相关论文: Basis discrepancies for extensions of valued field…
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small…
In this paper we revisit the problem of computing the closure of a set of attributes given a basis of dependencies or implications. This problem is of main interest in logics, in the relational database model, in lattice theory, and in…
Expansion of real numbers is a basic research topic in number theory. Usually we expand real numbers in one given base. In this paper, we begin to systematically study expansions in multiple given bases in a reasonable way, which is a…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
We characterize those valued fields for which the image of the valuation ring under every polynomial in several variables contains an element of maximal value, or zero.
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is expressed as a product of certain degrees that appear…
We study model theoretic properties of valued fields (equipped with a real-valued multiplicative valuation), viewed as metric structures in continuous first order logic. For technical reasons we prefer to consider not the valued field…
The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one…
It is shown that an anisotropic orthogonal involution in characteristic two is totally decomposable if it is totally decomposable over a separable extension of the ground field. In particular, this settles a characteristic two analogue of a…
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
We investigate the existence of "generic derivations" in exponential fields. We show that exponential fields without additional compatibility conditions between derivation and exponentiation cannot support a generic derivation.
We study existential theories of henselian valued fields of positive characteristic with parameters from a trivially valued subfield. Compared to previous work, we relax perfectness and separability assumptions, and instead work with the…
Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems, or from fitting extrapolation parameters to reference…
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
In this paper, we show that \phi is a dependent formula if and only if all \phi-types have an extension to a \phi-isolated \phi-type that is an "elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain…