We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model’s infection rates are varied through a control parameter, for which two natural transition points are defined as: i. λT , the value up to which the infection dies out exponentially fast if introduced at a single site, and ii. ...

We consider the system ⎧ ⎨ ⎩ −Δ p u = λF (x, u, v), x ∈ Ω, −Δ q v = λH(x, u, v), x ∈ Ω, u = 0 = v, x ∈ ∂Ω, where F (x, u, v) = [g(x)a(u) + f (v)], H(x, u, v) = [g(x)b(v) + h(u)], Ω is a bounded domain in R N (N ≥ 1) with smooth boundary ∂Ω, λ is a real positive parameter and Δ s z = div (|∇z| s−2 ∇z), s > 1, (s = p, q) is a s-laplacian operator. Here g is a C 1 sign-changing function that may b...

The electronic structures and charge transport properties of 1,3,5-tripyrrolebenzene (TPB) and its substituted derivatives with –F and –CN groups have been investigated by DFT calculations in combination with the Marcus hopping model. The dimer geometry was optimized by density functional theory method with dispersion force correction being included (DFT-D). Consequently, the charge transfer in...

Using Polyakov’s functional integral approach and the Liouville action functional defined in [ZT87c] and [TT03a], we formulate quantum Liouville theory on a compact Riemann surface X of genus g > 1. For the partition function 〈X〉 and correlation functions with the stress-energy tensor components 〈n i=1 T (zi ) ∏l k=1 T̄ (w̄k)X〉, we describe Feynman rules in the background field formalism by expan...

The dominant eigenvalue (Λ) is the long run growth rate of the epidemic and provides a threshold criterion such that outbreak will grow if Λ > 1 and decline if Λ < 1. In this model, which ignores susceptible depletion, Λ is always the effective reproduction number (Reff ) in that it is the average number of secondary infections in a population comprised of community-treated and hospital-treated...

The lower limit to string coupling unification in weakly coupled heteroticstrings was shown by Kaplunovsky to be around ΛH ∼ 5 × 1017 GeV. Incontrast, under the scenario of an intermediate scale desert, the SU(3)C ×SU(2)L × U(1)Y ([321]) Minimal Supersymmetric Standard Model (MSSM)unification scale is ΛU ∼ 2.5 × 1016 GeV. Optical unification was proposed by Giedt as a ro...

Let G = (V + s,E) be a graph and let S = (d1, ..., dp) be a set of positive integers with ∑ dj = d(s). An S-detachment splits s into a set of p independent vertices s1, ..., sp with d(sj) = dj , 1 ≤ j ≤ p. Given a requirement function r(u, v) on pairs of vertices of V , an S-detachment is called r-admissible if the detached graph G satisfies λG′(x, y) ≥ r(x, y) for every pair x, y ∈ V . Here λH...

In this paper, we analyze the Lax-Wendroff discontinuous Galerkin (LWDG) method for solving linear conservation laws. The method was originally proposed by Guo et al. in [11], where they applied local discontinuous Galerkin (LDG) techniques to approximate high order spatial derivatives in the Lax-Wendroff time discretization. We show that, under the standard CFL condition τ ≤ λh (where τ and h ...

Proof. The result follows by direct manipulation of the terms. Lemma S2 Suppose that the k×k matrices A and B have bounded spectral norms ‖A‖ ≤ λ and ‖B‖ ≤ λ, for some fixed positive constant λ. Then ∥∥∥Ah −Bh∥∥∥ ≤ hλh−1 ‖A−B‖ , for h = 1, 2, .... (A.1) Proof. We establish this result by backward induction. It is clear that it holds for h = 1. For h = 2, using the identity A −B = A(A−B) + (A−B)...

We consider a general Schrödinger operator L + V on a domain E ⊂ R, and its associated positive ground state h solution to the maximal eigenvalue problem L(h) + V h = λh. In this work, an interacting particle model approximating the pair (h, λ) is studied. When V ≤ 0, a basic version of this particle system consists of N walkers evolving independently according to the Markov generator L, each w...