Search results for "Solutions"
showing 10 items of 757 documents
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
2017
Abstract We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the solution tends to the fundamental solution, (iii) optimal L 2 -decay of mild solutions in all dimensions, (iv) L 2 -decay of weak solutions via energy methods. The first result relies on a delicate analysis of the definition of classical solutions. After proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of (ii). Next we use Fourier analysis techniques to obtain the optimal dec…
Decalcifying effects of antimicrobial irrigating solutions on root canal dentin
2012
Objective: The aim of this study was to determine the decalcifying efficacy of 7% maleic acid (MA), 2% chlorhexidine (CHX), and combinations of 7% MA + 0.2% cetrimide (CTR) and 2% CHX + 0.2% CTR, in four time periods. Study Design: Four specimens per tooth were obtained from a 2-mm thick slice of the cervical third of the root of ten human incisors. At 1, 2, 3 and 5 minutes of immersion, the concentrations of Ca2+ were measured by atomic absorption spectrophotometry. The results were analyzed using the Mann-Whitney U-test. Results: Statistically significant differences were seen for the extracted calcium in all time periods. The amount of calcium extracted by 7% MA was the highest at all fo…
Estimating radiant fields in flat heterogeneous photoreactors by the six-flux model
2006
Heterogeneous photoreactor modeling is a task complicated by the integro-differential nature of the Radiation Transfer Equation (RTE) when scattering phenomena are important. In the present work, a novel “Six Flux Model” (SFM) is proposed, which may be regarded as a step forward with respect to the previously proposed “Two Flux Model” (TFM). In order to validate the newly proposed model, Monte Carlo simulations of an indefinite plane-slab photoreactor have been performed. As no simplifying assumptions are involved in this case, the information obtained may be regarded as “pseudo-experimental,” and therefore compared with the predictions of both TFM and SFM models. Results show that the nove…
Periodic solutions for a class of second-order Hamiltonian systems
2005
Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.© 2005 Texas State University - San Marcos.
Protein diffusion through charged nanopores with different radii at low ionic strength
2014
[EN] The diffusion of two similar molecular weight proteins, bovine serum albumin (BSA) and bovine haemoglobin (BHb), through nanoporous charged membranes with a wide range of pore radii is studied at low ionic strength. The effects of the solution pH and the membrane pore diameter on the pore permeability allow quantifying the electrostatic interaction between the chargedpore and the protein. Because of the large screening Debye length, both surface and bulk diffusion occur simultaneously. By increasing the pore diameter, the permeability tends to the bulk self-diffusion coefficient for each protein. By decreasing the pore diameter, the charges on the pore surface electrostatically hinder …
Analysis of a parabolic cross-diffusion population model without self-diffusion
2006
Abstract The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to disappear. The last assumption complicates the analysis since these terms usually provide H 1 estimates of the solutions. The existence proof is based on a positivity-preserving backward Euler–Galerkin approximation, discrete entropy estimates, and L 1 weak compactness arguments. Furthermore, employing the entropy–entropy production method, we show for special stationary solutions that the transient solution converges exponentially fast to its…
Selective and Sensitive Chromogenic Detection of Cyanide and HCN in Solution and in Gas Phase
2013
Two triphenylmethane based chemodosimeters for selective and chromogenic sensing of cyanide anions in aqueous environments and of hydrogen cyanide in gas phase were prepared and studied.
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Application of sequential injection analysis to pharmaceutical analysis.
2005
Sequential injection analysis is a well established tool for automation of pharmaceutical analysis. A short historical background of this technique is given as well as a brief discussion on the basic principles and potentials. The current applications of SIA in the pharmaceutical analysis are also described and discussed. The manifolds developed offer good analytical characteristics and are suitable for analysis of drug formulations, process analysis, drug-dissolution, drug-release testing and functional assays for screening potential drugs. The results obtained are in good agreement with those furnished by the application of the reference methods presented in the pharmacopoeias.
Development of predictive retention-activity relationship models of tricyclic antidepressants by micellar liquid chromatography.
1999
The distribution of tricyclic antidepressants from plasma to brain, where these drugs exert their main clinical action, and other organs is related to transport events across the cell membranes of the different tissues. It could be expected that all the molecular features that condition the transport processes (mainly hydrophobicity and molar total charge) also control the pharmacokinetic and biochemical behavior. Micellar liquid chromatography (MLC) has been proposed to emulate in vitro the partitioning process in the biomembranes. The use of micellar solutions of Brij35 as mobile phases in reversed-phase liquid chromatography has proven to be valid to predict the biological activities of …