let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...

In this article, we aim to describe a new operator J_(s,a,μ)^(δ,λ) via convolution. Moreover, present subclass C_Σm (τ;β) related m-fold symmetric bi-univalent functions in the open unit disk Θ={z∈C∶|z| ˂ 1 }. Finally, an estimate Hankel determinant for are given.

Abstract . To any pair (M , θ ) , where M is a family of finite subsets of N , compact in the pointwise topology, and 0 < θ < 1 , we associate a Tsirelson-type Banach space T θ M . It is shown that if the Cantor-Bendixson index of M is greater than n and θ > 1 n then T θ M is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than ω then T θ M does not contain any l , while if t...

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...

We are given a finite set of m points (guards) G in the plane R 2 and an angle 0 ≤ Θ ≤ 2π. A Θ-cone is a cone with apex angle Θ. We call a Θ-cone empty (with respect to G) if it does not contain any point of G. A point p ∈ R is called Θ-guarded if every Θ-cone with apex located at p is non-empty. Moreover, the set of all Θ-guarded points is called Θ-region. We first show how to construct a data...

1 Problem Discuss the motion of an unbalanced tire that rolls without slipping on a horizontal surface, subject to conservation of energy. In what sense(s) can this system be said to contain " hidden momentum? " 2 Solution 2.1 The Motion We consider the tire to be a hoop of radius a and mass M that is unbalanced due to an additional mass m at some fixed point on the rim, as shown in the figure ...

Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...

In this article, we introduce the lacunary difference sequence spaces w0(M , θ,∆ n m, p, q), w1(M , θ,∆ n m, p, q) and w∞(M , θ,∆ n m, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of qlacunary ∆nm-statistical convergent sequences. Further, we study the relationship between q-lacunary ∆nm-statis...

We describe a method for recovering the underlying parametrization of scattered data (m(i)) lying on a manifold M embedded in high-dimensional Euclidean space. The method, Hessian-based locally linear embedding, derives from a conceptual framework of local isometry in which the manifold M, viewed as a Riemannian submanifold of the ambient Euclidean Space R(n), is locally isometric to an open, c...