The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum fieldâ€¦ (More)

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group Uq(sl2). It defines an Ising-type lattice model with positive Boltzmann weightsâ€¦ (More)

From September, 1967, to January, 1974, a clinical trial was carried out by the WHO Melanoma Group to evaluate the efficacy of elective lymph-node dissection in the treatment of malignant melanoma ofâ€¦ (More)

Results of a prospective randomized clinical trial conducted by the WHO Collaborating Centers for the Evaluation of Methods of Diagnosis and Treatment of Melanoma are reported.â€¦ (More)

The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. O-doubles of Novikov, which generalize theâ€¦ (More)

We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices â€” lattices whose faces are planar quadrilaterals inscribable into a circle. We show thatâ€¦ (More)

We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equationâ€”equation that makes manifest the symmetries of aâ€¦ (More)

Using a modified version of the tetrahedron equations we construct a new family of N-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particularâ€¦ (More)

We report progress in constructing Boltzmann weights for integrable 3dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can beâ€¦ (More)

We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linearâ€¦ (More)