578,603 research outputs found
Lexicographic choice functions
We investigate a generalisation of the coherent choice functions considered
by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no
Archimedeanity condition. We define our choice functions on vector spaces of
options, which allows us to incorporate as special cases both Seidenfeld et
al.'s (2010) choice functions on horse lotteries and sets of desirable gambles
(Quaeghebeur, 2014), and to investigate their connections. We show that choice
functions based on sets of desirable options (gambles) satisfy Seidenfeld's
convexity axiom only for very particular types of sets of desirable options,
which are in a one-to-one relationship with the lexicographic probabilities. We
call them lexicographic choice functions. Finally, we prove that these choice
functions can be used to determine the most conservative convex choice function
associated with a given binary relation.Comment: 27 page
Polynomial functions on non-commutative rings - a link between ringsets and null-ideal sets
Regarding polynomial functions on a subset of a non-commutative ring ,
that is, functions induced by polynomials in (whose variable commutes
with the coefficients), we show connections between, on one hand, sets such
that the integer-valued polynomials on form a ring, and, on the other hand,
sets such that the set of polynomials in that are zero on is an
ideal of .Comment: 9 pages, conference paper for "advances in algebra ..." at Ton Duc
Thang University, Vietnam, Dec 18-20, 201
Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov Functions
This work addresses the problem of estimating the region of attraction (RA)
of equilibrium points of nonlinear dynamical systems. The estimates we provide
are given by positively invariant sets which are not necessarily defined by
level sets of a Lyapunov function. Moreover, we present conditions for the
existence of Lyapunov functions linked to the positively invariant set
formulation we propose. Connections to fundamental results on estimates of the
RA are presented and support the search of Lyapunov functions of a rational
nature. We then restrict our attention to systems governed by polynomial vector
fields and provide an algorithm that is guaranteed to enlarge the estimate of
the RA at each iteration
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