Search results for "Mathematica"
showing 10 items of 7971 documents
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
A navigation and control algorithm for the position tracking of underwater vehicles
2014
In this paper we consider position control of underwater vehicles through inversion of differential kinematics based on uncalibrated, relative to the water, velocity sensors and unknown marine current. An estimation algorithm, based on the above measurements, estimates calibration parameters and marine current, assuring convergence of the estimated velocities to the true quantities. A kinematic control algorithm assures convergence to zero of the position tracking error. An extension of the basic estimation algorithm has been considered, in which position measurements are considered sampled at low rate and randomly spaced in time. Computer simulations are given of the proposed position trac…
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Invariant approximation results in cone metric spaces
2011
Some sufficient conditions for the existence of fixed point of mappings satisfying generalized weak contractive conditions is obtained. A fixed point theorem for nonexpansive mappings is also obtained. As an application, some invariant approximation results are derived in cone metric spaces.
Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point
2014
This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value prob…
On the numerical solution of some finite-dimensional bifurcation problems
1981
We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.
Strict quasi-concavity and the differential barrier property of gauges in linear programming
2014
Concave gauge functions were introduced to give an analytical representation of cones. In particular, they give a simple and a practical representation of the positive orthant. There is a wide choice of concave gauge functions with interesting properties, representing the same cone. Besides the fact that a concave gauge cannot be identically zero on a cone(), it may be continuous, differentiable and even on its interior. The purpose of the present paper is to present another approach to penalizing the positivity constraints of a linear programme using an arbitrary strictly quasi-concave gauge representation. Throughout the paper, we generalize the concept of the central path and the analyti…
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Resonance of minimizers forn-level quantum systems with an arbitrary cost
2004
We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls ( i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead of looking for minimizers on the sphere one is reduced to look just for minimizers on the sphere . Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal mi…
Discretization estimates for an elliptic control problem
1998
An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function like where h is the discretization parameter and is an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization proc…