Search results for "Partial"
showing 10 items of 1477 documents
PIP-Space Valued Reproducing Pairs of Measurable Functions
2019
We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space Z : = Z ( X , μ ), where ( X , μ ) is a measure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbert spaces; (ii) Y is a Hilbert space, but Z is a pip-space; (iii) Y and Z are both pip-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space Y. Examples are presented for each case.
Instruction-based clinical eye-tracking study on the visual interpretation of divergence : how do students look at vector field plots?
2018
Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N = 41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88…
Banach Partial *-Algebras and Quantum Models
2007
C*-algebras are, as known, the basic mathematical ingredient of the Haag- Kastler (Haag and Kastler 1964) algebraic approach to quantum systems, with infinitely many degrees of freedom. The usual procedure starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra AV of local observables in V. The uniform completion A of the algebra generated by the AV ’s is then considered as the C*-algebra of observables of the system
Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source
2002
In this paper we deal with a Cauchy–Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, ut - Δu + |u|2 γ-2u |∇u|2 = |u|p-2u. We prove that if p ≥ 1, γ ≥ ½ and p < 2 γ + 2, then there exists a global weak solution for all initial data in L1 (Ω). We also see that there exists a non-negative solution if the initial datum is non-negative.
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 …
Determination of sugars in depilatory formulations: a green analytical method employing infrared detection and partial least squares regression.
2011
A green analytical method was developed for the analysis of sugar-based depilatories. Three independent partial least squares (PLS) regression models were built for the direct determination of glucose, fructose and maltose without any sample pretreatment based on their attenuated total reflectance - Fourier transform infrared (ATR-FTIR) spectra. The models showed adequate prediction capabilities with root-mean-square-errors of prediction ranging from 7.04 to 12.55 mg sugar g(-1) sample. As a reference procedure, gradient liquid chromatography with on-line infrared detection, employing background correction based on cubic smoothing splines, was used. The analysis revealed changes in the suga…
ATR-FTIR spectroscopy as a quality control system for monitoring the storage of blood products
2021
Blood screening is a fundamental part of disease diagnosis and monitoring health. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy offers an innovative solution to streamlining the process, especially for multianalyte detection in aqueous samples. However, samples always undergo a storage phase before they are processed for testing and blood transfusion. In this study, we investigated the effect of standard storage procedures on the macromolecular composition of whole blood, and plasma collected in blood tubes for diagnostic purposes and initial screening of blood products. Periphery blood samples were collected from 10 volunteers and then stored for 14 days a…
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…
Comparison of two partial least squares infrared spectrometric methods for the quality control of pediculosis lotions.
2006
Two vibrational spectroscopy procedures have been developed and compared for the direct and simultaneous determination of piperonyl butoxide and tetramethrin, the active ingredients of alcoholic capillary lotions, for hair pediculosis diseases. Nine lotions, purchased from the Spanish market, were analyzed using both, attenuated total reflectance (ATR) and transmission FT-IR measurements, and based on the use of partial least squares (PLS) multivariate calibration. A reduced set of 15 matched standards (11 for calibration and 4 for validation) was employed using both measurement modes. The spectral wave number ranges between 1757 and 1712 cm(-1) was selected to determine tetramethrin by bot…
Chromatographic multivariate quality control of pharmaceuticals giving strongly overlapped peaks based on the chromatogram profile
2004
In the present paper, the simultaneous quantification of two analytes showing strongly overlapped chromatographic peaks (alpha = 1.02), under the assumption that both available equipment and training of the laboratory staff are basic, is studied. A pharmaceutical preparation (Mutabase) containing two drugs of similar physicochemical properties (amitriptyline and perphenazine) is selected as case of study. The assays are carried out under realistic working conditions (i.e. routine testing laboratories). Uncertainty considerations are introduced in the study. A partial least squares model is directly applied to the chromatographic data (with no previous signal transformation) to perform quali…