For two vertices u and v in a connected graph G, the set I(u, v) consists of all those vertices lying on a u − v geodesic in G. For a set S of vertices of G, the union of all sets I(u, v) for u, v ∈ S is denoted by I(S). A set S is convex if I(S) = S. The convexity number con(G) is the maximum cardinality of a proper convex set in G. A convex set S is maximum if |S| = con(G). The cardinality of a maximum convex set in a graph G is the convexity number of G. For a nontrivial connected graph H, a connected graph G is an H-convex graph if G contains a maximum convex set S whose induced subgraph is S = H. It is shown that for every positive integer k, there exist k pairwise nonisomorphic graphs H1, H2,...,Hk of the same order and a graph G that is Hi-convex for all i (1 ≤ i ≤ k). Also, for every connected graph H of order k ≥ 3 with convexity number 2, it is shown that there exists an H-convex graph of order n for all n ≥ k + 1. More generally, it is shown that for every nontrivial connected graph H, there exists a positive integer N and an H-convex graph of order n for every integer n ≥ N.
Paper deals with subject of identification of aerostatic journal bearings dynamic properties with use of Rotor Kit Bently Nevada superstructure. Different bearing types were experimentally investigated and their static and dynamic characteristics were identified. Various methods of identification were used and spectral and modal properties of the system were calculated. Computer program was revised on the basis of experimental data. The influence of non-diagonal stiffness and damping elements was investigated by numeric stimulation. and Obsahuje seznam literatury
We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used.
Young (12 years old) Norway spruce {Picea abies [L.] Karst.) trees were exposed to ambient CO2 or ambient + 350 |niiol(C02) moL' continuously over 2 growing seasons in open-top chambers, under field conditions of a mountain stand. Comprehesive analysis of CO2 assimílation was performed after 4 and 22 weeks of the second growing season to evaluate the influence of elevated atmospheric CO2. A combination of gas exchange and a mathematical model of ribulose-l,5-bisphosphate carboxylase/oxygenase (RuBPCO) activity was ušed. After 4 weeks of exposure no statistically significant stimulation of the radiant energy and CO2 saturated rate of CO2 uptake (ENsat) by the elevated CO2 concentration was found. Yet after 24 weeks a statistically significant depression of Ejvjsa, (38 %) and carboxylation efficiency (32 %) was observed. Depression of photosynthetic activity by elevated CO2 resulted from a decrease in the RuBPCO carboxylation rate. The electron transport rate was also modified similarly to the rate of RuBP formation. An accompanying decrease in nitrogen content of the needles (by 12 %) together with an increase in total saccharides (by 34 %) was observed after 24 weeks of exposure to enhanced CO2.