where X and Y are square matrices whose diagonal elements (where i = j) are unity, and whose subdiagonal elements (where i > j) are zero, whilst D is a diagonal matrix, that is, one whose off-diagonal elements (where i ?¿ j) are zero [1]. Where this factorization exists, it is unique [1]. Where it does not exist, there exists another factorization of the form (1) in which the matrices X and Y d...

Boghossian (Philos Perspect 8:33–50, 1994) argued (a) that externalism is incompatible with a transparency thesis according to which we can know priori whether any two of our occurrent thoughts have the same or distinct content, and (b) this integral commonsense conception rationality, requires apriority logical abilities. Stalnaker (Our knowledge internal world, Oxford University Press, Oxford...

This paper introduces a Hopf algebra structure on family of reduced pipe dreams. We show that this is free and cofree, construct surjection onto commutative permutations. The dream contains subalgebras with interesting sets generators Hilbert series related to subsequences Catalan numbers. Three other relevant include the Loday–Ronco complete binary trees, special lattice walks quarter plane, ν...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

Convergence of diagonal Padé approximants is studied for a class of functions which admit the integral representation F(λ) = r1(λ) R 1 −1 tdσ(t) t−λ + r2(λ), where σ is a finite nonnegative measure on [−1, 1], r1, r2 are real rational functions bounded at ∞, and r1 is nonnegative for real λ. Sufficient conditions for the convergence of a subsequence of diagonal Padé approximants of F on R \ [−1...