In the last decade, advances in satisfiability-modulo-theories (SMT) solvers have powered a new generation of software tools for verification and testing. These tools transform various program analysis problems into the problem of satisfiability of formulas in propositional or first-order logic, where they are discharged by SMT solvers, such as Z3 from Microsoft Research. This paper briefly sum...

Tutte conjectured that every 4-edge connected graph admits a nowhere-zero Z3-flow and Jaeger, Linial, Payan and Tarsi conjectured that every 5-edge connected graph is Z3-connected. In this paper, we characterize the triangularly connected graphs G that are Γ-connected for any Abelian group Γ with |Γ| ≥ 3. Therefore, these two conjectures are verified for the family of triangularly connected gra...

We study the strong coupling dynamics of the heterotic E8 ×E8 string theory on the orbifolds T /Z3 and C /Z3 using the duality with the Horava-Witten M-theory picture. This leads us to a conjecture about the low energy description of the five dimensional E0-theory (the CFT that describes the the singularity region of M-theory on C/Z3) compactified on S /Z2.

Ten Azotobacter cultures were isolated from the maize rhizosphere and their auxin producing ability was measured colourimetrically. The auxin production by three efficient Azotobacter cultures (Z1, Z3, Z4) was also measured in the presence of filter sterilized L-tryptophan (at 10G, 10G and 10G M). Azotobacter culture Z4 gave relatively higher auxin production and was selected for further experi...

This paper deals with the relation between the automorphism groups of some paving matroids and Z3, where Z3 is the additive group of modulo 3 over Z. It concludes that for paving matroids under most cases, Z3 is not isomorphic to the automorphism groups of these paving matroids. Even in the exceptional cases, we reasonably conjecture that Z3 is not isomorphic to the automorphism groups of the c...

Let Fq be a finite field of characteristic p having q elements, where q = p and p ≥ 5. Let SL(2,Z3) be the special linear group of 2 × 2 matrices with determinant 1 over Z3. In this note we establish the structure of the unit group of FqSL(2,Z3). 2010 MSC: 16U60, 20C05

Jak2 tyrosine kinase is essential for animal development and hyperkinetic Jak2 function has been linked to a host of human diseases. Control of this pathway using Jak2-specific inhibitors would therefore potentially serve as a useful research tool and/or therapeutic agent. Here, we used a high-throughput program called DOCK to predict the ability of 20,000 small molecules to interact with a str...

We begin with the simplest possible introduction to supergravity. Then we discuss its spin 3/2 stress tensor; these results are new. Next, we discuss boundary conditions on fields and boundary actions for N = 1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N = 4 super Yang-Mills theory. All models are in 3 + 1 dimensions. YITP-SB-06-21

We consider compactification of the SO(32) heterotic string on a 6-dimensional Z3 orbifold with one discrete Wilson line. A complete set of all possible embeddings is given. The unbroken subgroups of SO(32) are tabulated. The extended gauge symmetry SU(3), recently discussed by J. E. Kim [hep-th/0301177] for semi-realistic E8 × E8 heterotic string models, occurs for several embeddings, as well ...

As a first step towards studying vector bundle moduli in realistic heterotic compactifications, we identify all holomorphic rational curves in a Calabi-Yau threefold X with Z3⊕Z3 Wilson lines. Computing the homology, we find that H2(X,Z) = Z ⊕Z3⊕Z3. The torsion curves complicate our analysis, and we develop techniques to distinguish the torsion part of curve classes and to deal with the non-tor...