Let G be a k-connected graph of order n. In [1], Bondy considered a degree sum condition for a graph to have a hamiltonian cycle, say, to be covered by one cycle. He proved that if σk+1(G) > (k+1)(n− 1)/2, then G has a hamiltonian cycle. On the other hand, concerning a degree sum condition for a graph to be covered by two cycles, Enomoto et al. [4] proved that if k = 1 and σ3(G) ≥ n, then G can...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

The Taguchi design of experiments was used to test the relative importance of medium components and environmental factors on poly(β-hydroxybutyrate)(PHB) production by Ralstonia eutropha. The optimum condition was obtained as: fructose concentration, 15 g/L; C/N ratio, 7.4; agitation speed 200 rpm; culture time, 40 h; temperature, 25 ° C; seed age, 15 h. At optimu...

We give a sufficient condition for a simple graph G to have k pairwise edge-disjoint cycles, each of which contains a prescribed set W of vertices. The condition is that the induced subgraph G[W ] be 2k-connected, and that for any two vertices at distance two in G[W ], at least one of the two has degree at least |V (G)|/2 + 2(k − 1) in G. This is a common generalization of special cases previou...

Expansive soils can be found in many parts of the world particularly in arid and semi-arid regions. These soilspose a significant hazard to civil engineering structures due to its high swelling and shrinkage potential. This paperpresents the results of an experimental program developed to investigate the effect of cyclic drying and wetting on theswelling potential of expansive soils with variou...

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

Let G be an edge-colored graph. A heterochromatic path of G is such a path in which no two edges have the same color. dc(v) denotes the color degree of a vertex v of G. In a previous paper, we showed that if dc(v) ≥ k for every vertex v of G, then G has a heterochromatic path of length at least dk+1 2 e. It is easy to see that if k = 1, 2, G has a heterochromatic path of length at least k. Sait...

to study general combining ability (gca) and estimation of heterosis in sunflower inbred lines for seed yield and other three agronomic traits, 68 inbred lines crossed with open pollination variety lakumka. in next year inbred lines along with topcrosses were planted in rcbd with 2 replications under two moisture conditions in sararood agricultural research station. analysis of variance in both...

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

Heterogeneous proton exchange membranes (PEM) are synthesized using the dry phase inversion technique. The casting solutions are prepared by dispersing a finely ground cation exchange resin particle in N,N-dimethylacetamide (DMAc) solution of polyvinyl-chloride (PVC). Results show that ion exchange capacity is increased with the addition of 1 %-wt nanosilica (from 0.14 to 0.27 meq/g) while it i...