Transforming a hierarchical into a unitary-weight representation.
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Let be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra with homogeneous generators . We show that for acyclic, the cohomology of the quotient
We show that each element in the semigroup of all non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of , which form a cone consisting of all upper (or lower) triangular intensity matrices.
A subset of the plane is called a two point set if it intersects any line in exactly two points. We give constructions of two point sets possessing some additional properties. Among these properties we consider: being a Hamel base, belonging to some -ideal, being (completely) nonmeasurable with respect to different -ideals, being a -covering. We also give examples of properties that are not satisfied by any two point set: being Luzin, Sierpiński and Bernstein set. We also consider natural generalizations...
We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or , where denotes the “centered” fractional part of . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet -functions at .