Search results for "solution"
showing 10 items of 5638 documents
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 …
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
2004
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
Aqueous enzymatic process assisted by microwave extraction of oil from yellow horn (Xanthoceras sorbifolia Bunge.) seed kernels and its quality evalu…
2013
Abstract In this study, aqueous enzymatic process (AEP) assisted by microwave extraction (ME) of oil from yellow horn ( Xanthoceras sorbifolia Bunge.) seed kernel was investigated. Central composite design (CCD) and response surface methodology (RSM) were used to optimise an enzyme cocktail (cellulase, hemicellulase, pectinase) for AEP. The main factors of ME were also studied. A maximal oil extraction yield of 55.8% was achieved under optimal conditions. Moreover, scanning electron microscope (SEM) was applied to characterise the extraction process. Analysing chemical composition of the extracted oil by GC–MS showed that the content of unsaturated fatty acids by this emerging method (91.18…
Complementary mobile-phase optimisation for resolution enhancement in high-performance liquid chromatography.
2000
An optimisation methodology in high-performance liquid chromatography (HPLC) is presented for the selection of two or more mobile phases having an optimal complementary resolution. The complementary mobile phases (CMPs) are selected in such a way that each one resolves optimally only some compounds in the mixture, while the remainder, resolved by the other mobile phase(s), can overlap among them. The methodology is based on the computation of a peak purity measurement for each solute, using an asymmetrical peak model for peak simulation. Two global resolution criteria (product of elementary resolutions and worst elementary resolution) and two methods for solving the problem (a systematic ex…
Quality control Fourier transform infrared determination of diazepam in pharmaceuticals
2007
A quality control procedure has been developed for the determination of diazepam in pharmaceuticals using Fourier transform infrared (FTIR) spectroscopy. The method involves the off-line extraction of diazepam with chloroform by sonication and direct determination in the extracts through peak area measurement in the interval between 1672 and 1682 cm(-1) using a baseline correction defined between 1850 and 1524 cm(-1). For standardization it was used an external calibration line established from standard solutions of diazepam in chloroform. The method provides a limit of detection of 0.04 mg per tablet (n=5), a relative standard deviation (R.S.D.) of 0.5% for 5 independent measurements of a …
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…
Enantiomeric quality control of antihistamines in pharmaceuticals by affinity electrokinetic chromatography with human serum albumin as chiral select…
2007
The present paper deals with the enantiomeric separation of six antihistaminic enantiomers by affinity electrokinetic chromatography (AEKC)-partial filling technique using human serum albumin (HSA) as chiral selector. A multivariate optimization approach of the most critical experimental variables in enantioresolution, running pH, HSA concentration and HSA plug length (SPL) was carried out since there are interactions between variables that could not be considered in an univariate optimization. The estimated and experimental resolution values obtained for antihistaminic enantiomers varied from 1.13 (for orphenadrine) to 2.15 (for brompheniramine). The optimum experimental conditions for ena…
A theoretical study of solvent effects on the conformational equilibria of neutral glycine in aqueous solution
2003
Abstract In this work conformational equilibrium of neutral glycine in solution is systematically investigated by using DFT and MP2 methods combined with solvent continuum models. A systematic exploration of the potential energy surface and full geometry optimizations for several conformers have been carried out in the gas phase and aqueous solution at the MP2/6-31+G** and B3LYP/6-31+G** levels. Zero-point and thermal contributions to the free energy have been obtained at the B3LYP level. Both theoretical levels lead to very similar results, in geometrical and energetic terms, both in the gas phase and in solution. Solvent effects play an important role on the conformational equilibria of n…
Amino Acid Chemistry in Solution: Structural Study and Vibrational Dynamics of Glutamine in Solution. An ab Initio Reaction Field Model
1998
The self-consistent reaction field (SCRF) theory was used to study structural and vibrational features of the amino acid L-glutamine in solution. Raman and infrared spectra of this molecule in solutions of H 2O and D2O were recorded and measured. The bands were firstly assigned on the basis of the isotopic shifts. An ab initio quadratic force field at the 6-31 +G* level was achieved. The calculation simulated a polar solvent by placing the molecule in an ellipsoidal cavity surrounded by a continuum dielectric. The theoretical results, in terms of structural parameters, vibrational frequencies and descriptions, and infrared intensities, were in satisfactory agreement with the experimental da…