A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

in order to examine the effect of the quantity of nitrogen fertilizer and bush density on vegetative and productive function of henna medicinal plant (lawsonia inermis)  factorial experimentation in the form of block plan was carried in three stages in agriculture research center in south of kerman  province in corp of 2012. the first factor containing nitrogen fertilizer in 4 levels including ...

In this paper we obtain the bound on the average sensitivity of the weighted sum function. This confirms a conjecture of Shparlinski. We also compute the weights of the weighted sum functions and show that they are almost balanced.

where the constant c = c(L, p) > 0 does not depend of n and Pn, and μn(L, h, p) → ∞, as n → ∞, depending on geometrical properties of the curve L and the weight function h in neighborhoods of {zj}mj=1. The classical results of (2)-type can be found in [5], [8]. The estimation of (2)-type was investigated by [6], [7, pp.122-133], [4], [1]-[3] and others. In this work, we investigate the conditio...

Let D be a pseudoconvex domain in Ckt × C n z and let φ be a plurisubharmonic function in D. For each t we consider the ndimensional slice of D, Dt = {z; (t, z) ∈ D}, let φ be the restriction of φ to Dt and denote by Kt(z, ζ) the Bergman kernel of Dt with the weight function φ. Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0) we prove that logKt(z, z) is ...

In the present article we extend the best constant approximant operator from Lorentz spaces Γp,w to Γp−1,w for any 1 < p <∞ and w ≥ 0 a locally integrable weight function, and from Γ1,w to the space of all measurable functions L0. Then we establish several properties of the extended best constant approximant operator and finally, we prove a generalized version of the Lebesgue Differentiation Th...

In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound on the average sensitivity of the weighted sum Boolean function remains unchanged after the simplification.

Using recent results of Berman and Boucksom [BB2] we show that for a non-pluripolar compact set K ⊂ C d and an admissible weight function w = e −φ any sequence of so-called optimal measures converges weak-* to the equilibrium measure µ K,φ of (weighted) Pluripotential Theory for K, φ.