Search results for " solution"

Highly selective fluorescence detection of hydrogen sulfide by using an anthracene-functionalized cyclam-CuII complex

2013

An anthracene-functionalised cyclam-copper(II) complex for the detection of HS- in aqueous environments has been prepared. This probe displays poor fluorescence but can selectively and sensitively detect HS- anions in water over other anions, biothiols and common oxidants such as H2O2 through remarkably enhanced emission. This turn-on response in the presence of the HS- anion is ascribed to a demetallation reaction that inhibits emission quenching observed in the initial complex as a result of the presence of the paramagnetic Cu2+ centre. Moreover, real-time fluorescence imaging measurements confirm that probe [Cu(1)](2+) can be easily used to detect intracellular HS- at micromolar concentr…

Stability and bioaccessibility of EGCG within edible micro-hydrogels. Chitosan vs. gelatin, a comparative study

2016

Micro-hydrogels are very promising systems for the protection and controlled delivery of sensitive bioactives, but limited knowledge exists regarding the impact of this encapsulation on their bioaccessibility. In this work, two different hydrogel-forming biopolymers (gelatin and chitosan) were compared as wall materials for the microencapsulation of a model flavonoid, (−)-epigallocatechin gallate (EGCG). Results showed that gelatin was more adequate as wall material for the encapsulation of EGCG than chitosan, achieving higher encapsulation efficiencies (95% ± 6%), being more effective in delaying EGCG release and degradation in aqueous solution and exhibiting a 7 times higher bioaccessibil…

Betacyanins as phenol antioxidants. Chemistry and mechanistic aspects of the lipoperoxyl radical-scavenging activity in solution and liposomes.

2009

Reaction kinetics of betanin and its aglycone betanidin towards peroxyl radicals generated from the azo-initiated oxidation of methyl linoleate in methanol, and of a heterogeneous aqueous/soybean phosphatidylcholine liposomal system, were studied by monitoring formation of linoleic acid hydroperoxides and consumption of the pigments. Betanin was a weak retarder in methanol, and an effective chain breaking antioxidant in the liposomal model, indicating that kinetic solvent effects and partition in lipid bilayers may affect its activity. Betanidin behaved as a chain terminating antioxidant in both models. Kinetic parameters characterizing peroxyl radical-scavenging activity showed that betani…

On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

2016

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Singular solutions to a quasilinear ODE

2005

In this paper, we prove the existence of infinitely many radial solutions having a singular behaviour at the origin for a superlinear problem of the form $-\Delta_pu=|u|^{\delta-1}u$ in $B(0,1)\setminus\{0\}\subset\mathbb R^N$,\, $u=0$ for $|x|=1$, where $N>p>1$ and $\delta>p-1$. Solutions are characterized by their nodal properties. The case $\delta+1 <\frac{Np}{N-p}$ is treated. The study of the singularity is based on some energy considerations and takes into account the classification of the behaviour of the possible solutions available in the literature. By following a shooting approach, we are able to deduce the main multiplicity result from some estimates on the rotation numbers asso…

Thin obstacle problem : Estimates of the distance to the exact solution

2018

We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution and any function that satisfies the boundary condition and is admissible with respect to the obstacle condition (i.e., they are valid for any approximation regardless of the method by which it was found). Computation of the estimates does not require knowledge of the exact solution and uses only the problem data and an approximation. The estimates provide guaranteed upper bounds of the error (error majorants) and vanish if and only if the approximation c…

Nonlinear nonhomogeneous Neumann eigenvalue problems

2015

We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.

On Weakly Singular Integral Equations of the Second Kind

1988

Multiple periodic solutions for Hamiltonian systems with not coercive potential

2010

Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. © 2009 Elsevier Inc. All rights reserved.

Local behaviour of singular solutions for nonlinear elliptic equations in divergence form

2012

We consider the following class of nonlinear elliptic equations $$\begin{array}{ll}{-}{\rm div}(\mathcal{A}(|x|)\nabla u) +u^q=0\quad {\rm in}\; B_1(0)\setminus\{0\}, \end{array}$$ where q > 1 and $${\mathcal{A}}$$ is a positive C 1(0,1] function which is regularly varying at zero with index $${\vartheta}$$ in (2−N,2). We prove that all isolated singularities at zero for the positive solutions are removable if and only if $${\Phi\not\in L^q(B_1(0))}$$ , where $${\Phi}$$ denotes the fundamental solution of $${-{\rm div}(\mathcal{A}(|x|)\nabla u)=\delta_0}$$ in $${\mathcal D'(B_1(0))}$$ and δ0 is the Dirac mass at 0. Moreover, we give a complete classification of the behaviour near zero of al…