‎let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎in this paper we obtain some new results about the dependence of $|p(rz)|$ on $|p(rz)| $ for $r^2leq rrleq k^2$‎, ‎$k^2 leq rrleq r^2$ and for $rleq r leq k$‎. ‎our results refine and generalize certain well-known polynomial inequalities‎.

1 Approximation of binomial with Poisson Consider the binomial distribution b(k, n, p) = n k p k (1 − p) n−k , 0 ≤ k ≤ n Assume that n is large, and p is small, but np → λ at the limit. For a fixed λ: b(0, n, p) = n 0 p 0 (1 − p) n = (1 − p) n = (1 − λ/n) n → e −λ b(1, n, p) = n 1 p(1 − p) n−1 = np 1 − p b(0, n, p) = λ 1 − λ/n b(0, n, p) → λe −λ b(2, n, p) = n 2 p 2 (1 − p) n−2 = n(n − 1)p 2 2(...

Let k,p,q be three positive integers. A graph G with order n is said to k-placeable if there are k edge disjoint copies of in the complete on vertices. (p,q)-graph a p q edges. Packing results have proved useful study complexity properties. Bollobás et al. investigated k-placeability (n,n−2)-graphs and (n,n−1)-graphs k=2 k=3. Motivated by their results, this paper characterizes girth at least 9...

Determining the size of minimum vertex cover of a graph G, denoted by β(G), is an NP-complete problem. Also, for only few families of graphs, β(G) is known. We study the size of minimum vertex cover in generalized Petersen graphs. For each n and k (n > 2k), a generalized Petersen graph P (n, k), is defined by vertex set {ui, vi} and edge set {uiui+1, uivi, vivi+k}; where i = 1, 2, . . . , n and...

We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...