Characterization of preclones by matrix collections

Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure conditions.Comment: 11 page

Clones with finitely many relative R-classes

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A iff each one is a substitution instance of the other using operations from C. We study the clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde

Shoot growth and crown development: effect of crown position in three-dimensional simulations

Trees have been increasingly considered as modular organisms, with individual shoots forming autonomous units that respond semi-independently to their surrounding environment. However, there is evidence for fairly strict hormonal control of tree crown development. Studies on the hydraulic architecture of trees suggest a closer functional connection between shoots and crown development than is postulated by the theory of branch autonomy. We studied how shoot growth pattern influences growth and crown architecture in young Scots pine trees simulated by the LIGNUM model assuming that (a) the growth of a shoot mainly depends on its light climate and (b) the growth of a shoot is influenced by its position within the crown. We determined shoot position within the crown based on a recently developed vigor index. The vigor index compares the relative axis cross-sectional area from the base of the tree to each shoot and gives a value of 1 to the pathway of the greatest cross-sectional area. All other shoots attain values between 0 and 1 depending on their cross-sectional areas and the cross-sectional areas of the branches leading there from the main axis. The shoot light climate is characterized by annually intercepted photosynthetically active radiation. We compared the results from simulations (a) and (b) against an independent data set. The addition of a within-shoot position index (the vigor index) to our simulation (simulation b) resulted in a more realistic tree form than that obtained with simulation (a) alone. We discuss the functional significance of the results as well as the possibilities of using an index of shoot position in simulations of crown architecture

Different berries and berry fractions have various but slightly positive effects on the associated variables of metabolic diseases on overweight and obese women

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