Theorem 3.2 A consequence system (L,`) enjoys Craig interpolation with respect to an L-function var, if (i) there is a Craig generalized translation schema from (L,`) to another consequence system (L′,`′) with respect to var and an L′-function var′; (ii) (L′,`′) enjoys Craig interpolation with respect to var′. Proof: Let (h1, h2, h) be a Craig generalized translation schema from (L,`) to (L′,`′...

Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs containing neither of H1, H2 as induced subgraphs have bounded size. What if, instead, we exclude a graph H1 with a vertex whose deletion gives a clique, and the complement H2 of another such graph? This no longer implies bounded size, but it implies tightly restricted structure that we describe. The...

Let H1, H2 be two hash functions. We wish to construct a new hash function H that is collision resistant if at least one of H1 or H2 is collision resistant. Concatenating the output of H1 and H2 clearly works, but at the cost of doubling the hash output size. We ask whether a better construction exists, namely, can we hedge our bets without doubling the size of the output? We take a step toward...

We present two hierarchical identity-based encryption (HIBE) schemes, denoted as H1 and H2, from Type-3 pairings with constant sized ciphertexts. Scheme H1 achieves anonymity while H2 is non-anonymous. The constructions are obtained by extending the IBE scheme recently proposed by Jutla and Roy (Asiacrypt 2013). Security is based on the standard decisional Symmetric eXternal Diffie-Hellman (SXD...

Let H1 and H2 be Hilbert spaces and let B(H1,H2) be the space of bounded linear operators A : H1 → H2. An operator A ∈ B(H1,H2) is said to be Fredholm if first, the kernel ofA is finite-dimensional, and second the image ofA is closed and has finite codimension. An application of the open mapping theorem shows that the closedness requirement on the image is redundant. A well-known example of Fre...

Vernalization requirement is a key component in determining the overall fitness of developmental patterns of barley to its environment. We have used previously reported markers and spring-sown growth habit nursery to characterize the genotypes of barley germplasm in an applied barley breeding ground to establish a baseline of information required to understand the relationship between adaptatio...

RNase H1 from Halobacterium sp. NRC-1 (Halo-RNase H1) is characterized by the abundance of acidic residues on the surface, including bi/quad-aspartate site residues. Halo-RNase H1 exists in partially folded (I) and native (N) states in low-salt and high-salt conditions respectively. Its folding is also induced by divalent metal ions. To understand this unique folding mechanism of Halo-RNase H1,...

We find and study a five-parameter family of four-dimensional partial differential systems in two variables from the viewpoints of its symmetry and holomorphy properties. 1. Main results In this paper, we present a 5-parameter family of four-dimensional partial differential systems in two variables explicitly given by (cf. [3, 18]) dq1 = ∂H1 ∂p1 dt+ ∂H2 ∂p1 ds, dp1 = − ∂H1 ∂q1 dt− ∂H2 ∂q1 ds, d...

We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...