We establish a relative spannedness for log canonical pairs, which is generalization of the basepoint-freeness varieties with log-terminal singularities by Andreatta--Wiśniewski. Moreover, we quasi-log pairs.

We give a tropical description of the counting real log curves in toric degenerations varieties. treat case genus zero and all non-superabundant higher-genus situations. The proof relies on deformation theory is version Nishinou–Siebert approach to correspondence theorem for complex curves. In dimension two, we use similar techniques study with Welschinger signs obtain new Mikhalkin’s invariants.

The data systems, policies and procedures, corporate culture, and public face of an agency or institution make up its organizational interface. This case study describes how user interfaces for the Bureau of Labor Statistics web site evolved over a 5-year period along with the larger organizational interface and how this co-evolution has influenced the institution itself. Interviews with BLS st...