Search results for " formula"

Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term

2001

Abstract Our aim in this article is to study the following nonlinear elliptic Dirichlet problem: − div [a(x,u)·∇u]+b(x,u,∇u)=f, in Ω; u=0, on ∂Ω; where Ω is a bounded open subset of RN, with N>2, f∈L m (Ω) . Under wide conditions on functions a and b, we prove that there exists a type of solution for this problem; this is a bounded weak solution for m>N/2, and an unbounded entropy solution for N/2>m⩾2N/(N+2). Moreover, we show when this entropy solution is a weak one and when can be taken as test function in the weak formulation. We also study the summability of the solutions.

Perfluoroalkyl substances in Breast milk, infant formula and baby food from Valencian Community (Spain)

2016

Environmental and human exposures to perfluoroalkyl substances (PFASs) are of emerging concern since they are persistent and bioaccumulative. The present study reports PFASs levels in human milk, infant formulas and baby food (dry cereals and pots) from the Valencian Community (Spain) in order to evaluate the infant exposure to these substances through the diet. The results show that perfluorobutanoic acid (PFBA) and perfluorooctanoic acid (PFOA) were in all the samples of the four selected matrices (except PFOA in one sample of dry cereal baby food). Perfluoroheptanoic acid (PFHpA) and perfluorodecanoic acid (PFDA) were also detected in 70% of the breast milk samples. In infant formulas, P…

Theoretical study of a Bénard Marangoni problem

2011

[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…

Calcium bioavailability in human milk, cow milk and infant formulas—comparison between dialysis and solubility methods

1999

Abstract The percentages of total, soluble and dialysable calcium of human milk, cow milk and milk and soy based infant formulas were determined in order to detect possible differences in the calcium bioavailability of the samples. For this purpose an in vitro method was applied to these four calcium sources. The ranking of the analysed samples in terms of calcium bioavailability depends on the criteria applied. Calcium ranked dialysis percentage was: cow milk>human milk>soy based formula>milk based formulas. Calcium ranked solubility percentage was: human milk>cow milk>soy-based formula>milk-based formulas. Comparison of the results of the in vitro assay with the information available on i…

A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

2010

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Evaluation of nutritional parameters in infant formulas and powdered milk by Raman spectroscopy

2007

It has been made a critical evaluation of the application of near infrared Fourier transform-Raman spectroscopy for the simultaneous determination of the most important nutritional parameters such as energetic value, carbohydrate, protein and fat contents of infant formula and powdered milk samples based on the use of partial least squares (PLS) regression analysis. A highly heterogeneous population of 23 samples, covering a wide range of infant food formula and powdered milk, were obtained from the Spanish market. Raman spectra, obtained by excitation with a Nd:YAG laser at 1064 nm, show no disturbing fluorescence effects; therefore sample spectra can be recorded without any previous prepa…

Solution of a cauchy problem for an infinite chain of linear differential equations

2005

Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.

Regularity of solutions of cauchy problems with smooth cauchy data

1988

Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems

2002

AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.

Experimental Study of Central Baffle Flume

2019

In this paper, the hydraulics of a central baffle flume (CBF) were experimentally studied. Extensive experimental runs were carried out to highlight the effects of different geometrical parameters such as baffle length, contraction ratio, and the length of upstream and downstream guide walls. Two different approaches, i.e., the Π theorem of dimensional analysis coupled with the incomplete self-similarity theory and the energy balance equation, were applied to deduce the stage–discharge formula of a CBF characterized by different geometrical parameters. The stage–discharge relationship deduced by the dimensional analysis approach was more accurate than that obtained by the energy approach. F…