We give a new Becchi-Rouet-Stora-Tyutin operator for the superstring. It implies a quadratic gauge-fixed action, and a new gauge-invariant action with first-class constraints. The infinite pyramid of spinor ghosts appears in a simple way through ghost gamma matrices. [email protected] and [email protected]

In 1987, Stanley conjectured that if a centrally symmetric Cohen–Macaulay simplicial complex Δ of dimension d-1 satisfies h i (Δ)=d for some i≥1, then j all j≥i. Much more recently, Klee, Nevo, Novik, and Zheng polytope P d g (∂P)=d i-d i-1 d/2≥i≥1, j-d j-1 d/2≥j≥i. This note uses stress spaces to prove both these conjectures.

We give a new, manifestly spacetime-supersymmetric method for calculating superstring scattering amplitudes, using the ghost pyramid, that is simpler than all other known methods. No pictures nor non-vertex insertions are required other than the usual b and c ghosts of the bosonic string. We evaluate some tree and loop amplitudes as examples. [email protected] and [email protected]...

We generalize the Hadwiger(-Danzer-Grünbaum-Klee) theorem on line transversals for an unbounded family of compact convex sets to the case of transversal planes of arbitrary dimension. This is the first Helly-type theorem known for transversals of dimension between 1 and d− 1.

The Schauder conjecture that every continuous single-valued map from a compact convex subset of a topological vector space into itself has a fixed point was stated in [12, Problem 54]. In a recent year, Cauty [2] gave a positive answer to this question by a very complicated approximation factorization. Very recently, Dobrowolski [3] established Cauty’s proof in a more accessible form by using t...

Symbolic execution is a widely used approach for automatic regression test generation and bug vulnerability finding. The main goal of this paper to present practical symbolic execution-based LLVM programs with complex input data structures. based on the well-known idea lazy initialization, which frees user from providing constraints structures manually. Thus, it provides us fully even program. ...