Continuing our first paper in this series, we study multiple limits in infinite-dimensional multiple categories. The general setting is chiral multiple categories a weak, partially lax form with directed interchanges. After defining multiple limits we prove that all of them can be constructed from (multiple) products, equalisers and tabulators all of them assumed to be respected by faces and de...

Distance measurements to Type Ia supernovae (SNe Ia) at cosmological distances indicate that the Universe is accelerating and that a large fraction of the critical energy density exists in a component with negative pressure. Various hypotheses on the nature of this “dark energy” can be tested via their prediction for the equation of state of this component. If the dark energy is due to a scalar...

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1, 1 . . . 1], [21 . . . 1], [31 . . . 1], [zz̄1 . . . 1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.

Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented) simplicial site, the category of finite ordinals. We prove here that K has characterisations similar to the classical ones for the simplicial analogue, by generators and relations, or by the existence of a universal symmetric cubical monoid...

Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we...

Production of Mrenda (Corchorus olitorius) in Kenya has been low due to various reasons, such as poor agronomic practices like incorrect fertilizer rates. Observations from the Mrenda growing areas showed that there is high unmet demand for crop in local market and even for export. This is due to yields being low, 2-4 tons/ha as compared to expected yield of 5-8 tons/ha. Therefore, the main obj...

A recently discovered relation between 4D and 5D black holes is used to derive exact (weighted) BPS black hole degeneracies for 4D N = 8 string theory from the exactly known 5D degeneracies. A direct 4D microscopic derivation in terms of weighted 4D D-brane bound state degeneracies is sketched and found to agree.