309 research outputs found
Cell decomposition for semi-affine structures on p-adic fields
We use cell decomposition techniques to study additive reducts of p- adic
fields. We consider a very general class of fields, including fields with
infinite residue fields, which we study using a multi-sorted language. The
results are used to obtain cell decomposition results for the case of finite
residue fields. We do not require fields to be Henselian, and we allow them to
be of any characteristic.Comment: 22 page
Integration and Cell Decomposition in -minimal Structures
We show that the class of -constructible functions is closed
under integration for any -minimal expansion of a -adic field
. This generalizes results previously known for semi-algebraic
and sub-analytic structures. As part of the proof, we obtain a weak version of
cell decomposition and function preparation for -minimal structures, a
result which is independent of the existence of Skolem functions. %The result
is obtained from weak versions of cell decomposition and function preparation
which we prove for general -minimal structures. A direct corollary is that
Denef's results on the rationality of Poincar\'e series hold in any -minimal
expansion of a -adic field .Comment: 22 page
Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
We give a definition, in the ring language, of Z_p inside Q_p and of F_p[[t]]
inside F_p((t)), which works uniformly for all and all finite field
extensions of these fields, and in many other Henselian valued fields as well.
The formula can be taken existential-universal in the ring language, and in
fact existential in a modification of the language of Macintyre. Furthermore,
we show the negative result that in the language of rings there does not exist
a uniform definition by an existential formula and neither by a universal
formula for the valuation rings of all the finite extensions of a given
Henselian valued field. We also show that there is no existential formula of
the ring language defining Z_p inside Q_p uniformly for all p. For any fixed
finite extension of Q_p, we give an existential formula and a universal formula
in the ring language which define the valuation ring
Cell Decomposition for semibounded p-adic sets
We study a reduct L\ast of the ring language where multiplication is
restricted to a neighbourhood of zero. The language is chosen such that for
p-adically closed fields K, the L\ast-definable subsets of K coincide with the
semi-algebraic subsets of K. Hence structures (K,L\ast) can be seen as the
p-adic counterpart of the o-minimal structure of semibounded sets. We show that
in this language, p-adically closed fields admit cell decomposition, using
cells similar to p-adic semi-algebraic cells. From this we can derive
quantifier-elimination, and give a characterization of definable functions. In
particular, we conclude that multi- plication can only be defined on bounded
sets, and we consider the existence of definable Skolem functions.Comment: 20 page
Craniofacial and intracranial Langerhans cell histiocytosis
Main Teaching Point: Multiple osteolytic calvarial lesions in a child raise suspicion of Langerhans cell histiocytosis
Tracking learning feedforward control for high speed CD-ROM
The periodic disturbances caused by the inherent eccentricity and unbalancing in compact disc systems is one of the prominent radial tracking problems in high-speed and high density optical storage systems. To compensate these periodic disturbances, a learning feedforward compensation (LFF) method is presented and investigated. Computer simulations and experimental evaluation on the high speed CD-ROM product show that the proposed LFF provides a effective way to improve the radial tracking performance by reducing the radial error by 85%
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