Abstract Background Diabetes is one of the most common causes for peripheral neuropathy which warrants early diagnosis and treatment. The conventional nerve conduction studies appear to be normal if few roots are escaping lesion. In view identifying a better clinical testing method, late response index comprising parameter F wave was constructed compared with diagnosing ability other parameters...

Thompson’s groups have been extensively studied since their introduction by Thompson in the 1960s, despite the fact that Thompson’s account [7] appeared only in 1980. They have provided examples of infinite finitely presented simple groups, as well as some other interesting counterexamples in group theory (see for example, Brown and Geoghegan [3]). Cannon, Floyd and Parry [4] give an excellent ...

We prove that there is a coincidence index for the inclusion F (x) ∈ Φ(x) when Φ is convex-valued and satisfies certain compactness assumptions on countable sets. For F we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g. F is a Vietoris map). For the special case F = id, the obtained fixed point index is defined if Φ is countably condensing; the a...

Let G = (V,E) be a connected simple graph. A labeling f : V → Z2 induces an edge labeling f : E → Z2 defined by f(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ Z2, let vf (i) = |f−1(i)| and ef(i) = |(f+)−1(i)|. A labeling f is called friendly if |vf (1) − vf(0)| ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if(G) = ef (1) − ef(0). The set {if(G) | f is a...

Let f(x) be a differentiable function on the real line R, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass through P . We prove that if f ′′ is continuous and nonnegative on R, f ′′ ≥ m > 0 outside a closed interval of R, and f ′′ has finitely many zeros onR, then any point P below the graph of f...

Any vertex labeling f : V → {0, 1} of the graph G = (V, E) induces a partial edge labeling f∗ : E → {0, 1} defined by f∗(uv) = f(u) if and only if f(u) = f(v). The balance index set of G is defined as {|f∗−1(0) − f∗−1(1)| : |f−1(0) − f−1(1)| ≤ 1}. In this paper, we first determine the balance index sets of rooted trees of height not exceeding two, thereby completely settling the problem for tre...

With the proliferation of XML data and applications on the Internet, efficient XML query processing techniques are in great demand. Answering queries using XML indexes is a natural approach. A number of XML indexes have been proposed in the literature; among them, F&B Index is one powerful index as it is the smallest index that answers all twig queries. However, an F&B Index suffers from the fo...