Some two-component generalizations of the Novikov equation, except Geng-Xue are presented, as well their Lax pairs and bi-Hamiltonian structures. Furthermore, we study Hamiltonians equation discuss homogeneous local properties them.

It is a well-known result that stable curve of compact type over \({\mathbb {C}}\) having two components hyperelliptic if and only both are the point intersection Weierstrass for each them. With use admissible covers, we generalize this characterization in ways: curves higher gonality smooth one node; trigonal non-rational any number nodes.

Signal transduction systems mediate the response and adaptation of organisms to environmental changes. In prokaryotes, this signal transduction is often done through Two Component Systems (TCS). These TCS are phosphotransfer protein cascades, and in their prototypical form they are composed by a kinase that senses the environmental signals (SK) and by a response regulator (RR) that regulates th...