there is no doubt that the way to gain access to religious rulings and doctrines is the sunna of the prophet and the imams, as only second to the holy qur’ān, which is reported in thousands of traditions in various tradition books. in the meantime, every theologian and ḥadīth researcher has to leave behind two stages for a proper understanding of traditions: in the first stage, he is to conside...

In this paper, we analyse the proper curve $\gamma(s)$ lying on pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along curve, pseudosphere. Next, find condition for to become $V_{k} -$ slant helix in Minkowski space. Moreover, another $\beta(\bar{s})$ pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ which \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbra...

Last quarter, we introduced the closed diagonal condition for a prevariety to be a prevariety, and the “universally closed” condition for a variety to be complete. Earlier this quarter, we verified that in the case of complex prevarieties, these conditions are equivalent to the analytic topology being Hausdorff and compact, respectively. As we’ve discussed, in the scheme context a prevariety co...

Given a Polish space X and a countable collection of analytic hypergraphs on X, I consider the σ-ideal generated by Borel anticliques for the hypergraphs in the family. It turns out that many of the quotient posets are proper. I investigate the forcing properties of these posets, certain natural operations on them, and prove some related dichotomies.

reservoir models with many grid blocks suffer from long run time; it is hence important to deliberatea method to remedy this drawback. usual upscaling methods are proved to fail to reproduce fine gridmodel behaviors in coarse grid models in well proximity. this is attributed to rapid pressure changesin the near-well region. standard permeability upscaling methods are limited to systems with lin...