a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

Let G be a graph of order n and size m. A labeling of G is a bijective mapping θ : V(G) → {1, 2, . . . , n}, and we call Θ(G) the set of all labelings of G. For any graph G and any labeling θ ∈ Θ(G), let SL(G, θ) = ∑ e∈E(G)min{θ(u) : u ∈ e}. In this paper, we consider the S-Labeling problem, defined as follows: Given a graph G, find a labeling θ ∈ Θ(G) that minimizes SL(G, θ). The S-Labeling pr...

In the 1930’s, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski’s question and its variants continue to generate interest in the geometric and analytic aspects of coverings by planks in the present time as well. The paper is of a survey type with some new results and with a list of open research problems on the ...

tact, whereas those for a = 0.02 imply only 25% more frequent contacts than the all-ornone hypothesis but with rather high though rapidly diminishing attack rates. 10 Schuman and Doull, Amer. Jour. Pub. Health, 30, Supplement to March, 1940, p. 21, state: "From these estimates of carrier prevalence and froni the average annual increment in Shick-negatives, an estimate may be made of the number ...

For a system of smooth Jordan curves asymptotics for Christoffel functions is established almost everywhere for measures belonging to Szegő’s class. 1 The result Let μ be a finite Borel-measure on the plane with compact support consisting of infinitely many points. The Christoffel functions associated with μ are defined as λn(z, μ) = inf Pn(z)=1 ∫ |Pn|dμ, where the infimum is taken for all poly...