We study finite imaginaries in certain valued fields, and prove a conjecture of Cluckers and Denef.

The concept of vector-valued multiresolution analysis on local field of positive characteristic was considered by Abdullah [Vector-valued multiresolution analysis on local fields of positive characteristic, Analysis. 34(2014) 415-428]. We construct the associated wavelet packets for such an MRA and investigate their properties by virtue of the Fourier transform. Moreover, it is shown how to obt...

The Laplace transform theory of Banach space valued functions and the field of evolution equations presently offer many research problems which are of general interest in mathematical analysis. Although there is a longstanding relationship between the two fields, it was not until recently that the basic transform principles for Banach space valued functions could be formulated in a satisfactory...

We examine fields in which model theoretic algebraic closure coincides with relative field theoretic algebraic closure. These are perfect fields with nice model theoretic behaviour. For example, they are exactly the fields in which algebraic independence is an abstract independence relation in the sense of Kim and Pillay. Classes of examples are perfect PAC fields, model complete large fields a...

We study the monoid of global invariant types modulo domination-equivalence in context o-minimal theories. reduce its computation to problem proving that it is generated by classes 1-types. show this hold Real Closed Fields, where generators correspond convex subrings monster model. Combined with [C. Ealy, D. Haskell and J. Maríková, Residue field domination real closed valued fields, Notre Dam...

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative but associative up to second order only. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebra...

The goal of segmentation is to partition an image into a finite set of regions, homogeneous in some (e.g., statistical) sense, thus being an intrinsically discrete problem. Bayesian approaches to segmentation use priors to impose spatial coherence; the discrete nature of segmentation demands priors defined on discrete-valued fields, thus leading to difficult combinatorial problems. This paper p...

A frame-like action for arbitrary mixed-symmetry bosonic massless fields in Minkowski space is constructed. The action is given in a simple form and consists of two terms for a field of any spin. The fields and gauge parameters are certain tensor-valued differential forms. The formulation is based on the unfolded form of equations for mixed-symmetry fields.

The valued function fields with given value group and residue field or with given genus and residue field are studied.

We explain how to compute in the algebraic closure of a valued field. These computations heavily rely on the Newton Polygon Algorithm. They are made in the same spirit as the dynamic algebraic closure of a field. They give a concrete content to the theorem saying that a valued field does have an algebraically closed valued extension. The algorithms created for that purpose can be used to perfor...