Abstract: Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice. We investigate the integrable structure of the representative for the gauge equivalence class of matrices, which is isomorphic to the affine Jacobi ...

Abstract — In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given. 2000 Mathematics Sub...

We study the high-dimensional limit of free energy associated with inference problem finite-rank matrix tensor products. In general, we bound from above by unique solution to a certain Hamilton-Jacobi equation. Under additional assumptions on nonlinearity in equation which is determined explicitly model, identify solution. Two notions solutions, weak solutions and viscosity are considered, each...