(A.1) Rē− R̄r = γ[2b(R2σ2 e + σ2 − 2R σ σe) + 2w∗ R σ σe − 2w∗ σ2], where ē = E+[e] and σe = Var+(e). Suppose agents were expecting debt to be safe, then ē = 1 and σe = 0, so we have Rs(b) = R̄r + γ[2bσ2 − 2w∗ σ2] = R̄r − 2γ(w∗ − b)σ2. This proves the first part of the proposition. Suppose agents were expecting Hegemon debt to be risky, then ē = R̄/RH and σe = σ/R r H since we assumed eL = RL/R r H...

A shortening of C on the coordinate i is the [n − 1, k − 1, d] linear code obtained by leaving only such codewords and deleting the ith coordinate. Let [n] := {1, . . . , n}, E ⊂ [n], Ē = [n]\E. For a matrix M with n columns we denote by M(E) the submatrix formed by all the columns with numbers in E. The support of a vector x ∈ H n q is defined as supp(x) = {i : xi 6= 0}. Given a subcode A ⊂ C,...

This technical report provides accompanying proofs for the paper: Verifying Spatial Properties of Array Computations. We show three properties of the lattice model of the stencil specification language. 1) that it is sound with respect to the equational theory of region specifications; 2) that is it sound with respect to the theory of region approximation; 3) that the inference algorithm is sou...

Let P1 = 〈v1, v2, v3, . . . , vn〉 and P2 = 〈u1, u2, u3, . . . , un〉 be two hamiltonian paths of G. We say that P1 and P2 are independent if u1 = v1, un = vn , and ui = vi for 1 < i < n. We say a set of hamiltonian paths P1, P2, . . . , Ps of G between two distinct vertices are mutually independent if any two distinct paths in the set are independent. We use n to denote the number of vertices an...

It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous Schlesinger-type dynamical system. The conformal factor of the metric coincides (up to some explicitly computable factor) with the τ -function of the Ernst equation in the...

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...

We recall that a nicely semiramified division algebra is defined to be a defectless finitedimensional valued central division algebra D over a field E with inertial and totally ramified radical-type (TRRT) maximal subfields [7, Definition, page 149]. Equivalent statements to this definition were given in [7, Theorem 4.4] when the field E is Henselian. These division algebras, as claimed in [7, ...

In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph G(V,E) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties 0<P(e)<1. In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable...