This supplementary appendix contains proofs of some results contained in the paper. Specifically, Section S1 provides proofs of Theorem 4 and its corollary, concerning the asymptotic distribution of flexible random effects estimators. Section S1 also proves Theorem 5, its corollary, and Theorem 6 concerning the bias and the asymptotic distribution of estimated marginal effects. Section S2 prove...

Learning-based model predictive control (LBMPC) is a technique that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance. This technical note provides proofs that elucidate the reasons for our choice of measurement model, as well as giving proofs concerning the stochastic converge...

Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generaliz...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.

This is a corrigendum for our paper [MM]. The main results are correct, but we offer some changes to the definitions and proofs concerning interpreted recursive program schemes.

in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.