This article examines the psychological doctrines of Ashʿarite theologian and polymath Fakhr al-Dīn al-Rāzī (d. 606/1210). The starting point discussion is his critical reception Avicenna’s ca. 428/1037) theories. I focus on al-Rāzī’s early works philosophy, in particular <em>al-Mab</em><em>āḥith al-mashriqiyya</em> famous commentary <em>al-Ish</em><em>...

We construct the first examples of manifolds, the simplest one being S3×S4×R5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls. According to the soul theorem of J. Cheeger and D. Gromoll [CG72], a complete open manifold of nonnegative sectional curvature is diffeomorphic to the total space of the normal bundle of a compact totally geodesic s...

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain’s equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain’s equation, formulated in a two-component form, we...

We see the Sun, Moon. and stars in the heavens as if placed on the inside of a sphere. But even early man had ideas about the distances to these heavenly objects. The Greek philosopher Anaxagoras living in Athens 2500 years ago claimed that the Sun is a fiery rock larger than the whole Peloponnesian peninsula. This implies a distance to the Sun larger than 20,000 km. Anaxagoras. however, was ac...

Most potential funders wish to see a business plan as a first step in deciding whether or not to invest. However, much of the literature on how to write a business plan fails to emphasize that different types of funder look at business plans from different perspectives. Using a real time methodology this article highlights the different investment criteria of bankers, venture capital fund manag...

Despite the increasing importance of business angels (BAs) as crucial players in growth high-potential early-stage startups, their motivations are not fully understood. Many perceptions BAs deviate significantly from more conventional views economic and financial models. To gain a comprehensive understanding BAs’ goals, qualitative techniques marketing consumer behaviour additional lenses (incl...

Point Our Souls to Christ: Lessons from Leviticus