Let H be a subgraph of a graph G, and let V ⊆ X. We say that an H-design (V, C) of order u and index μ is embedded into a G-design (X,B) of order v and index λ, μ ≤ λ, if there is an injective mapping f : C → B such that B is a subgraph of f(B) for every B ∈ C. The mapping f is called the embedding of (V, C) into (X,B). For every pair of positive integers v, λ, we determine the minimum value of...

Suppose G is a graph, r is a positive real number and S(r) is a circle of perimeter r. For a positive real number t ≤ r, a (t, r)circular consecutive colour-list assignment L is a mapping that assigns to each vertex v of G an interval L(v) of S(r) of length t. A circular L-colouring of G is a mapping f : V (G) → S(r) such that for each vertex v, f(v) ∈ L(v) and for each edge uv, the distance be...

A Total Mean Cordial labeling of a graph G = (V,E) is a mapping f : V (G) → {0, 1, 2} such that f(xy) = ⌈

Let Zm be the cyclic group of order m ≥ 3. A graph G is Zm-connected if G has an orientation D such that for any mapping b : V (G) 7→ Zm with ∑ v∈V (G) b(v) = 0, there exists a mapping f : E(G) 7→ Zm − {0} satisfying ∑ e∈E+ D (v) f(e) − ∑ e∈E− D (v) f(e) = b(v) in Zm for any v ∈ V (G); and a graph G is strongly Zm-connected if, for any mapping θ : V (G) → Zm with ∑ v∈V (G) θ(v) = |E(G)| in Zm, ...

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪→ H ↪→ V ∗ with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V ∗. The system is given by dx+A(dt, x) = f(t, x)γ(dt) +B(t)u(dt), x(0...

The monitoring of crops is of vital importance for food and environmental security in a global and European context. The main goal of this study was to assess the crop mapping performance provided by the 100 m spatial resolution of PROBA-V compared to coarser resolution data (e.g., PROBA-V at 300 m) for a 2250 km test site in Bulgaria. The focus was on winter and summer crop mapping with three ...