We show that, under Drinfeld’s degeneration [D] of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [EV] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [TL] for Yangians.

Abstract. Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. This convergence also yields portfolio turnpikes for ge...

A Lagrangian or an affine Hamiltonian is called totally singular if it is defined by affine functions in highest velocities or momenta respectively. A natural duality relation between these Lagrangians and affine Hamiltonians is considered. The energy of a second order affine Hamiltonian is related with a dual corresponding Lagrangian of order one. Relations between the curves that are solution...

The central objects of study in this thesis are affine difference algebraic groups. Similar to the case of affine algebraic groups, these groups can all be realized as subgroups of some general linear group defined by algebraic difference equations. However, the defining equations here are not simply polynomials in the matrix entries but difference polynomials, i.e., the defining equations invo...

A bstract We uncover a connection between two seemingly separate subjects in integrable models: the representation theory of affine Temperley-Lieb algebra, and algebraic structure solutions to Bethe equations XXZ spin chain. study solution analytically by computational geometry, find that space encodes rich information about algebra. Using these connections, we compute partition function comple...

Quasi-Monte Carlo (QMC) rules 1/N ∑N−1 n=0 f(ynA) can be used to approximate integrals of the form ∫ [0,1]s f(yA) dy, where A is a matrix and y is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications fr...