this paper explores the flexile flow lines where setup times are sequence- dependent. the optimization criterion is the minimization of total weighted completion time. we propose an iterated greedy algorithm (iga) to tackle the problem. an experimental evaluation is conducted to evaluate the proposed algorithm and, then, the obtained results of iga are compared against those of some other exist...

For \natural enough" systems of ordinal notation we show that times iterated local reeection schema over a suuciently strong arithmetic T proves the same 0 1-sentences as ! times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at-numbers. We also derive the following more general \mixed" formulas estimating the consistency strength...

We develop a class of integrals on a manifold called exponential iterated integrals, an extension of K. T. Chen’s iterated integrals. It is shown that these integrals can be used to compute the matrix entries of certain solvable representations of the fundamental group of the manifold. In particular we find that exponential iterated integrals separate the elements of groups of fibered knots.

We explore the algebraic properties of a generalized version iterated-sums signature, inspired by previous work F. Király and H. Oberhauser. In particular, we show how to recover character property associated linear map on tensor algebra considering deformed quasi-shuffle product words. introduce three non-linear transformations signatures, close in spirit Machine Learning applications, some th...