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Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2003)

RAIRO - Operations Research - Recherche Opérationnelle

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.

Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)

RAIRO - Operations Research

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.

Transgression and Clifford algebras

Rudolf Philippe Rohr (2009)

Annales de l’institut Fourier

Let W be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra S P with homogeneous generators p 1 , , p r . We show that for W acyclic, the cohomology of the quotient H ( W / < p ...

Triangular stochastic matrices generated by infinitesimal elements

Inheung Chon, Hyesung Min (1999)

Czechoslovak Mathematical Journal

We show that each element in the semigroup S n of all n × n non-singular upper (or lower) triangular stochastic matrices is generated by the infinitesimal elements of S n , which form a cone consisting of all n × n upper (or lower) triangular intensity matrices.

Two point sets with additional properties

Marek Bienias, Szymon Głąb, Robert Rałowski, Szymon Żeberski (2013)

Czechoslovak Mathematical Journal

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 σ -ideal, being (completely) nonmeasurable with respect to different σ -ideals, being a κ -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...

Two problems related to the non-vanishing of L ( 1 , χ )

Paolo Codecà, Roberto Dvornicich, Umberto Zannier (1998)

Journal de théorie des nombres de Bordeaux

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 ( ( x y / q ) ) , ( 0 x , y < q ) , where ( ( u ) ) = u - [ u ] - 1 / 2 denotes the “centered” fractional part of x . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet L -functions at s = 1 .

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