For simplicity, we follow the rules: n denotes a natural number, a, b, r denote real numbers, x, y, z denote points of En T , and e denotes a point of En. The following propositions are true: (1) x − y − z = x − z − y. (2) If x + y = x + z, then y = z. (3) If n is non empty, then x 6= x + 1.REALn. (4) For every set x such that x = (1 − r) · y + r · z holds x = y iff r = 0 or y = z and x = z iff...

We identify the untwisted moduli of heterotic orbifold compactifications for the case, when the gauge twist is realized by a rotation. The Wilson lines are found to have both continuous and discrete parts. For the case of the standard Z3 orbifold we classify all possibilities of breaking the gauge group E(6)⊗SU(3) by nine of the eighteen Wilson moduli and by additional discrete Wilson lines. Ne...

We investigate D-branes in a Z3 × Z3 orbifold with discrete torsion. For this class of orbifolds the only known objects which couple to twisted RR potentials have been non-BPS branes. By using more general gluing conditions we construct here a D-brane which is BPS and couples to RR potentials in the twisted and in the untwisted sectors. ∗ [email protected]

A new type of four-dimensional string vacua with Scherk–Schwarz supersymmetry breaking is considered. The construction involves ZN × ZM freely acting orbifolds, defined in terms of rotations and translations in the internal space. Tachyons are either absent or limited to a given region of the tree-level moduli space. Particular attention is devoted to an interesting Z3 × Z3 heterotic example.

Abstract ProB provides a constraint solver for the B-method written in Prolog and can make use of different backends based on SAT SMT solving. One such backend translates B Event-B operators to SMT-LIB using Z3 solver. This translation uses quantifiers axiomatize some operators, which are not well-handled by Z3. Several relational constraints as transitive closure supported this translation. In...

Side chains of conjugated polymers play an important role in their properties. To investigate the influence of side chains on photovoltaic properties, two conjugated polymers with benzo[1,2-b:3,4-b]dithiophene (BDT) and 4,7-dithiophen-2,1,3-benzothiadiazole (DTBT) units, Z3 and Z4, were designed and synthesized. These two polymers have identical conjugated main chains and very similar side chai...

In C. elegans, germline blastomeres are initially kept transcriptionally quiescent by the maternally loaded CCCH zinc-finger protein PIE-1. PIE-1 disappears upon the birth of the primordial germ cells Z2 and Z3, yet these cells appear to remain quiescent. We have previously demonstrated that there is a chromatin-based repression that succeeds PIE-1 degradation. The chromatin in Z2/Z3 loses cert...

For z1, z2, z3 ∈ Z, the tristance d3(z1, z2, z3) is a generalization of the L1-distance on Z to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticode Ad of diameter d is a subset of Z with the property that d3(z1, z2, z3) 6 d for all z1, z2, z3 ∈ Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determin...