This paper presents a backward stable preprocessing technique for (nearly) ill-posed semidef5 inite programming, SDP, problems, i.e., programs for which the Slater constraint qualification, 6 existence of strictly feasible points, (nearly) fails. 7 Current popular algorithms for semidefinite programming rely on primal-dual interior-point, 8 p-d i-p methods. These algorithms require the Slater c...

We answer a question posed by Lampert and Slater [7]. Consider a sequence of real numbers qn in the interval [0, 1] defined by q0 = 0, q1 = 1, and, for n ≥ 1, qn+1 equals an average of preceding terms in the sequence. The weights used in the average are provided by a triangular array pn,k of probabilities whose row sums are 1. What is the limiting behavior of a sequence qn so defined? For the L...

Relationships between the quantum invariants of the torus knots T3,2k and some q-series identities are studied. In particular, new generalizations of the Slater identities (83) and (86) are obtained. §