A remark on embedded bipartite graphs
Abstract A use of Euler's formula in Zaks ( J. Combin. Theory Ser. B 32 (1982) , 95–98) is replaced by an elementary argument on permutations.
Extending an extension of Grinberg's theorem
Abstract Grinberg's well-known necessary condition for a planar graph to be Hamiltonian was extended by Shimamoto to a condition for having a 2-factor. We derive a necessary condition for a planar graph to contain a collection of n disjoint circuits, none of which separates any other two. All is done in terms of the numbers p k which denote the numbers of k -gonal faces.
Fatigue effects on the coordinative pattern during cycling: kinetics and kinematics evaluation.
The aim of the present study was to analyze the net joint moment distribution, joint forces and kinematics during cycling to exhaustion. Right pedal forces and lower limb kinematics of ten cyclists were measured throughout a fatigue cycling test at 100% of PO(MAX). The absolute net joint moments, resultant force and kinematics were calculated for the hip, knee and ankle joint through inverse dynamics. The contribution of each joint to the total net joint moments was computed. Decreased pedaling cadence was observed followed by a decreased ankle moment contribution to the total joint moments in the end of the test. The total absolute joint moment, and the hip and knee moments has also increased with fatigue. Resultant force was increased, while kinematics has changed in the end of the test for hip, knee and ankle joints. Reduced ankle contribution to the total absolute joint moment combined with higher ankle force and changes in kinematics has indicated a different mechanical function for this joint. Kinetics and kinematics changes observed at hip and knee joint was expected due to their function as power sources. Kinematics changes would be explained as an attempt to overcome decreased contractile properties of muscles during fatigue.