Search results for "Combinatorics"
showing 10 items of 1770 documents
Quasianalytic Denjoy-Carleman classes and o-minimality
2003
We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure conditions. Some of these structures do not admit analytic cell decomposition, and they show that there is no largest o-minimal expansion of the real field.
Two Questions of L. A. Shemetkov on Critical Groups
1996
Throughout the paper we consider only finite groups. Let X be a class of groups. A group G is called s-critical for X , or simply X-critical, if G is not in X but all proper subgroups of G are in X. w Ž .x Ž . Following Doerk and Hawkes 3, VII, 6.1 , we denote Crit X the class s of all X-critical groups. Knowledge of the structure of the groups in Ž . Crit X for a class of groups X can often help one to obtain detailed s information for the structure of the groups belonging to X. Ž w Ž .x. O. J. Schmidt see 5, III, 5.2 studied the N-critical groups, where N is the formation of the nilpotent groups. These groups are also called w x Schmidt groups. In 2 , answering to a question posed by Shem…
LR(k) Parsing
1990
In this chapter we shall generalize the notion of strong LL(k) parsing presented in Chapter 5 and consider a method for deterministic left parsing that applies to a slightly wider class of context-free grammars than does the strong LL(k) parsing method. This method will be called “canonical LL(k) parsing”. As in strong LL(k) parsing, the acronym “LL(k)” means that the input string is parsed (1) in a single Left-to-right scan, (2) producing a Left parse, and (3) using lookahead of length k.
A local approach to a class of locally finite groups
2003
This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe cℒ̄ of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.
Lp-Spaces
1998
For (X, ℜ, μ) a positive measure space, it has already been noted that μ - a.e. equality is an equivalence relation, and the relation ≤ μ-a.e. a preorder, on.This section studies the structure of the equivalence classes into which μ-a,e. equality partitions.Since the set X/X( ℜ) is always u-null (2.7.7 a)), only the function values on the set X(ℜ) have any significance when equivalence classes are formed: whether we form equivalence classes by partitioning or by partitioningX(ℜ) the resulting structures will be isomorphic. Nevertheless, it is natural to allow functions on an arbitrary X ⊃ X(ℜ). Our choice is to form μ-equivalence classes by partitioning the set X(ℜ). For arbitrary X ⊃ X(ℜ),…
Analytic extension of non quasi-analytic Whitney jets of Roumieu type
1997
Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr≥ 1 for every r ∈ ℕ and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function ƒ on ℝn belonging to the non quasi-analytic (Mr)-class of Roumieu type, there is an element g of the same class which is analytic on ℝnF and such that Dα ƒ(x) = Dαg(x) for every σ ∈ ƒ0n SBAP and x ∈ F.
Generators of Random Processes in Ultrametric Spaces and Their Spectra
2009
The L 2(\( \mathbb{S} \)) space of square integrable functions on an ultrametric space \( \mathbb{S} \) has rather specific structure. As a consequence in a natural way there appear in L 2(\( \mathbb{S} \)) the operators of which unitary counterparts in L 2(ℝn) would be difficult to construct. Such class of self-adjoint operators emerge from theory of random processes on ultrametric spaces. In this paper we collect known material on spectral properties of the generators of random processes on \( \mathbb{S}_B \) an ultrametric space of sequences. (The set of p-adic numbers is a subset of \( \mathbb{S}_B \).) Then we discuss structure of the eigenspaces of the generators.
Classification générique de synthèses temps minimales avec cible de codimension un et applications
1997
In this article we consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraints belonging to a manifold of codimension one, for systems of the form v = X + uY, v ϵ R2, R3, |u| ≤ 1 under generic assumptions. The analysis is localized near the terminal manifold and is motivated by the problem of controlling a class of chemical systems.
Co-learnability and FIN-identifiability of enumerable classes of total recursive functions
1994
Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. number…
Exceptional Configurations of Quantum Walks with Grover’s Coin
2016
We study search by quantum walk on a two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. We show what the most natural coin transformation -- Grover's diffusion transformation -- has a wide class of exceptional configurations of marked locations, for which the probability of finding any of the marked locations does not grow over time. This extends the class of known exceptional configurations; until now the only known such configuration was the "diagonal construction" by [AR08].