This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric sense. This class includes many of the well-known cases.

The aim of this work was to develop a selective cloud point extraction method for the separation and preconcentration of copper(II) prior to spectrophotometric determination. For this purpose dithizone was used as a complexing agent and the experimental solution was acidified with sulfuric acid. Triton X-114 was used as a surfactant and after phase separation, based on the cloud point of th...

We are going to solve this problem in three steps. Step 1 In the first step, we find all solutions of (1) that are of the special form u(x, t) = X(x)T (t) for some function X(x) that depends on x but not t and some function T (t) that depends on t but not x. This is where the name “separation of variables” comes from. It is of course too much to expect that all solutions of (1) are of this form...

This note surveys and compares results in [12] and [21, 22] on the separation of variables construction for soliton solutions of curvature equations including the Kähler-Ricci flow and the Lagrangian mean curvature flow. In the last section, we propose some new generalizations in the Lagrangian mean curvature flow case.

We investigate the exact overlaps between eigenstates of integrable spin chains and a special class states called “integrable initial/final states”. These satisfy integrability constraint, they are closely related to boundary conditions. derive new algebraic relations for states, which lead set recursion overlaps. solve these thus we overlap formulas, valid in XXX Heisenberg chain its higher ge...