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[en] Exact canonically conjugate momenta Π2μ in quadrupole nuclear collective motions are proposed. The basic idea lies in the introduction of a discrete integral equation for the strict definition of canonically conjugate momenta to collective variables ϕ2μ. A part of our collective Hamiltonian, the Π2μ-dependence of the kinetic part of the Hamiltonian, is given exactly. Further, ϕ2μ-dependence of the kinetic part of the Hamiltonian is also given
[en] We investigate the τ-function of the quadrilateral lattice using the nonlocal ∂-bar-dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach.
[en] The center of buoyancy of an arbitrary shaped body is defined in analogy to the center of gravity. The definitions of the buoyant force and center of buoyancy in terms of integrals over the area of the body are converted to volume integrals and shown to have simple intuitive interpretations