Databases containing varied linguistic features can be build by condensing large corpora; in this work we need to cover a set of phonetic units with a minimal set of natural phonetic sentences. With this aim in view we compare three set covering methods: the greedy method, its inverse which we call the spitting method, and the pair exchange method. Each method is defined with several criteria g...

There are many results about generating pair-wise covering arrays with strength τ=2 have been reported, but fewer results are published for high-strength covering arrays with a higher-strength τ>2. In configuration testing of sensor networks, high-strength covering array is required to construct combinatorial test cases. To generate combinatorial test suite with higher-strength, a backtracking ...

A three-dimensional orbifold $(\Sigma, \gamma_i, n_i)$, where $\Sigma$ is a rational homology sphere, has universal abelian covering, whose covering group the first homology. singular pair $(X,C)$, $X$ normal surface singularity with $\mathbb Q$HS link and $C$ Weil divisor, gives rise on its boundary to an orbifold. One studies preceding notions in algebro-geometric setting, particular defining...

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

The pair correlation function g(2)(r) in a classical many-body system depends in a nontrivial way both on the number density F and on the pair interactions ν(r), and a long-standing goal of statistical mechanics has been to predict these effects quantitatively. The present investigation focuses on a restricted circumstance whereby simultaneous isothermal changes in F and ν(r) have exactly cance...

We study nonlocal symmetries of Plebanski’s second heavenly equation in an infinite-dimensional covering associated to a Lax pair with non-removable spectral parameter. show that all local sym...

A Covering Separating System on a setX is a collection of blocks in which each element of X appears at least once, and for each pair of distinct points a, b ∈ X, there is a block containing a and not b, or vice versa. An introduction to Covering Separating Systems is given, constructions are described for a class of minimal Covering Separating Systems and an application to Search Theory is pres...

A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function DE(v, 5, λ) are determined for all even integers v ≥ 5 and λ odd.

This paper introduces the sequence covering similarity, that we formally define for evaluating the similarity between a symbolic sequence (string) and a set of symbolic sequences (strings). From this covering similarity we derive a pair-wise distance to compare two symbolic sequences. We show that this covering distance is a semimetric. Few examples are given to show how this string semimetric ...

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...