We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at most 1.12776. The lower bound on the si...

There is not much information about the vitamin D content of fodders and hay. Most of it is from the United States and, more recently, Holland. Keener (1954) and Weits (1956) have summarized the available information. No such assessments apparently having been made in this country, an opportunity was taken to make a systematic study of the vitamin D activity of Scottish hill pastures. Monthly s...

Yutsis graphs are connected simple graphs which can be partitioned into two vertex-induced trees. Cubic Yutsis graphs were introduced by Jaeger as cubic dual Hamiltonian graphs, and these are our main focus. Cubic Yutsis graphs also appear in the context of the quantum theory of angular momenta, where they are used to generate summation formulae for general recoupling coefficients. Large Yutsis...

 Hoor al-Azim wetland, are a large and permanent wetland area located between Iran and Iraq.  By entering the flow to the wetland area, the geometry of the wetland, acts in the form of an inverted imperfect pyramid. So that by entering the water flow, the water level of wetland is simultaneous by increasing the surface. In this study by using the geometric relationships of pyramids, was acted t...

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...

Multiphase (MP) monoclinic and cubic Y2O3 nanoparticles, 40 nm in diameter, were densified by spark plasma sintering for 5–15 min and100 MPa at 1000 C, 1100 C, and 1500 C. Densification started with pressure increase at room temperature. Densification stagnated during heating compared to the high shrinkage rate in cubic single-phase reference nanopowder. The limited densification of the MP nano...