Search results for " solution"
showing 10 items of 3084 documents
Comparison of the Photoelectronic and Photocatalytic Activities of Various Anatase and Rutile Forms of Titania in Pure Liquid Organic Phases and in A…
1996
Various titania samples of industrial origin (Degussa and Tioxide) have been characterized by electrical photoconductance measurements and tested as photocatalysts in various liquid media (either pure organic liquids or aqueous solutions) as a function of their structure (anatase versus rutile). Anatase was constantly found more active than rutile, whatever the reaction chosen (mild oxidation of pure cyclohexane and 2-propanol; total degradation of phenol and nitrophenol isomers in water). In identical conditions, Degussa was found more active, but the intrinsic activity, expressed in moles converted per hour and per square meter of active surface, was found slightly higher for anatase Tiox…
Development of a polydimethylsiloxane–thymol/nitroprusside composite based sensor involving thymol derivatization for ammonium monitoring in water sa…
2014
This report describes a polydimethylsiloxane (PDMS)-thymol/nitroprusside delivery composite sensor for direct monitoring of ammonium in environmental water samples. The sensor is based on a PDMS support that contains the Berthelot's reaction reagents. To prepare the PDMS-thymol/nitroprusside composite discs, thymol and nitroprusside have been encapsulated in the PDMS matrix, forming a reagent release support which significantly simplifies the analytical measurements, since it avoids the need to prepare derivatizing reagents and sample handling is reduced to the sampling step. When, the PDMS-thymol/nitroprusside composite was introduced in water samples spontaneous release of the chromophore…
By-products in the rearrangement of N-methyl-N-phenylnitramine
1998
Abstract N-Methyl-N-phenylnitramine was rearranged in the aqueous dioxane — sulphuric acid mixture to 2-nitro- and 4-nitro-N-methylanilines. The isomer ratio was independent of the acidity within the range of −0.3 > Ho > −2.8. Some by-products were isolated and identified e.g. N-methyl-N-nitrosoaniline, its 2-nitro and 4-nitro derivatives, nitrosobenzene and 4′,4″-bis-(N-methylamino)-3′,3″-dinitrodiphenylmethane. The mechanism of the nitramine rearrangement is discussed.
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
2005
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
Numerical study of the long wavelength limit of the Toda lattice
2014
We present the first detailed numerical study of the Toda equations in $2+1$ dimensions in the limit of long wavelengths, both for the hyperbolic and elliptic case. We first study the formal dispersionless limit of the Toda equations and solve initial value problems for the resulting system up to the point of gradient catastrophe. It is shown that the break-up of the solution in the hyperbolic case is similar to the shock formation in the Hopf equation, a $1+1$ dimensional singularity. In the elliptic case, it is found that the break-up is given by a cusp as for the semiclassical system of the focusing nonlinear Schr\"odinger equation in $1+1$ dimensions. The full Toda system is then studie…
Families of solutions to the CKP equation with multi-parameters
2020
We construct solutions to the CKP (cylindrical Kadomtsev-Petviashvili)) equation in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions are called solutions of order N ; they depend on 2N − 1 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions up to order 5 and we study the patterns of their modulus in plane (x, y) and their evolution according to time and parameters.
Global existence and uniqueness result for the diffusive Peterlin viscoelastic model
2015
Abstract The aim of this paper is to present the existence and uniqueness result for the diffusive Peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids. The polymers are treated as two beads connected by a nonlinear spring. The Peterlin approximation of the spring force is used to derive the equation for the conformation tensor. The latter is the time evolution equation with spatial diffusion of the conformation tensor. Using the energy estimates we prove global in time existence of a weak solution in two space dimensions. We are also able to show the regularity and consequently the uniqueness of the weak solution.
Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition
2021
The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
2004
A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.