Absolute Idealist Powers

Thomas Hodgkin: medical immortal and uncompromising idealist.

What Kind of Idealist Was Leibniz ?

Since the publication of Montgomery Furth’s groundbreaking 1967 essay, ‘Monadology’, discussions of Leibniz’s phenomenalism have been one of the main staples of Anglo-American Leibniz-scholarship. By no means, however, has any consensus been reached with regard to this issue. I think one important reason for this failure in agreement has to do with how one goes about understanding a related con...

Inequalities for Matrix Powers and Absolute Values: A Generalization of London’s Conjecture

We provide an inequality for absolute row and column sums of the powers of a complex matrix. This inequality generalizes several other inequalities. As a result, it provides an inequality that compares the absolute entry sum of the matrix powers to the sum of the powers of the absolute row/column sums. This provides a proof for a conjecture of London, which states that for all complex matrices ...

Norman Bethune: Gifted Surgeon and a Strange Idealist.

Comparing Powers and Symbolic Powers of Ideals

We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...