METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES

Hausdorff Dimension of Measures via Poincaré Recurrence

We study the quantitative behavior of Poincaré recurrence. In particular, for an equilibrium measure on a locally maximal hyperbolic set of a C diffeomorphism f , we show that the recurrence rate to each point coincides almost everywhere with the Hausdorff dimension d of the measure, that is, inf{k > 0 : fx ∈ B(x, r)} ∼ r. This result is a non-trivial generalization of work of Boshernitzan conc...

Metric Properties of Engel Series Expansions of Laurent Series

Hausdorff Dimension of Metric Spaces and Lipschitz Maps onto Cubes

We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can be always mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urbański by showing that the transfinite Hausdorff...

Diophantine Approximation, Khintchine's Theorem, Torus Geometry and Hausdorff Dimension

A general form of the Borel-Cantelli Lemma and its connection with the proof of Khintchine's Theorem on Diophantine approximation and the more general Khintchine-Groshev theorem are discussed. The torus geometry in the planar case allows a relatively direct proof of the planar Groshev theorem for the set of ψ-approximable points in the plane. The construction and use of Haudsorff measure and di...

: the effect of sericin levels (silk glue protein) on rate of in vitro maturation, fertilization and culture of sheep oocytes

هدف از آزمایش اول بررسی اثر سطوح مختلف سریسین [0 (control), 0.1, 0.5, 1.0, 2.5 %] افزوده شده به محیط , ivm بر cumulus cell expansion، بلوغ هسته و توسعه متوالی جنین، در گوسفندان نژاد سنجابی در فصل تولید مثلی می باشد. از سرگیری میوز به وسیله خارج شدن اولین پولار بادی اندازه گیری و هم چنین درصد رسیدن جنین های دو سلولی به مرحله کلیواژ و بلاستوسیت نیز به عنوان نشانه ای از میزان شایستگی توسعه اولیه ج...