Osservazioni della cometa Pons-Brooks

I giornali delle sperienze e osservazioni relativi alla fisiologia della generazione e alla embriologia sperimentale

Reviewed by Mario A. Di Gregorio, M.A., Ph.D., F.L.S., Darwin College, Cambridge. The more the scope of research in the history of science widens, and the more intriguing the problems it touches appear to us, the more we feel the necessity to refer to the original sources represented by unpublished material. Thus archives are now invaluable points of reference in our research. It often happens ...

Evolution from TDM-PONs to Next-Generation PONs

An easy and efficient evolution method from a time-division multiplexing passive optical networks (TDM-PONs) to next-generation PONs is proposed and demonstrated. A single-type wavelength band combiner/splitter (WC) enables a simple and efficient evolution of TDM-PON maintaining the current PON infrastructure and wavelength plan. The feasibility of the proposed evolution architecture is shown b...

Brooks' Theorem and Beyond

We collect some of our favorite proofs of Brooks’ Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques in graph coloring, such as greedy coloring, Kempe chains, hitting sets, and the Kernel Lemma. We also discuss standard strengthenings of vertex coloring, such as list coloring, online list coloring, and Alon–Tarsi orientations, since analo...

Books in Running Brooks

No Quantum Brooks' Theorem

First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as tropical, cyclical, and commutative. I also define a step logarithm function and express with it the bounds on quantum graph invariants in closed...