Abstract The article analyzes Lev Vygotsky’s attempts to utilize Spinoza’s philosophical ideas in solving the methodological crisis of psychology 1920s and 1930s. Vygotsky had a manuscript, Uchenie ob emocijakh , where he scrutinized doctrines effects on Descartes Spinoza. Whilst Descartes’ doctrine built dualistic soul versus body premise, starting point was monistic. Despite his clear sympath...

We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the nonsymmetric setting an inequality of K. Ball [2] and we give a simple proof of the case of equality. As a corollary, we get some inequalities for logconcave functions and Legendre transforms which extend the recent result of Artstein, Klartag and Milman [1], wi...

The singular points of an irreducible plane cubic curve are quite limited: one knot/node, or one cusp. Our research starts originally with the Descartes Folium, which has a knot/node, and is able to have many group structures. The original results are concentrated in six directions: (i) special structures on affine algebraic varieties, (ii) theory of K-groups, (iii) isomorphisms of K-groups, (i...