Let F = (U1, U2;W ) be a forest with |U1| = |U2| = s, where s ≥ 2, and let G = (V1, V2, E) be a bipartite graph with |V1| = |V2| = n ≥ 2k + s, where k is a nonnegative integer. Suppose that the minimum degree of G is at least k+ s. We show that if n > 2k+ s then G contains the disjoint union of the forest F and k disjoint cycles. Moreover, if n = 2k+ s, then G contains the disjoint union of the...

Recently, in [4], we have discussed the following distributive equation of implications I(x, T1(y, z)) = T2(I(x, y), I(x, z)) over t-representable t-norms, generated from strict t-norms, in interval-valued fuzzy sets theory. In this work we continue these investigations, but with the assumption that T1 is generated from nilpotent t-norms, while T2 is generated from strict t-norms. As a byproduc...

A Roman dominating function on a graphG is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u ∈ V (G) for which f(u) = 0 is adjacent to at least one vertex v ∈ V (G) for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number γR(G) of G is the minimum weight of a Roman dominating function on G. A Ro...

This paper presents a new phase-based theory of verb-second and indeed model the left periphery. I argue that V-to-C movement verb to phase head Fin0 has profound repercussions on clausal syntax which explains well-known differences between Modern Germanic V2 languages Romance non-V2 with respect topicalisation. also explore how proposed analysis can account for linear restriction prefield in a...

BACKGROUND Pharmacokinetic estimates for intravenous paracetamol in individual adult cohorts are different to a certain extent, and understanding the covariates of these differences may guide dose individualization. In order to assess covariate effects of intravenous paracetamol disposition in adults, pharmacokinetic data on discrete studies were pooled. METHODS This pooled analysis was based...

We characterize a four-weight inequality involving the Hardy operator and Copson operator. More precisely, given p1,p2,q1,q2?(0,?), we find necessary sufficient conditions on non-negative measurable functions u1,u2,v1,v2 (0,?) for which there exists positive constant c such that inequality(?0?(?0tf(s)p2v2(s)p2ds)q2p2u2(t)q2dt)1q2?c(?0?(?t?f(s)p1v1(s)p1ds)q1p1u1(t)q1dt)1q1 holds every function f...

A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Define f(k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng an...

The elliptic relaxation approach of Durbin [1], which accounts for wall blocking e¤ects on the Reynolds stresses, is analysed herein from the numerical stability point of view, in the form of the v2 ¡ f . This model has been shown to perform very well on many challenging test cases such as separated, impinging and blu¤-body ‡ows, and including heat transfer. However, numerical convergence of th...

A bipartite graph G = (V1 ∪ V2, E) is (δ, d)-regular if ̨̨ d− d(V ′ 1 , V ′ 2 ) ̨̨ < δ whenever V ′ i ⊂ Vi, |V ′ i | ≥ δ|Vi|, i = 1, 2.Here, d(V ′ 1 , V ′ 2 ) = e(V ′ 1 , V ′ 2 )/|V ′ 1 ||V ′ 2 | stands for the density of the pair (V ′ 1 , V ′ 2 ). An easy counting argument shows that if G = (V1 ∪ V2 ∪ V3, E) is a 3-partite graph whose restrictions on V1 ∪V2, V1 ∪V3, V2 ∪V3 are (δ, d)regular, then ...