Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

routinely, a bolus of 5.000-10.000 iu human chorionic gonadotropin (hcg) is usedfor the final follicular maturation and ovulation as a standard method. hcg has thesame effect of luteinizing hormone (lh) with long half-life. it has the longlutheotrophic effect which increases the risk of ovarian hyper stimulation syndrome(ohss). recently, gonadotropin-releasing hormone agonist (gnrh-a) trigger h...

Instability in Jacobians is determined by the presence of an eigenvalue lying right half plane. The coefficients characteristic polynomial contain information related to specific matrix elements that play a greater destabilising role. Yet circuits, or cycles, constructed multiplying these together, form only subset all cycles comprising given system. This paper looks at three sign-restricted fo...