We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F . We show that the latter dependency can be made exponential in the rank difference rank(F )− rank(H), which often makes a significant change....

Anaerobic threshold is widely used for diagnosis of swimming aerobic endurance but the precise incremental protocols step duration for its assessment is controversial. A physiological and biomechanical comparison between intermittent incremental protocols with different step lengths and a maximal lactate steady state (MLSS) test was conducted. 17 swimmers performed 7×200, 300 and 400 m (30 s an...

The use of different commercial Bacillus thuringiensis (Bt) products in the Bajio guanajuatense area in Mexico began 12 yr ago, and resistance to Bt in this area has been reported for Plutella xylostella (L.) The current study provides a baseline response and resistance potential to Bt in field and laboratory strains of Bajio Trichoplusia ni (Hübner). Differences in susceptibility to Bt among T...

  Abstract   Background: Traumatic or congenital events can result in injury and functional   deficiency in the hand and we need to reconstruct the fingers at times. Studies are   available in the pediatric and adult age groups to assess the length of the thumb. But   to the best our knowledge no measurement of the relative clinical length of all fingers   has been reported in the literature. W...

A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity Of G, denoted by lak(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In case that the lengths of paths are not restricted, we then have the linear arboricity ofG, denoted by la(G). In this paper, the exact values of th...