Search results for "Computational Mathematic"

A secular equation for the Jacobian matrix of certain multispecies kinematic flow models

2010

The 1-Harmonic Flow with Values into $\mathbb S^{1}$

2013

We introduce a notion of solution for the $1$-harmonic flow, i.e., the formal gradient flow of the total variation functional with respect to the $L^2$-distance, from a domain of $\mathbb R^m$ into a geodesically convex subset of an $N$-sphere. For such a notion, under homogeneous Neumann boundary conditions, we prove both existence and uniqueness of solutions when the target space is a semicircle and the existence of solutions when the target space is a circle and the initial datum has no jumps of an “angle” larger than $\pi$. Earlier results in [J. W. Barrett, X. Feng, and A. Prohl, SIAM J. Math. Anal., 40 (2008), pp. 1471--1498] and [X. Feng, Calc. Var. Partial Differential Equations, 37…

On the propagation of error in certain non-linear algorithms

1959

On the structure of certain ultradistributions

2009

Let "o" be a nonempty open subset of the k-dimensional euclidean space Rk. In this paper we show that, if S is an ultradistribution in "o", belonging to a class of Roumieu type stable under differential operators, then there is a family f, 2 Nk 0, of elements of L1 loc("o") such that S is represented in the formP2Nk 0 D"a"f "a". Some other results on the structure of certain ultradistributions of Roumieu type are also given.

Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le ca…

1999

Consider a sub-riemannian geometry (U,D,g) where U is a neighborhood of 0 in R 3 , D is a Martinet type distribution identified to ker ω , ω being the 1-form: , q=(x,y,z) and g is a metric on D which can be taken in the normal form : , a=1+yF(q) , c=1+G(q) , . In a previous article we analyze the flat case : a=c=1 ; we describe the conjugate and cut loci , the sphere and the wave front . The objectif of this article is to provide a geometric and computational framework to analyze the general case. This frame is obtained by analysing three one parameter deformations of the flat case which clarify the role of the three parameters in the gradated normal form of order 0 where: , . More generall…

Estimates for the constants of Landau and Lebesgue via some inequalities for the Wallis ratio

2014

Comparison of electron density properties in frozen and relaxed electronic distributions.

2003

Two kinds of electron densities for several small molecules (H(2), FH, CH(3)CH(3), CH(3)NH(2), CH(3)OH, and CH(3)F) have been generated for a wide range of bond distances. The first one, as the sum of the electron density of the isolated fragments, and the second one by optimizing the electron density at each given geometrical disposition. A number of properties of this two electronic distributions have been compared (position of the bond critical points, electron density, Laplacian, curvatures, and local energies). The differences, associated to the bond formation, are found to be very important for most of the cases.

On finite element approximation of the gradient for solution of Poisson equation

1981

A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.

Iterative approximation to a coincidence point of two mappings

2015

In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.

OPKINE, a multipurpose program for kinetics

1991

The program OPKINE is presented for the study of reaction mechanisms and multicomponent analysis in dynamic conditions. This program is written in FORTRAN-77 for IBM 30/90 and VAX 8300 computers, and permits the simultaneous evaluation of both rate constants and initial reagent concentrations or, alternatively, rate constants and sensitivities. Up to 20 kinetic curves, with up to 400 points each, can be treated to evaluate up to 40 parameters. Integration of the system of differential equations is performed by means of the Runge–Kutta–Fehlberg method. OPKINE is provided with the Simplex, and modified versions of the Davidon–Fletcher–Powell and Gauss–Newton–Marquardt optimization methods. A …