Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...

For graphs F , G and H , we write F → (G, H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H . The graph F is Ramsey (G, H)-minimal if F → (G, H) but F ∗ 9 (G, H) for any proper subgraph F ∗ ⊂ F . We present an infinite family of Ramsey (K1,2, C4)-minimal graphs of any diameter ≥ 4.

We report here a study of the cause of the coloration of blue zhamanshinites, which are glassy impact melt rocks from the Zhamanshin crater in the USSR. We find that the blue color results from Rayleigh scattering from spherical, 100 nm-diameter inclusions of a separate Ca-Fe-Mg-P-rich silicate glass. These observations can best be explained by the operation of liquid immiscibility in the zhama...

Although only one small PG has been identified in dentin until now, a preliminary investigation has shown indications of the presence of several new proteoglycans (PGs) in rat incisor dentin. The aim of the present investigation was to isolate and characterize these PGs, which were labeled with 35S to facilitate the analysis. C18 chromatography resolved five dentin PGs. Based on SDS-polyacrylam...

In this research modified Kaolin by Cetyltrimethylammonium bromide is used as an adsorbent for the removal of Reactive Blue 21 from aqueous solutions. Response Surface Methodology was used to study the effect of independent variables, such as Reactive Blue 21 dye concentration (20, 40, 60, 80 and 100 mg/L), time (10, 20, 30, 40 and 50), initial pH (2, 4, 6, 8 and 10) and modified Kaolin dosage ...

Serabit el-Khâdim, located on the western coast of Sinai Peninsula, is site an ancient turquoise mine established in early 12th Dynasty (c. 1985 BCE) and active between 18th 20th Dynasties 1550–1136 BCE). The temple dedicated to Hathor at detail number offerings made, thereby recording level activity during each reign. last were made by Rameses VI (1143–1136 corresponding with collapse Late Bro...

Heavy metal pollution is a worldwide problem. This study was conducted in a turquoise mine in Nyshabour (Iran) to find accumulator plant(s). Concentrations of metals were determined both in the soil and the plants growing in the mine. Concentrations of total K, Ca, Na, Mg, Mn, Zn, Fe and Cu in the mine area were higher than the control soil. The results showed that four dominant vegetations nam...

Let R and B be two disjoint sets of red points and blue points, respectively, in the plane such that no three points of R ∪ B are co-linear. Suppose ag ≤ |R| ≤ (a + 1)g, bg ≤ |B| ≤ (b + 1)g. Then without loss of generality, we can express |R| = a(g1 + g2) + (a + 1)g3, |B| = bg1 + (b + 1)(g2 + g3), where g = g1 + g2 + g3, g1 ≥ 0, g2 ≥ 0, g3 ≥ 0 and g1+g2+g3 ≥ 1. We show that the plane can be sub...