This work discusses the design and construction of a robot for moving in small diameter pipes (down to 57 mm inside diameter), capable of negotiating curves, diameter changes, sharp bends and T-joints, intended for (semi) autonomous inspection of gas distribution mains. A number of fundamental design changes and improvements will be shown with respect to earlier designs. The new design is fully...

The dependence of the resistivity with changing diameter of heavily-doped self-seeded germanium nanowires was studied for the diameter range 40 to 11 nm. The experimental data reveal an initial strong reduction of the resistivity with diameter decrease. At about 20 nm a region of slowly varying resistivity emerges with a peak feature around 14 nm. For diameters above 20 nm, nanowires were found...

Diameter—the task of computing the length of a longest shortest path—is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no O(n)time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time f(k)(n+m) where k is a parameter and f is a function as small as possible. For our choices of...

In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n− 1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (S, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) ac...

We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)

The main result of the paper is to prove for every r ≥ 0 and n > n0(r) that every antichain on n vertices and consisting of more than ( n r ) sets contains two members whose symmetric difference is at least 2r + 2. The bound is best possible and all the extremal families are determined. For r ≥ 3 we show that n > 6(r + 1)2 is sufficient.

Abstract Diameter —the task of computing the length a longest shortest path—is fundamental graph problem. Assuming Strong Exponential Time Hypothesis, there is no $$O(n^{1.99})$$ O ( n 1.99 ) -tim...