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The proportion of students taking a first algebra course in middle school has doubled over the past generation and there have been calls to make eighth grade algebra universal. We use significant poli...
Structure of the Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)
Hopf algebra and algebra algebraic function
2014/12/29
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive el...
Combinatorial Hopf Algebra and Generalized Dehn-Sommerville Relations
Combination of hopf algebra hopf algebra linear function generating function combination
2014/12/29
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field k equipped with a character (multiplicative linear functional) : H → k. We show that the terminal object in the category ...
The algebra of quadrature formulae for generic nodes
algebra quadrature formulae generic nodes
2012/9/19
Consider the classical problem of computing the expected value of areal function fof thed-variate random variableXas a linear combination of its valuesf(z) at a finite set pointsz伕 D 伡Rd. The general ...
Representation theorem for multiply self-decomposable probability measures on generalized convolution algebra
Representation theorem multiply self-decomposable probability measures
2009/9/24
Representation theorem for multiply self-decomposable probability measures on generalized convolution algebra。
On the unconditional bundle convergence in L(2)-space over a von Neumann algebra
the unconditional bundle convergence L(2)-space a von Neumann algebra
2009/9/21
The Tandori theorem concerning the sufficient condition
for the unconditional a.e. convergence of orthogonal series is
generalized for the bundle convergence in La-space over a cr-fdte von
Neumann ...
ON THE EWGODHC HHLBEWT TRANSFORM IN L OVER A VON NEUMANN ALGEBRA
Ergodic Hilbert transform von Neumann algebra bundle convergence
2009/9/18
In this note a noncommutative version of Jajte's theorem
on the existence of the ergodic Hilbert transform is given. As
a noncommutative counterpart of the classical almost everywhere convergence
t...