Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k. As main results of the paper we show that for w ≤ 0, the category T has no non-trivial t-structures, but ...

At high energies, elastic hadronic cross sections, such as pp, pp, πp, are dominated by vacuum exchange, which in leading order of the 1/Nc expansion has been identified as the BFKL Pomeron or its strong AdS dual the closed string Reggeized graviton [1]. However the difference of particle anti-particle cross sections are given by a so-called Odderon, carrying C = -1 vacuum quantum numbers ident...

We present a novel abstraction for bounding the Clarke Jacobian of Lipschitz continuous, but not necessarily differentiable function over local input region. To do so, we leverage abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed compute Jacobian. formally prove that our forward-mode interval evaluation produces sound, domain-based over-ap...

We study Myers world-volume effective action of coincident D-branes. We investigate a system of N0 D0-branes in the near horizon geometry of Dp-branes with p = 2 or p = 4. The choice of coordinates can make the action simplified and tractable. For p = 4, we show that a certain point-like D0-brane configuration solving equations of motion of the action can expand to form a fuzzy two-sphere witho...

The Cappell-Shaneson decomposition theorem for self-dual sheaves asserts that on a space with only even-codimensional strata any selfdual sheaf is cobordant to an orthogonal sum of twisted intersection chain sheaves associated to the various strata. In sharp contrast to this result, we prove that on a space with only odd-codimensional strata (not necessarily Witt), any self-dual sheaf is cobord...

A subset $S$ of vertices a digraph $D$ is double dominating set (total $2$-dominating set) if every vertex not in adjacent from at least two $S$, and one (the subdigraph induced by has no isolated vertices). The domination number $2$-domination number) the minimum cardinality $D$. In this work, we investigate these concepts which can be considered as extensions graphs to digraphs, along with $2...