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Geometrical aspects of exact boundary controllability for the wave equation - a numerical study

M. Asch, G. Lebeau (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the wave equation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry of the controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and an energetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions...

GiANT: Graphical Algebraic Number Theory

Aneesh Karve, Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

While most algebra is done by writing text and formulas, diagrams have always been used to present structural information clearly and concisely. Text shells are the de facto interface for computational algebraic number theory, but they are incapable of presenting structural information graphically. We present GiANT, a newly developed graphical interface for working with number fields. GiANT offers interactive diagrams, drag-and-drop functionality, and typeset formulas.

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

A generalized form of the usual Lognormal distribution, denoted with γ , is introduced through the γ-order Normal distribution γ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of γ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

Shou-qiang Du, Yan Gao (2011)

Applications of Mathematics

In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

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