Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-Feedback Vertex Set, k2-Feedback Edge Set and (k1,k2){Feedback Vertex/Edge Set, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets f...

The trunk of a knot in S3, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots K1 and K2, we have tr(K1#K2)= max{tr(K1), tr(K2)}, confirming a conjecture of Ozawa. Another conjecture of Ozawa asserts that any width-minimizing embedding of a knot K also minimizes the trunk of K. We produce several families...

We prove a limit relation for the Dunkl–Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei ± ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkltype Bessel function of type AN−1 with multiplicity k2. For certain values of k2 an improved estimate is obtained from a corresponding limit rela...

A distinctive syndrome caused by hypermucoviscous Klebsiella pneumoniae (HMKP) including pyogenic liver abscess (PLA) is now becoming a globally emerging disease. In the present study, 22.8% (84/369) of K. pneumoniae clinical isolates associated with various types of invasive infections were identified as HMKP, with 45.2% associated with PLA. Multivariate regression analysis showed that male pa...

Let τ(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that τ(G) = k1+k2. The question at hand is whether the vertex set V (G) can be partitioned into two subsets V1 and V2 such that τ(G[V1]) ≤ k1 and τ(G[V2]) ≤ k2. We show that several classes of graphs have this partition property.

Multiplex-PCR assay for identification of Klebsiella pneumoniae isolates carrying gene clusters for biosynthesis of capsular polysaccharide (CPS) types K1 and K2 was developed. Genes wzc and orf10 of the cps cluster were applied as K1 and K2 specific markers respectively. The assay specificity was confirmed using 147 isolates of Klebsiella spp. including 77 K-antigen reference strains. The mult...

The K2K experiment has presented the first results on the observation of νμ. They show a depletion compared to the expectations and are consistent with neutrino oscillations with a mass-splitting in the range favoured by the Super-Kamiokande atmospheric neutrino measurements. Here we examine the extent by which the range of ∆m obtained from the K2K measurements can vary due to the uncertainties...