Search results for "algebra"

Motivic Pattern Extraction in Symbolic Domain

2008

This chapter offers an overview of computational research in motivic pattern extraction. The central questions underlying the topic, concerning the formalization of the motivic structures, the matching strategies and the filtering of the results, have been addressed in various ways. A detailed analysis of these problems leads to the proposal of a new methodology, which will be developed throughout the study. One main conclusion of this review is that the problems cannot be tackled using purely mathematic or geometric heuristics or classical engineering tools, but require also a detailed understanding of the multiple constraints derived by the underlying cognitive context.

Tsen–Lang Theory for Cpi-fields

1995

On totally permutable products of finite groups

2005

[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, PT, and PST-groups.

Learning from good examples

1995

The usual information in inductive inference for the purposes of learning an unknown recursive function f is the set of all input /output examples (n,f(n)), n ∈ ℕ. In contrast to this approach we show that it is considerably more powerful to work with finite sets of “good” examples even when these good examples are required to be effectively computable. The influence of the underlying numberings, with respect to which the learning problem has to be solved, to the capabilities of inference from good examples is also investigated. It turns out that nonstandard numberings can be much more powerful than Godel numberings.

Unification in first-order transitive modal logic

2019

We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤⁠. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…

Hartmanis-Stearns Conjecture on Real Time and Transcendence

2012

Hartmanis-Stearns conjecture asserts that any number whose decimal expansion can be computed by a multitape Turing machine is either rational or transcendental. After half a century of active research by computer scientists and mathematicians the problem is still open but much more interesting than in 1965.

O* - Dynamical Systems and * - Derivations of Unbounded Operator Algebras

1999

A spatial theory is developed for * - derivations of an algebra of unbounded operators, in terms of the concept of O*-dynamical systems. Three notions of spatiality emerge, depending on the nature of the corresponding generator. Special emphasis is put on O*-dynamical systems generated by one-parameter groups of *-automorphisms and their *-derivations.

Equivalence Problem of Composite Class Diagrams

2001

Multiplicity constraints in a UML composite class diagram may be inconsistent. An algorithm is given for eliminating all such inconsistencies. Using this algorithm an algorithm is constructed which for two given composite class diagrams solves the equivalence problem. These algorithms can be embedded in CASE tools for automated detection of multiplicity inconsistencies.

Star representations of E(2)

1990

We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.

Arithmetic Problems Formulation and Working Memory Load

1987

First, third, and fifth graders (French children in American-numbered grades) were asked to solve arithmetic problems in which an initial state was modified by two successive transformations. Three independent variables were manipulated systematically. First, the unknown state was either the final state (Sl) or the initial state (S2). Second, either the known state (01) or the transformations (02) appeared in the first place in the problem wording. Third, the question was either located at the end (Ql) or at the beginning (42) of the problem text. As anticipated, these modifications strongly affected the performances at every age: S1 appears clearly easier than S2; 0 1 leads to a better per…