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An approximate inverse LU preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative decomposition of the inverse of a matrix is obtained. This recursion in compact form is the base to build the proposed preconditioner that we call V–AISM. For nonsingular M-matrices and H-matrices of the invertible class the stability of the preconditioner is proved. Numerical results show that V–AISM is robust and competitive compared with other preconditioners.

Theobroma cacao is very important in the economy of many tropical countries, especially in Ecuador. The development and production of Theobroma cacao have been limited by the attack of diseases, pests, and currently by the impact caused by the water deficit. The loss of water in the crop causes a low production of the plantations. In addition, when genetic diversity is scarce, the possible combinations of genes capable of conferring biological adaptation and, consequently, the capacity to adapt to environmental variations, are reduced. Therefore, a viable option is to identify genes capable of conferring adaptation to water deficit stress. The objective of this research was to characterize genes of Theobroma cacao in response to water deficit. The sequencing and characterization of genes related to water stress were achieved and, finally, the hybridization profile of the genes (ABA, ODC, DEH, and ABS) in response to Actin (ACT) was analyzed. The ABS gene hybridized 100 % with DNA from rootstock EET399 in roots and 80 % with DNA from graft T24 in leaves. The OCD gene hybridized 80 % with DNA from rootstock IMC 67 and 25 % with the T800 graft in leaves. The DEH gene hybridized below the normalizing gene (ACT) in both rootstock EET400 (10 %) in root DNA and graft T12 (5 %) in leaves. Finally, the ABA gene did not hybridize with the DNA of the CCN51 rootstock or with the graft (T801) in both roots and leaves, respectively. This research is key to understand some molecular mechanisms of T. cacao in response to water deficit and can be considered as a viable strategy to reduce crop agronomic losses under the current environmental scenario. [ABSTRACT FROM AUTHOR]

Root-to-shoot signalling via xylem sap is an important mechanism by which plants respond to stress. This signalling could be mediated by alteration in the concentrations of inorganic and/or organic molecules. The effect of salt stress on the contents of xylem sap in Brassica olarecea has been analysed by mass spectrometry in order to quantify these changes. Subcellular location of arabinogalactan proteins (AGPs) by immunogold labelling and peroxidase isozymes was also analysed by isoelectrofocusing. The xylem sap metabolome analysis demonstrated the presence of many organic compounds such as sugars, organic acids and amino acids. Of these, amino acid concentrations, particularly that of glutamine, the major amino acid in the sap, were substantially reduced by salt stress. The xylem sap proteome analysis demonstrated the accumulation of enzymes involved in xylem differentiation and lignification, such as cystein proteinases, acid peroxidases, and a putative hydroxycinnamoyl-CoA:shikimate hydroxycinnamoyl transferase under salt stress. The peroxidase isozyme pattern showed that salt stress induced a high accumulation of an acid isoform. These results suggest that xylem differentiation and lignification is induced by salt stress. The combination of different methods to analyse the xylem sap composition provides new insights into mechanisms in plant development and signalling under salt stress. [ABSTRACT FROM AUTHOR]

It is well known that the Schur complement of some H-matrices is an H-matrix. In this paper, the Schur complement of any general H-matrix is studied. In particular, it is proved that the Schur complement, if it exists, is an H-matrix and the class to which the Schur complement belongs is studied. In addition, results are given for singular irreducible H-matrices and for the Schur complement of nonsingular irreducible H-matrices. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Two PPO preparations, one soluble and one particulate, were monitored at eight different developmental stages after anthesis of tomato fruits. Both PPO preparations showed significant decline after the 12th day postanthesis of fruit development. Although present in every cultivar tested, the two PPO preparations varied greatly in activity among the cultivars. The addition of 1-mM synthetic hexapeptides caused inhibition over 10% on PPO activity measured in both preparations. The antibrowning effect of the β-CD Cavasol W7M on PPO activity was also evaluated. Although the two families of compounds that we describe here, hexapeptides and CDs, react in very different ways either by physically blocking the active site of PPO or, alternatively, by chelating PPO substrates, they are common antibrowning compounds that can be commercially synthesized. These inhibitors are peptides and sugars, which are not likely to cause adverse health effects. [ABSTRACT FROM AUTHOR]

Two different polyphenol oxidase (PPO) fractions, soluble and particulate, were purified from unripe tomato fruits (Lycopersicon esculentum M. cv. Muchamiel). The PPO present in the soluble fraction was purified fivefold with a 43.5% yield after ammonium sulfate fractionation. PPO in the particulate was purified 4.56-fold with a 23% yield using the nonionic detergent Triton X-114. A strong correlation between tomato fruit PPO activity and the physiological disorder blossom-end rot (BER) was found, with a large increase of the PPO activity in the particulate fraction. Kinetic characterization, including kinetic parameters, pH and temperature profiles, substrate specificity and inhibitors showed similarities in both the soluble and the particulate enzyme(s). However, thermal stability of the particulate enzyme was significantly higher than stability of the soluble PPO, thus indicating possible structural differences. Cupric ions were activators, probably because of their ability to reactivate PPO partly denatured during purification. [ABSTRACT FROM AUTHOR]

Let Ax = b be a large, sparse, nonsymmetric system of linear equations. A new sparse approximate inverse preconditioning technique for such a class of systems is proposed. We show how the matrix A0-1 - A-1, where A0 is a nonsingular matrix whose inverse is known or easy to compute, can be factorized in the form UωVT using the Sherman—Morrison formula. When this factorization process is done incompletely, an approximate factorization may be obtained and used as a preconditioner for Krylov iterative methods. For A0 = sIn, where In is the identity matrix and s is a positive scalar, the existence of the preconditioner for M-matrices is proved. In addition, some numerical experiments obtained for a representative set of matrices are presented. Results show that our approach is comparable with other existing approximate inverse techniques. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical analysis of positive mathematical programming is presented, using specific quadratic objective functions. We have applied this model to analyze the effect of the E.U.''s “Agenda 2000” for agriculture in a particular Spanish region. [Copyright &y& Elsevier]