Kellerer’s theorem revisited

Cholera Bacteriophages Revisited

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The Wulff theorem revisited

The Six Circles Theorem revisited

Kolmogorov Theorem Revisited

Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be ofO(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful (...

Complex and detailed balancing of chemical reaction networks revisited

The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff’s Matrix Tree theorem for directed weighted graphs. This yields an elucidation of previously obtained results, in particular with respect to the Wegscheider conditions, and a new necessary a...