We derive closed-form expressions for the Jacobian of matrix exponential function both diagonalizable and defective matrices. The results are applied to two cases interest in macroeconometrics : a continuous-time macro model parameterization rotation matrices governing impulse response functions structural vector autoregressions .

We study a model of two-field ultra-slow-roll (USR) inflation bounded by curve in the field space. Curvature perturbations and non-Gaussianities can be enhanced both during USR phase from inhomogeneities at boundary. employ full non-linear $\delta N$ formalism to calculate probability distribution function (PDF) for curvature perturbation non-perturbatively show that effects significantly enhan...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...