Dynamic Matrix-Fracture Transfer Behaviour in Dual-Porosity Models

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Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

We consider improvements of Dirichlet's Theorem on space of matrices $M_{m,n}(R)$. It is shown that for a certain class of fractals $K\subset [0,1]^{mn}\subset M_{m,n}(R)$ of local maximal dimension Dirichlet's Theorem cannot be improved almost everywhere. This is shown using entropy and dynamics on homogeneous spaces of Lie groups.Comment: 27 page

Primate phylogeny: molecular evidence for a pongid clade excluding humans and a prosimian clade containing tarsiers

Interpretations of molecular data by the modern evolution theory are often sharply inconsistent with paleontological results. This is to be expected since the theory is only true for microevolution and yet fossil records are mostly about macroevolution. The maximum genetic diversity (MGD) hypothesis is a more coherent and complete account of evolution that has yet to meet a single contradiction. Here, molecular data were analyzed based on the MGD to resolve key questions of primate phylogeny. A new method was developed from a novel result predicted by the MGD: genetic non-equidistance to a simpler taxon only in slow but not in fast evolving sequences given non-equidistance in time. This ‘slow clock’ method showed that humans are genetically more distant to orangutans than African apes are and separated from the pongid clade (containing orangutan and African apes) 17.3 million years ago. Also, tarsiers are genetically closer to lorises than simian primates are, suggesting a tarsier-loris clade to the exclusion of simian primates. The validity and internal coherence of the primate phylogeny here were independently verified. The molecular split time of human and pongid calibrated from the fossil record of gorilla, or the fossil times for the radiation of anthropoids/mammals at the K/T boundary and for the Eutheria-Metatheria split in the Early Cretaceous, were independently confirmed from molecular dating calibrated using the fossil split times of tarsier-loris and two other pairs of mammals (mouse-rat and opossum-kangaroo). This remarkable and unprecedented concordance between molecules and fossils provides the latest confirmation of the inseparable unity of genotype and phenotype and the unmatched value of MGD in a coherent interpretation of life history