Narrow Results

For Σ a compact connected oriented surface, we consider homology cylinders over Σ: these are homology cobordisms with an extra homological triviality condition. When considered up to Y₂-equivalence, which is a surgery equivalence relation arising from the Goussarov-Habiro theory, homology cylinders form an Abelian group.

In this paper, when Σ has one or zero boundary component, we define a surgery map from a certain space of graphs to this group. This map is shown to be an isomorphism, with inverse given by some extensions of the first Johnson homomorphism and Birman-Craggs homomorphisms.

Stereology, an interdisciplinary field that enables three-dimensional interpretation of planar sections, contains several methods for evaluation of quantitative parameters. The existing leaf sampling procedures were modified and adapted for compound, trifoliate leaves. The similar sampling method could also be applied on other types of compound leaves. Using Trifolium species as model species, we suggested the new way of application of this method in agronomy — precise determination of volume densities of indigestible lignified tissues (which determines forage digestibility), and of chlorenchyma and intercellulars (important for the photosynthesis). Comparison of the results obtained by classic anatomical analysis of leaf cross sections with the results of stereological analysis showed that both methods could be successfully applied for analysis of compact tissues (epidermis, vascular and mechanical). For the tissues that contained intercellulars (palisade and spongy), stereological method gave more precise results, as it enabled separate determination of volume density of intercellulars. A further advantage is that several leaf segments are analyzed and observed from four different angles. The obtained results opened new possibilities of application of stereological method in botanical and agricultural research, especially in prediction of digestibility and nutritional value of forages.

A new _γ-detector array at Institute of modern physics in Lanzhou is now in construction. The spherical frame is designed using Solidworks, and is assembled by 4 kinds of irregular polygons. 32 detectors could be placed on this frame in maximum, which are arranged with 4-4-4-8-4-4-4 configuration.