In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show nth number is interpreted as ways tile 1×n board with cells labeled 1,2,...,n using colored 1×1 squares 1×2 dominoes, where there are p kind colors for q dominoes. Then circular also present...

We raise and investigate the algorithmic complexity of the following problem. Given a graph G = (V; E) and p-element sets L(v) for its vertices v 2 V such that jL(u) L(v)j p + r for all edges uv 2 E, do there exist q-element subsets C (v) L(v) with C (u) \ C (v) = ; for all uv 2 E ? Here p; q; r are positive integers, p q and p + r 2q. We characterize precisely which triples (p; q; r) admit a p...

ν = q · P M = E − E is the lepton’s energy loss in the nucleon rest frame (in earlier literature sometimes ν = q · P ). Here, E and E′ are the initial and final lepton energies in the nucleon rest frame. Q = −q2 = 2(EE′−−→k · −→k )−ml −ml′ where ml(ml′) is the initial (final) lepton mass. If EE′ sin(θ/2) ≫ m2l , m2l′ , then ≈ 4EE′ sin(θ/2), where θ is the lepton’s scattering angle with respect ...

1399) Topology of the potential energy surface (PES) along the PT and ET reaction coordinates (q p and q e) predicted by the theory with no solvent overlap (q e and q p orthogonal,) and at the condition pH = pK a (AH) and E applied = E CPET = E ET. The solvent overlap ̅ í µí¼† = 0 quantifies the coupling between the solvent modes along the PT and ET reaction coordinates. The SPET is kinetically ...

Let τ(G) and τG(e) denote the number of spanning trees of a graph G and the number of spanning trees of G containing edge e of G, respectively. Ferrara, Gould, and Suffel asked if, for every rational 0 < p/q < 1 there existed a graph G with edge e ∈ E(G) such that τG(e)/τ(G) = p/q. In this note we provide constructions that show this is indeed the case. Moreover, we show this is true even if we...