The combined matrix of a nonsingular real matrix is the Hadamard (entrywise) product ∘ ( −1 ) . It is well known that row (column) sums of combined matrices are constant and equal to one. Recently, some results on combined matrices of different classes of matrices have been done. In this work, we study some classes of matrices such that their combined matrices are nonnegative and obtain the relation with the sign pattern of . In this case the combined matrix is doubly stochastic.
Elsevier Ayala, G.; Diez, F.; Gasso Matoses, MT.; Jones, BE.; Martin-Portugues, R.; MartinPortugues, R.; Ramiro-Aparicio, J. (2016)
AbstractPulmonary delivery is being becoming a popular route for delivering active pharmaceutical ingredients that cannot be administered through by the standard oral route, as well as offering an improved alternative to the parenteral route. The use of hard capsules in dry powder inhalers (DPIs) to deliver formulations to the lung has been in use since 1970, and recently there has been an interest in changing from metered-dose devices to capsulebased ones because they are simple to formulate, cheap to manufacture, and patient-friendly. The original inhalation grade hard capsules were made from gelatin, which becomes brittle when exposed to low humidities. Inhalation grade hypromellose (HPMC, carrageenan gelling agent) has been developed in the last few years to overcome come this problem and has been shown to have better aerosolization properties. Hard capsules are made by a dipping process in which a surface lubricant is an essential processing aid for removing dried capsule shells from the manufacturing pins. This lubricant has been shown to have an effect on powder retention in capsules that are used for the inhalation of medicines. The capsule manufacturing process depends on many factors. The response is a function giving the the internal lubricant content (ILC) from 0 to 48 hours. Two of them were chosen by experts in order to evaluate their influ- Additionally we want to know if the mean ILC is between the tolerance limits. A bootstrap confidence region is used to estimate local confidence regions of the response.
We study the combined matrix of a nonsingular H-matrix. These matrices can belong to two different H-matrices classes: the most common, invertible class, and one particular class named mixed class. Different results regarding diagonal dominance of the inverse matrix and the combined matrix of a nonsingular H-matrix belonging to the referred classes are obtained. We conclude that the combined matrix of a nonsingular H-matrix is always diagonally dominant and then it is an H-matrix. In particular, the combined matrix in the invertible class remains in the same class.
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