Ice plays key roles in regulating hydrological, ecological, biogeochemical, and socioeconomic functions of lakes. Long-term in situ lake ice phenological records indicate that is trending toward later freeze-up, earlier breakup, a shorter duration. Parallel to study using process-based models, ...

We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...

Commutativity rules play an essential role when building multirate signal processing systems. In this letter, we focus on the interchangeability of block decimators and expanders. We, formally, prove that commutativity between these two operators is possible if and only if the data blocks are of an equal length corresponding to the greatest common divisor of the integer decimation and expansion...

Hall’s Theorem is a basic result in Combinatorics which states that the obvious necesssary condition for a finite family of sets to have a transversal is also sufficient. We present a sufficient (but not necessary) condition on the sizes of the sets in the family and the sizes of their intersections so that a transversal exists. Using this, we prove that in a bipartite graph G (bipartition {A,B...