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    Spin Glass and ferromagnetism in disordered Cerium compounds

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    The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling JijJ_{ij} between the localized magnetic moments given by a generalization of the Mattis model which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving T/JT/{J} {\it versus} JK/JJ_K/J where TT is the temperature, JKJ_{K} and J{J} are the strengths of the intrasite Kondo and the intersite random couplings, respectively. If JK/JJ_K/{J} is small, when temperature is decreased, there is a second order transition from a paramagnetic to a spin glass phase. For lower T/JT/{J}, a first order transition appears between the spin glass phase and a region where there are Mattis states which are thermodynamically equivalent to the ferromagnetism. For very low T/J{T/{J}}, the Mattis states become stable. On the other hand, it is found as solution a Kondo state for large JK/JJ_{K}/{J} values. These results can improve the theoretical description of the well known experimental phase diagram of CeNi1xCuxCeNi_{1-x}Cu_{x}.Comment: 17 pages, 5 figures, accepted Phys. Rev.

    The effect of the AltSB gene on root growth in nutrient solution of isogenic sorghum hybrids.

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    AltSB, a major gene of the Multidrug and Toxic Compound Extrusion (Mate) family confers tolerance to aluminum toxicity in sorghum. This gene is a transporter gene that is responsible for the exudation of citric acid in the presence of toxic level of aluminum in the soil. The citrate complexes with the toxic aluminum forming a nontoxic compound. During the past several years, isogenic sorghum breeding lines, both cytoplasmic male-sterile lines (A and B-lines) and fertility restoring pollinator lines (R-lines) for this AlTSB gene have been developed at Embrapa Maize and Sorghum. These isogenic lines for AlTSB were used to develop sixteen isogenic sorghum hybrids with zero, one and two alleles for tolerance to aluminum toxicity. These sixteen hybrids are essentially genetically equal but with variation in the dose of the AlTSB allele. Seedlings of these isogenic hybrids were evaluated for root growth in nutrient solution with 0, 11, 20, 27 and 39?M aluminum for seven days at four intervals (0, 3, 5, and 7days). One dose of the gene had a very significant effect on maintaining root growth up to a concentration of 27 ?M aluminum. A second dose of the gene continued to have a positive effect for some of the isogenic hybrids confirming the effect of partial dominance for this gene. The presence of the AlTSB gene in sorghum cultivars used in regions with acid soils or subsoils will contribute to the development of a better and deeper root system and promote greater and more sustainable productivity
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