We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite @math -systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems.
The invention relates to a negative electrode for an alkaline electrolyte electric cell. The main electrode material is nickel lanthanide and is characterized by the fact that it also includes a mercury compound. It is applicable to secondary electric cells, in particular of the nickel- or silver-hydrogen type. Cells embodying such negative electrodes exhibit improved capacity irrespective of temperature and electrolyte concentration conditions as compared with like cells in which the mercury compound is not used with the nickel lanthanide.