Search results for "relation"
showing 10 items of 10542 documents
On orderability of fibred knot groups
2003
It is known that knot groups are right-orderable, and that many of them are not bi-orderable. Here we show that certain bred knots in S 3 (or in a homology sphere) do have bi-orderable fundamental group. In particular, this holds for bred knots, such as 41, for which the Alexander polynomial has all roots real and positive. This is an application of the construction of orderings of groups, which are moreover invariant with respect to a certain automorphism.
Weak associativity and restricted rotation
2009
A restricted rotation induced by a weak associative law is introduced. The corresponding equivalence relation is identical to the Glivenko congruence on Tamari lattices, i.e. lattices of binary trees endowed by the well-known rotation operation.
A space on which diameter-type packing measure is not Borel regular
1999
We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.
A Greedy Algorithm for Hierarchical Complete Linkage Clustering
2014
We are interested in the greedy method to compute an hierarchical complete linkage clustering. There are two known methods for this problem, one having a running time of \({\mathcal O}(n^3)\) with a space requirement of \({\mathcal O}(n)\) and one having a running time of \({\mathcal O}(n^2 \log n)\) with a space requirement of Θ(n 2), where n is the number of points to be clustered. Both methods are not capable to handle large point sets. In this paper, we give an algorithm with a space requirement of \({\mathcal O}(n)\) which is able to cluster one million points in a day on current commodity hardware.
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),…
On the decision problem for the guarded fragment with transitivity
2002
The guarded fragment with transitive guards, [GF+TG], is an extension of GF in which certain relations are required to be transitive, transitive predicate letters appear only in guards of the quantifiers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. This answers the question posed in (Ganzinger et al., 1999). Moreover, we show that the problem is 2EXPTIME-complete. This result is optimal since the satisfiability problem for GF is 2EXPTIME-complete (Gradel, 1999). We also show that the satisfiability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satisfiability pr…
On the Finite Satisfiability Problem for the Guarded Fragment with Transitivity
2005
We study the finite satisfiability problem for the guarded fragment with transitivity. We prove that in case of one transitive predicate the problem is decidable and its complexity is the same as the general satisfiability problem, i.e. 2Exptime-complete. We also show that finite models for sentences of GF with more transitive predicate letters used only in guards have essentially different properties than infinite ones.
A Local Approach to Certain Classes of Finite Groups
2003
Abstract We develop several local approaches for the three classes of finite groups: T-groups (normality is a transitive relation) and PT-groups (permutability is a transitive relation) and PST-groups (S-permutability is a transitive relation). Here a subgroup of a finite group G is S-permutable if it permutes with all the Sylow subgroup of G.
S_Kernel: A New Symmetry Measure
2005
Symmetry is an important feature in vision. Several detectors or transforms have been proposed. In this paper we concentrate on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. It is easily proven that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its flipped version. For the measure we compute a modified difference between respective surfaces of a pattern and its kernel. That founds an efficient algorithm to attention focusing on symmetric patterns.
A code to evaluate prolate and oblate spheroidal harmonics
1998
Abstract We present a code to evaluate prolate ( P n m ( x ), Q n m ( x ); n ≥ m , x > 1) and oblate ( P n m ( ix ), Q n m ( ix ); n ≥ m , x > 0) spheroidal harmonics, that is, spherical harmonics ( n and m integers) for real arguments larger than one and for purely imaginary arguments. We start from the known values (in closed form) of P m m and P m +1 m and we apply the forward recurrence relation over n up to a given degree n = N Max . The Wronskian relating P 's and Q 's, together with the evaluation of the continued fraction for Q m+N staggeredMax m / Q m+N staggeredMax -1 m , allows the calculation of Q m+N staggeredMax m and Q m+N staggeredMax -1 m . Backward recurrence is then appli…