We adapt the dual-null foliation to functional Schr\"odinger representation of quantum field theory and study behavior probes in plane-wave space-times near null-singularity. A comparison between Einstein-Rosen Brinkmann patch, where latter extends beyond first, shows a seeming tension that can be resolved by comparing configuration spaces. Our analysis concludes support exclusively configurati...

We find a necessary and sufficient condition for the Ruelle operator of a weakly Hölder continuous potential on a topologically mixing countable Markov shift to act with spectral gap on some rich Banach space. We show that the set of potentials satisfying this condition is open and dense for a variety of topologies. We then analyze the complement of this set (in a finer topology) and show that ...

For semi-linear wave equations with null form non-linearities on R, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also exhibit a set of localized data for which the corresponding solutions are strongly focused, which in geometric terms means that a wave travels along an specific incoming null geo...

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set K, there exists another compact set K ′ such that for any p, q 6∈ K , if there exists a “fastest null geodesic”, γ, between p an...

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set K, there exists another compact set K ′ such that for any p, q 6∈ K , if there exists a “fastest null geodesic”, γ, between p an...

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. We introduce null functional dependencies (NFDs) and null inclusion dependencies (NINDs) to cater for the situation when a database is incomplete and thus contains null values. If a NFD or NIND is weakly satissed in a database, then there...

Scientists regularly decide the statistical significance of their findings by determining whether they can, with sufficient confidence, rule out the possibility that their findings could be attributed to random variation—the ‘null hypothesis.’ For this, they rely on tables with critical values pre-computed for the normal distribution, the t-distribution, etc. This paper provides such tables (an...

Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a pri...

Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a {−1, 0, 1}-basis. We devise an algorit...

In the paper we formulate a Covering Property Axiom CPA cube , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in R (which are strongly meager) as well as uncountable γ-sets in R which are not strongly meager. These sets must be of cardinality ω1 < c, since every γ-set is universally null, while CPA cube implies that every unive...