Search results for "solutions"

Rational solutions to the mKdV equation associated to particular polynomials

2021

International audience; Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.

Approche de deux théories sur l’origine des conflits et démocratie au regard de la sapientielle africaine

2020

National audience

The mKdV equation and multi-parameters rational solutions

2021

Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .

Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…

Steady‐state solutions of the aerotaxis problem

2022

We study the steady-state system of aerotaxis equations in higher dimensions.It is shown that the existence and multiplicity of solutions depend on the totalmass of the colony of bacteria, the energy function, and the boundary conditions.

Growth and characterization of anodic films on Sc in aqueous solutions

2008

Temperature effect on solubility of aroma compounds in various aqueous solutions

2005

International audience; Solubility of nine aroma compounds (methyl ketones, ethyl esters, aldehyde and alcohol) in various aqueous solutions was measured by the mutual solubility method from -10 to +10degreesC. Influence of both, the nature (carbohydrates and polyols) and the substrate concentration (from 0 to 57.5g/100g) on aroma solubility in aqueous solutions was studied. Aroma solubility in water decreased when aroma hydrophobicity increased. Aroma solubility in various aqueous solutions decreased when substrate concentration increased; their solubility was higher in polyols solutions than in polysaccharides ones. Temperature effect on aroma solubility showed a noncontinuous evolution f…

About the link between the detailed description of transitions in a ion and the average-ion models.

2009

We study the link which exists between microscopic (detailed) models for the evolution of the electronic configurations in a population of ions and the macroscopic (average ion) models. Rigorous asymptotics are presented in situations where they exist (large temperature; almost empty or almost full shells), and numerical simulations are presented.

Preorganization and reorganization as related factors in enzyme catalysis: the chorismate mutase case.

2003

In this paper a deeper insight into the chorismate-to prephenate-rearrangement, catalyzed by Bacillus subtilis chorismate mutase, is provided by means of a combination of statistical quantum mechanics/molecular mechanics simulation methods and hybrid potential energy surface exploration techniques. The main aim of this work is to present an estimation of the preorganization and reorganization terms of the enzyme catalytic rate enhancement. To analyze the first of these, we have studied different conformational equilibria of chorismate in aqueous solution and in the enzyme active site. Our conclusion is that chorismate mutase preferentially binds the reactive conformer of the substrate--that…

Quality of Inclusive Educational System for Work with Students with Autism Different Needs in Italy

2015

The need for realization of inclusive education, which is the basis of a sustainable education, will require new challenges in the Education System. The system used in Italy can be used as an example. Italy passed avant-garde laws concerning the integration and inclusion of special needs students into the general school system already more than thirty years ago, in the 1970s. However, even after all this time and experience, there are still unresolved problems, which testifies to the complexities of the matter. This research offers an insight into the quality of the existing Italian inclusive education system specifically in relation to students with autism. Thereby it hopes to provide educ…