A tree is said to be -magic if there exits a super magic labeling such that then the vertices of is partioned into three color classes , , so that the vertex labels in ∈ {1,2,3} are all consecutive labels. In this paper we have given -magic labeling of a class of trees with diameter four that...

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical methods based on the stationary point, proper...

Our goal here is to prove the existence of a nontrivial critical point to the following functional,by using the well-known Mountain-Pass Theorem with Cerami Palais-Smale condition when (•) grows faster than ||

In this paper we consider the problem —Δ = () + () in Ω, = 0 on , where λ ∈ (0, ∞), Ω is a strictly convex bounded and domain in R with ≥ 2, 1 < < 2, — 1 < < : (0, ∞) → (0, ∞) is a nonincreasing, and locally Lipchitz continuous function (that may be singular at 0) and : [0, ∞) → (0, ∞) is a contnuous and nondecreasing function satisfying inf<0 () > 0, 0 < lim∞ () < ∞. We prove that there exists λ* > 0 such that for 0 λ λ* the above problem has at least two positive solutions in Π (Ω) and that λ = 0 is a bifurcation point...</lim∞></<>

Let Ω be a bounded domain in ℝ We characterize the set of positive principal eigenvalues for the Dirichlet periodic parabolic problem = λ () in Ω × ℝ, under the assumptions that is a function such that ζ → () is continuously differentiable and nonincreasing in [0, ∞) a.e. () ∈ Ω...

A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA...

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's marginal contribution during the bargaining process. The...

Left-truncation or censoring of lifetime observation occurs in many applications. For instance, a crack on the body of a plane may become visible after it starts, a study may permit a process that has progressed to certain level, or a clinical trial may admit a subject who contracted the disease...

In the standard probabilistic approach to information retrieval it is commonly assumed that the occurrence of query terms are conditionally independent given a relevant or non-relevant document. Together with the Probability Ranking Principle, this assumption has led to the development of binary...