Abstracts - Facultatea de Matematică

elevant circumstances : selective dissociation, creation of particular molecular states,
remote detection, high frequency laser generation, etc.
These models are expressed in terms of equations that are bi-linear (the control multiplies
the state). After an initial presentation of the applications and mathematical
implications of the experimental settings, we will discuss in this talk two types of results:
ensemble controllability and numerical algorithms. While in the first, geometrical
Lie group controllability theory is used, in the second we will deal with numerical algorithms
and their relationship with the designing of optimal control cost functionals.
Relationships with both theoretical works on PDE control and experimental algorithms
will also be presented.
Local uniform linear openness of multifunctions and calculus of
Bouligand–Severi tangent sets
Corneliu URSESCU
“Octav Mayer” Institute of Mathematics, Romanian Academy, Ia¸si Branch
8 Carol I blvd., 700506 Ia¸si, România
corneliuursescu@yahoo.com
Let X and Y be linear spaces, and let F : X → Y be a multifunction. For every
tangency concept τ and for every point (a, b) ∈ X × Y the equality
graph(τF (a, b)) = τgraph(F )(a, b)
defines a multifunction τF (a, b) : X → Y , and moreover, the equality
τ F −1 (b)(a) = (τF (a, b)) −1 (0)
is expected. Here, F −1 : Y → X stands for the inverse of the multifunction F . In
the following we consider the specific tangency concept K which originates from the
tangent half-lines considered by Bouligand (1931) and Severi (1931). The multifunction
KF (a, b) was introduced by Aubin (1981). Because of the elementary inclusion
the equality
K F −1 (b)(a) ⊆ (KF (a, b)) −1 (0),
K F −1 (b)(a) = (KF (a, b)) −1 (0)
is strongly expected. This equality is established at all points (a, b) ∈ graph(F ) assuming
local uniform linear openness of F . Local uniform linear openness of F is investigated
through a metric result concerning local uniform ω−openness of F . It is also established
the equivalence between local uniform ω−openness of F and local metric regularity of
F .
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