A fractional [a, b]-factor of a graph G is function h from E(G) to [0, 1] satisfying \(a \le d_G^h(v) b\) for every vertex v G, where \(d_G^h(v) = \sum\limits_{e \in E(v)} {h(e)} \) and E(v) {e uv : u ? V (G)}. called b]-covered if contains with h(e) 1 any edge e G. (a, b, k)-critical covered — Q ? V(G) ?Q? k. In this article, we demonstrate neighborhood condition be covered. Furthermore, claim...

Let G be a graph with p vertices and q edges. A total neighborhood prime labeling of is in which the edges are assigned labels from 1 to + such that gcd each non degree vertex equal 1. admits called graph. In this paper, we examine trees as (n, k, m) double star trees, spiders, caterpillars firecrackers.

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

Living in a disadvantaged neighborhood is associated with poor health outcomes even after accounting for individual-level socioeconomic factors. The chronic stress of unfavorable neighborhood conditions may lead to dysregulation of the stress reactivity and inflammatory pathways, potentially mediated through epigenetic mechanisms such as DNA methylation. We used multi-level models to examine th...

In this paper, we carry a detailed study of mechanical systems with configuration space Q −→ Q/G for which the base Q/G variables are being controlled. The overall system ́s motion is considered to be induced from the base one due to the presence of general nonholonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable ki...

and Applied Analysis 3 4. The ε-Method for Resonant Centers We recall in this section the ε-method developed in [23] which we apply here to resonant centers. We consider system (2) which we write into the form ?̇? = P (x, y) = px + F 1 (x, y) , ?̇? = Q (x, y) = −q y + F 2 (x, y) , (5) where F 1 (x, y) and F 2 (x, y) are analytic functions without constant and linear terms, defined in a neighborho...

Let $$S\subset\mathbb R^n$$ be a nonempty set. Given $$d\in [0,n)$$ and cube $$\overline{Q}\subset\mathbb with side length $$l=l(\overline{Q}) \in (0,1]$$ , we show that if the $$d$$ -Hausdorff content $$\mathcal H^d_{\infty}(\overline{Q}\cap S)$$ of set $$\overline{Q}\cap S$$ satisfies inequality S)<\overline{\lambda}l^{d}$$ for some $$\overline{\lambda}\in (0,1)$$ then $$\overline{Q}\setminus...

Let M be a closed symplectic manifold and suppose M → P → B is a Hamiltonian fibration. Lalonde and McDuff raised the question whether one always has H∗(P ;Q) = H∗(M ;Q) ⊗ H∗(B;Q) as vector spaces. This is known as the c–splitting conjecture. They showed, that this indeed holds whenever the base is a sphere. Using their theorem we will prove the c–splitting conjecture for arbitrary base B and f...