A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class G, we let gn be the number of graphs in G which have n vertices. A recent result of Norine et al. [12] shows that for all minor-closed class G, there is a constant c such that gn ≤ c nn!. Our main results show that the growth rate of gn is far from arbit...

We reviewed 98 children (133 hips) with developmental dysplasia of the hip who underwent arthrography immediately after closed reduction by overhead traction. We followed the patients to skeletal maturity to investigate whether soft-tissue interposition influences acetabular development and avascular necrosis over the long term. The shape of the limbus and the thickness of the soft-tissue inter...

To achieve the soft-switching condition and stabilize the output voltage of quasi-resonant converters, the paper proposes a double closed-loop control method (DCCM). In the inner loop, soft-switching is guaranteed with the off-time of the switch determined by the zero-crossing signal of the switching voltage. In the outer loop, the output voltage is regulated to be constant against load variati...

25 The Traveling Salesman Problem (TSP) is still one of the most researched topics in computational mathematics, and we introduce a variant of it, namely the study of the closed k-walks in graphs. We 2 G. Bullington, R. Gera, L. Eroh And S.J. Winters search for a shortest closed route visiting k cities in a non complete graph without weights. This motivates the following definition. Given a set...

We present a framework to study control systems with feedback loops closed over wireless communication links. We show the choice of communication parameters can greatly affect the performance of such systems. The trade-offs of data rate, time delay and packet loss in the communication link layer design are illustrated with a numerical example of an inverted pendulum. Packet loss is shown to sig...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

Control of soft-bodied systems is challenging, as the absence of rigidity typically implies distributed deformations and infinite degrees-of-freedom. In this paper, we demonstrate closedloop control of three elastomer beams that vary in bending stiffness. The most stiff beam is comprised of a single prismatic structure made from a single elastomer. In the next beam, increased flexibility is int...

If a closed smooth n-manifold M admits a finite cover M̂ whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M , we show that the systole Sys(M, g) and the volume Vol(M, g) of the riemannian manifold (M, g) are related by the following isosystolic inequality: Sys(M, g) n ≤ n!Vol(M, g). The inequality can be regarded as a generalization of Burago and Hebda’s ineq...