A problem to account for the direct electron-positron annihilation in positron-hydrogen scattering above the positronium formation threshold has been resolved within the time independent formalism. The generalization of the optical theorem is derived for the case when an absorption potential is present in the Hamiltonian. With this theorem the annihilation cross section is fully determined by s...

Hadronic annihilation rate of 1 heavy quarkonium is given to next-to-leading order in αs and leading order in v using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet QQ̄ component, and the annihilation of S-wave color-octet QQ̄ component of the quarkonium. The notorious infrared divergences due to soft gluons,...

Measurements of positron-on-molecule annihilation have established that positrons bind to a variety of molecules via vibrational Feshbach resonances. Data for deeply bound states in benzene and 1-chlorohexane and for positronically excited (i.e., second) bound states in alkanes are used to establish the dependence of annihilation rates on the binding energy and incident positron energy. With th...

A set S of vertices in a graph G is a dominating set if every vertex of V − S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for a...

A 2-rainbow dominating function (2RDF) of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2} such that for any vertex v ∈ V (G) with f(v) = ∅ the condition ⋃ u∈N(v) f(u) = {1, 2} is fulfilled, where N(v) is the open neighborhood of v. The weight of a 2RDF f is the value ω(f) = ∑ v∈V |f(v)|. The 2-rainbow domination number of a graph G, denoted by γr2...

The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n2 and α ′ = a, or (2) a < n2 and there is a vertex v ∈ V (G) such that α(G − v) = a(G), where α is the critical independence number of the graph....

A set S of vertices in a graph G is a 2-dominating set if every vertex of G not in S is adjacent to at least two vertices in S. The 2-domination number γ2(G) is the minimum cardinality of a 2-dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the nondecreasing degree sequence of G is at most the number of edges in G. The conjectu...

The signed-particle Monte Carlo method for solving the Wigner equation has made multi-dimensional solutions numerically feasible. The latter is attributable to the concept of annihilation of independent indistinguishable particles, which counteracts the exponential growth in the number of particles due to generation. After the annihilation step, the particles regenerated within each cell of the...