$ eigenvalue is minimised by $n$ disks for all $0<\alpha<\alpha_{n}$ and, combined with analytic estimates, that this value is expected to grow with $n^{1/N}$

On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

A systematic AQbD approach for optimization of the most influential experimental parameters on analysis of fish spoilage-related volatile amines

The volatile amines trimethylamine (TMA) and dimethylamine (DMA) could be used as important spoilage indices for seafood products, assisting in the determination of the rejection period. In the present study, a systematic analytical duality-by-design (AQbD) approach was used as a powerful strategy to optimize the most important experimental parameters of headspace solid-phase microextraction (HS-SPME) and gas chromatography-mass spectrometry (GC-MS) conditions for the quantification of TMA and DMA in Sparus aurata. This optimization enabled the selection of the best points in the method operable design region for HS-SPME extraction (30 min; 35 ◦C; NaOH 15 M and NaCl 35%, w/v) and GC-MS analysis (80 ◦C; gradient 50 ◦C/min; flow rate 1 mL/min and splitless mode). The rejection day, estimated through the TMA concentration (>12 mg/100 g, at days 9–10), was compared with sensory (quality index method: day 7–8), physical (Torrymeter: day 8–9), and microbial (day 9–10) analysis, corroborating the suitability of the proposed approach for estimating the period for which they will retain an acceptable level of eating quality from a safety and sensory perspective.info:eu-repo/semantics/publishedVersio

Chemical Differentiation of Sugarcane Cultivars Based on Volatile Profile and Chemometric Analysis

Sugarcane (SC) is a perennial grass widely cultivated in tropical and subtropical regions. However, its cultivation in Europe is residual, where Madeira Island, Portugal, is the only region where SC continues to be extensively cultivated. For the first time, the volatile profiles of regional cultivars were established by solid-phase microextraction combined with gas chromatography− mass spectrometry. Different volatile profiles for each cultivar were recognized, identifying 260 volatile organic compounds belonging to 15 chemical classes, such as aldehydes, alcohols, ketones, hydrocarbons, esters, and terpenes. Chemometric analysis procedure, namely, one-way ANOVA with Tukey’s test, principal component analysis, partial least-square analysis, linear discriminant analysis, and hierarchical clustering analysis, allowed the differentiation between all regional cultivars. This study represents an important contribution for the maintenance of biodiversity and subsistence of the SC industry in Europe. Furthermore, it is also a valuable contribution to establish the typicality of traditional SC-based products, such as SC honey.info:eu-repo/semantics/publishedVersio

A Predictive Strategy Based on Volatile Profile and Chemometric Analysis for Traceability and Authenticity of Sugarcane Honey on the Global Market

Sugarcane honey (SCH) is a syrup produced on Madeira Island and recognized by its unique aroma, a complex attribute of quality with an important influence on the final consumer’s acceptance of the product, and determined by a complex mixture of a large number of volatile organic compounds (VOCs) generated during its traditional making process and storage. Therefore, the purpose of this study was to establish the volatile profile of genuine SCH produced by a regional certified producer for seven years and compare it with syrups from non-certified regional producers and with producers from different geographical regions (Spain, Egypt, Brazil and Australia), as a powerful strategy to define the volatomic fingerprint of SCH. Different volatile profiles were recognized for all samples, with 166 VOCs being identified belonging to different chemical classes, including furans, ketones, carboxylic acids, aldehydes and alcohols. Chemometric analysis allowed (i) the differentiation between all syrups, being more pronounced between SCH and other syrups; and (ii) the identification of 32 VOCs as potential markers for the traceability and authenticity of SCH on the global market.info:eu-repo/semantics/publishedVersio

Effect of processing and storage on the volatile profile of sugarcane honey: A four-year study

Sugarcane honey (SCH) is a syrup from Madeira Island recognized by its unique and excellent aroma, associated to volatile organic compounds (VOCs) generated during the well-defined five stages of its traditional making process. The establishment of volatile profile throughout all SCH-making stages during four years, allowed the evaluation of the influence of each stage in the typical characterisitcs of SCH. One hundred eighthy seven VOCs were identified, being associated to several origins and formation pathways. VOCs formed during stage 1 and 2 were originate from raw material, and its oxidation (i.e. enzymatic browning) and thermal degradation (i.e. lipid oxidation, Maillard reactions, Strecker degradation). In stage 3 and 4, the caramelization and melanoidin degradation also occurred, while in stage 5, the thermal degradation continues, followed by microbial activity. Chemometric analysis allowed to identify 35 VOCs as potential markers for processing control by the producers and as guarantee of the typicality and authenticity of SCH. Based on the obtained results, we propose for the first time an innovative schematic diagram explaining the potential reactions and pathways for VOCs formation during the different steps of the SCH production.info:eu-repo/semantics/publishedVersio

Physiological arousal quantifying perception of safe and unsafe virtual environments by older and younger adults

Physiological arousal has been increasingly applied to monitor exploration (or navigation) of a virtual environment (VE), especially when the VE is designed to evoke an anxiety-related response. The present work aims to evaluate human physiological reactions to safe and unsafe VEs. We compared the effect of the presence of handrails in the VE in two different samples, young and older adults, through self-reports and physiological data: Electrodermal activation (EDA) and electrocardiogram (ECG) sensors. After navigation, self-report questionnaires were administered. We found that the VEs evoked a clearly differentiated perception of safety and unsafety demonstrated through self-reports, with older adults being more discriminative in their responses and reporting a higher sense of presence. In terms of physiological data, the effect of handrails did not provoke significant differences in arousal. Safety was better operationalized by discriminating neutral/non-neutral spaces, where the reaction of older adults was more pronounced than young adults. Results serve as a basis for orienting future experiments in the line of VE and applied physiology usage in the architectural spaces design process. This specific work also provided a basis for the development of applications that integrate virtual reality and applied biofeedback, tapping into mobility and ageing.info:eu-repo/semantics/publishedVersio