A necessary and sufficient condition for the stabilisation of a matrix and its principal submatrices

We present a necessary and sufficient condition for the existence of a real diagonal matrix such that its product with a given real square matrix is Hurwitz together with all its principal submatrices. We also give an explicit formula for a matrix which, in particular, supplies all the involved matrices with negative distinct eigenvalues.     

Design of progressively censored group sampling plans for Weibull distributions: An optimization problem

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan combines grouping of items, sudden death testing in each group and progressive group removals, and its decision criterion is based on the uniformly most powerful life test. A mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant. The optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost. Excellent approximately optimal solutions are also provided in closed-forms. The sampling plan is considerably flexible and allows to save experimental time and cost. In general, our methodology achieves solutions that are quite robust to small variations in the Weibull shape parameter. A numerical example about a manufacturing process of gyroscopes is included for illustration.     

Polymerization and copolymerization of styrene by Ph2Zn‐metallocene‐MAO initiator systems.

Combined systems including diphenylzinc, Ph₂Zn, a metallocene, and methylaluminoxane, MAO, have been employed to initiate styrene polymerization. These initiator systems have been also used to initiate the copolymerization of styrene with p‐alkylsubstituted styrenes and with α‐olefins. Both polymerization and copolymerization processes depend on the nature of the metallocene included in the initiator system, the presence of Ph₂Zn, the temperature and the solvent used. Titanocenes produced syndiotactic polystyrene, s‐PS, while zirconocenes gave atactic polystyrene, a‐PS, with a certain content, less the 20% of s‐PS. For copolymerizations the conversion to polymer was also influenced by the comonomer nature and its molar proportion in the initial feed, as well as the sort of metallocene, titanocene or zirconocene included.