Search results for "principal"

The diamond partial order in rings

2013

In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.

Principal eigenvalue of a very badly degenerate operator and applications

2007

Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…

Rectifiable Measures in R n and Existence of Principal Values for Singular Integrals

1995

Principal Values of Cauchy Integrals, Rectifiable Measures and Sets

1991

The extensive studies started by A. P. Calderon in the sixties and continued by many authors up today have revealed that the Cauchy integrals $$ {C_{\Gamma }}f(z) = \int_{\Gamma } {\frac{{f\left( \zeta \right)d\zeta }}{{\zeta - z}}} $$ behave very well on sufficiently regular, not necessarily smooth, curves F, see [CCFJR], [D] and [MT].

Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

2006

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …

Effects of Plant Density on the Number of Glandular Trichomes and on Yield and Quality of Essential Oils from Oregano.

2016

Plants yields are influenced by agronomic techniques. Plant density is a complex issue and extremely important when maximizing both crop quality, and biomass and essential oil yields. Plants belonging to the Origanum vulgare subspecies hirtum (Link) Ietswaart were grown adopting four types of plant density and were characterized in biometric and chemical terms. The samples were analyzed using the ANOVA (Principal Component Analysis) statistical method regarding biometric aspects, EO yield and peltate hair density. Essential oil (EO) was extracted by hydrodistillation and analyzed using GC-FID and GC-MS. GC-FID and GC-MS analysis led to the identification of 45 compounds from the EO. Plant …

Monitoring of chicken meat freshness by means of a colorimetric sensor array

2012

A new optoelectronic nose to monitor chicken meat ageing has been developed. It is based on 16 pigments prepared by the incorporation of different dyes (pH indicators, Lewis acids, hydrogenbonding derivatives, selective probes and natural dyes) into inorganic materials (UVM-7, silica and alumina). The colour changes of the sensor array were characteristic of chicken ageing in a modi¿ed packaging atmosphere (30% CO2¿70% N2). The chromogenic array data were processed with qualitative (PCA) and quantitative (PLS) tools. The PCA statistical analysis showed a high degree of dispersion, with nine dimensions required to explain 95% of variance. Despite this high dimensionality, a tridimensional re…

Multivariate data analysis of quality parameters in drinking water.

2001

The quality of water destined for human consumption has been treated as a multivariate property. Since most of the quality parameters are obtained by applying analytical methods, the routine analytical laboratory (responsible for the accuracy of analytical data) has been treated as a process system for water quality estimation. Multivariate tools, based on principal component analysis (PCA) and partial least squares (PLS) regression, are used in the present paper to: (i) study the main factors of the latent data structure and (ii) characterize the water samples and the analytical methods in terms of multivariate quality control (MQC). Such tools could warn of both possible health risks rela…

Feature selection strategies for quality screening of diesel samples by infrared spectrometry and linear discriminant analysis.

2012

Abstract A rapid approach has been developed for the characterization of diesel quality, based on attenuated total reflectance – Fourier transform infrared (ATR-FTIR) spectrometry, which could be useful for diagnosing the sample quality condition. As a supervised technique, linear discriminant analysis (LDA) was employed to process the spectrometric data. The role of variable selection methods was also evaluated. Successive projection algorithm (SPA) and genetic algorithm (GA) feature selection techniques were applied prior to the discriminative procedure. It was aimed to compare the effect of feature selection procedures on classification capability of IR spectrometry for the diesel sample…

Detection of batch effects in liquid chromatography-mass spectrometry metabolomic data using guided principal component analysis.

2014

Metabolomics based on liquid chromatography-mass spectrometry (LC-MS) is a powerful tool for studying dynamic responses of biological systems to different physiological or pathological conditions. Differences in the instrumental response within and between batches introduce unwanted and uncontrolled data variation that should be removed to extract useful information. This work exploits a recently developed method for the identification of batch effects in high throughput genomic data based on the calculation of a delta statistic through principal component analysis (PCA) and guided PCA. Its applicability to LC-MS metabolomic data was tested on two real examples. The first example involved t…