Anomalous dimensions of heavy operators from magnon energies

We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. Motivated by a geometrical interpretation of the central charges of su(2|2), we propose a simple and minimal all loop expression that interpolates between the anomalous dimensions computed in the gauge theory and energies computed in the dual string theory. The discussion makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. The symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. We compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. We find the reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation so that the boundary condition on the open spin chain spoils integrability. We also explain the interpretation of the double coset ansatz in the magnon language.NCS201

Anomalous dimensions of heavy operators from magnon energies

We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. Motivated by a geometrical interpretation of the central charges of su(2|2), we propose a simple and minimal all loop expression that interpolates between the anomalous dimensions computed in the gauge theory and energies computed in the dual string theory. The discussion makes use of a description in terms of magnons, generalizing results for a single maximal giant graviton. The symmetries of the problem determine the structure of the magnon boundary reflection/scattering matrix up to a phase. We compute a reflection/scattering matrix element at weak coupling and verify that it is consistent with the answer determined by symmetry. We find the reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation so that the boundary condition on the open spin chain spoils integrability. We also explain the interpretation of the double coset ansatz in the magnon language.NCS201

Landscape and soil regionalization in southern Brazilian Amazon and contiguous areas: methodology and relevance for ecological studies

Soils of a large tropical area with differentiated landscapes cannot be treated uniformly for ecological applications. We intend to develop a framework based on physiography that can be used in regional applications. The study region occupies more than 1.1 million km² and is located at the junction of the savanna region of Central Brazil and the Amazon forest. It includes a portion of the high sedimentary Central Brazil plateau and large areas of mostly peneplained crystalline shield on the border of the wide inner-Amazon low sedimentary plain. A first broad subdivision was made into landscape regions followed by a more detailed subdivision into soil regions. Mapping information was extracted from soil survey maps at scales of 1:250000-1:500000. Soil units were integrated within a homogenized legend using a set of selected attributes such as taxonomic term, the texture of the B horizon and the associated vegetation. For each region, a detailed inventory of the soil units with their area distribution was elaborated. Ten landscape regions and twenty-four soil regions were recognized and delineated. Soil cover of a region is normally characterized by a cluster composed of many soil units. Soil diversity is comparable in the landscape and the soil regions. Composition of the soil cover is quantitatively expressed in terms of area extension of the soil units. Such geographic divisions characterized by grouping soil units and their spatial estimates must be used for regional ecological applications