Nomenclature a = semi-major axis ; e = eccentricity ; ν = true anomaly ; φ(ν) = fundamental matrix of relative motion ; B(ν) = input matrix in the dynamic model of relative motion ; R(ν) = φ(ν)B(ν) = φ(ν)B(ν) = primer vector evolution matrix ; uf = φ(νf )Xf − φ(ν1)X1 6= 0 = boundary conditions ; N = number of velocity increments ; νi, ∀ i = 1, · · · , N = impulses application times ; ∆vi = impu...

Solution. Let X = E ∪ F with E,F ∈ M such that E ∩ F = ∅, E is null for ν−, and F is null for ν. Let U ⊂ X. If U ⊂ E then ν(U) = ν(U) = λ(U) − μ(U) ≤ λ(U), so λ(U) ≥ ν(U). Similarly, if U ⊂ F then μ(U) ≥ ν−(U). Now if V = U ∩ E and W = U ∩ F then V and W are measurable and ν(U) = ν(V ) ≤ λ(V ) (by the previous argument) ≤ λ(U) since λ is a positive measure. Similarly, ν−(U) = ν−(W ) ≤ μ(W ) ≤ μ...

ABSTRACT Fast neutrino (ν)-flavour conversion (FFC) is a possible game-changing ingredient in core-collapse supernova (CCSN) theory. In this paper, we examine the impact of FFC on explosive nucleosynthesis by including effects conjunction with asymmetric ν emission into nucleosynthetic computations parametric way. We find that ejecta compositions are not appreciably affected for elements lighte...

Let ν be a finite, finitely subadditive outer measure on P(X). Define ρ(E)= ν(X)− ν(E′) for E ⊂ X. The measurable sets Sν and Sρ and the set S = {E ⊂ X/ν(E) = ρ(E)} are investigated in general, and in the presence of regularity or modularity assumptions on ν . This is also done for ν0(E) = inf{ν(M)/E ⊂ M ∈ Sν}. General properties of ν are derived when ν is weakly submodular. Applications and nu...

Maximal ν µ − ν τ oscillations, the seesaw mechanism and the Exact Parity Model Abstract We examine one simple mechanism which leads to approximate maximal ν µ −ν τ oscillations in the standard seesaw model. In particular, we show that this scheme could be implemented in the Exact Parity Model (also known as the mirror matter model). Within this framework the solar neutrino problem is solved by...

For a finite graph G, we study the maximum 2-edge colorable subgraph problem and related ratio μ(G) ν(G), where ν(G) is matching number of size largest in any pair (H,H′) disjoint matchings maximizing |H|+|H′| (equivalently, forming subgraph). Previously, it was shown that 4 5≤μ(G) ν(G)≤1, class graphs achieving 5 completely characterized. In this paper, first show decompositions into paths eve...