The theory of generic difference fields

Download
2003
Yıldırım, İrem
A difference field M , is a field with a distinguished endomorphism, is called a generic difference field if it is existentially closed among the models of the theory of difference fields. In the language Ld, by a theorem of Hrushovski, it is characterized by the following: M is an algebraically closed field, s is an automorphism of M, and if W and V are varieties defined over M such that W is a subset of VU s (V ) and the projection maps W to V and W to s(V ) are generically onto, then there is a tuple a in M such that (a, s ( a)) in W. This thesis is a survey on the theory of generic difference fields, called ACFA, which has been studied by Angus Macintyre, Van den Dries, Carol Wood, Ehud Hrushovski and Zoe Chatzidakis. ACFA is the model completion of the theory of algebraically closed difference fields. It is very close to having full quantifier elimination, but it doesn't. We can eliminate quantifiers down to formulas with one quantifier and hence obtain the completions of ACFA. This entails the decidability of the theory ACFA as well as its extensions obtained by specifying the characteristic. The fixed field of s is a pseudo-finite field.

Suggestions

Neural network calibrated stochastic processes: forecasting financial assets
Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01)
If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
On the foundations of parameter estimation for generalized partial linear models with B-splines and continuous optimization
TAYLAN, PAKİZE; Weber, Gerhard Wilhelm; Liu, Lian; Yerlikaya-Ozkurt, Fatma (Elsevier BV, 2010-07-01)
Generalized linear models are widely used in statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms with a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on the penalized maximum likelihood and the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines, which is attract...
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity
Taşeli, Hasan (Elsevier BV, 2004-03-01)
The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
Unified treatment of spacelike and timelike SO(3,1) Yang-Mills fields
Dundarer, AR (Springer Science and Business Media LLC, 2001-07-01)
SO(3, 1) valued Yang-mills fields stemming from spacelike and timelike vectors that were studied separately in earlier works are unified by introducing a parameter lambda that takes values in the interval [-1, 1].
Steering of redundant robotic manipulators and spacecraft integrated power and attitude control-control moment gyroscopes
Altay, Alkan; Tekinalp, Ozan; Department of Aerospace Engineering (2005)
In this thesis, recently developed Blended Inverse (B-inverse) steering law is applied to two different redundant actuator systems. First, repeatability of Binverse is demonstrated on a redundant robotic manipulator. Its singularity avoidance and singularity transition performance is also demonstrated on the same actuator system. It is shown that B-inverse steering law provides singularity avoidance, singularity transition and repeatability. Second, its effectiveness is demonstrated for an Integrated Power ...
Citation Formats
İ. Yıldırım, “The theory of generic difference fields,” M.S. - Master of Science, Middle East Technical University, 2003.