Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Digital Forestry: A white paper

Digital Forestry has been proposed as “the science, technology, and art of systematically acquiring, integrating, analyzing, and applying digital information to support sustainable forests.” Although rooted in traditional forestry disciplines, Digital Forestry draws from a host of other fields that, in the past few decades, have become important for implementing the concept of forest ecosystem management and the principle of sustainable forestry. Digital Forestry is a framework that links all facets of forestry information at local, national, and global levels through an organized digital network. It is anticipated that a new set of principles will be established when practicing Digital Forestry concept for the evolution of forestry education, research, and practices as the 21st century unfolds.

Droplet oscillations in high gradient static magnetic field

In high intensity and high gradient magnetic fields the volumetric force on diamagnetic material, such as water, leads to conditions very similar to microgravity in a terrestrial laboratory. In principle, this opens the possibility to determine material properties of liquid samples without wall contact, even for electrically non-conducting materials. In contrast, AC field levitation is used for conductors, but then terrestrial conditions lead to turbulent flow driven by Lorentz forces. DC field damping of the flow is feasible and indeed practiced to allow property measurements. However, the AC/DC field combination acts preferentially on certain oscillation modes and leads to a shift in the droplet oscillation spectrum.What is the cause? A nonlinear spectral numerical model is presented, to address these problems.