A characterization of nonlinear spectral radius preserving maps is obtained for the usual and triple products of nonnegative MATRICES.

In this paper we highlight the connection between certain classes of regular subgroups of the affine group AGLn (F), F a field, and associative nilpotent F-algebras of dimension n. We also describe how the classification of projective congruence classes of square MATRICES is equivalent to the classification of regular subgroups of particular shape.

Let MnMn be the set of all nn-by-nn real MATRICES, and let RnRn be the set of all nn-by-11 real (column) vectors. An nn-by-nn matrix R=[rij]R=[rij] with nonnegative entries is called row stochastic, if ∑ nk=1rik∑ k=1nrik is equal to 1 for all ii, (1≤ i≤ n)(1≤ i≤ n). In fact, Re=eRe=e, where e=(1, … , 1)t∈ Rne=(1, … , 1)t∈ Rn. A matrix R∈ MnR∈ Mn is called integral row stochastic, if each row has exactly one nonzero entry, +1+1, and other entries are zero. In the present paper, we provide an algorithm for constructing integral row stochastic MATRICES, and also we show the relationship between this algorithm and majorization theory.

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In this paper, the theoretical issues governing release characteristics of a solute of composite materials are validated experimentally, using composites of cross-linked poly (hydroxyethyl methacrylate) (PHEMA) particles dispersed within ethylene vinyl acetate copolymer (EVAc) MATRICES, and composites of cross-linked poly (methacrylic acid) (PMAA) particles dispersed within poly (dimethyl siloxane) (PDMS) networks which were prepared. Using theophylline and caffeine as the model drugs, the results of release, permeation and swelling experiments were employed to validate the theoretical issues. In PHEMA-EVA cMATRICES, due to equilibrium swelling, Fickian diffusional release kinetics was observed. In PMAA-PDMS MATRICES, which contained 19%wt, 23.7%wt, 28.5%wt, 33.2%wt and 38%wt PMAA, because of osmotic rupturing. pseudo-zero-orderrelease kinetics preceded by a marked burst effect was observed. In all the cases, the experimental results were in good agreement with the theoretical criteria for equilibrium swelling versus osmotic rupturing. For the model predicting the extent of equilibrium swelling, the maximum deviation of the swelling ratio compared to the experimental results for different MATRICES was only 8.4%.

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