2,008 research outputs found
The Star of David Rule
In this note, a new concept called {\em -matrix} is proposed, which is
an infinite lower triangular matrix obeying the generalized rule of David star.
Some basic properties of -matrices are discussed and two conjectures on
-matrices are presented, one of which states that if a matrix is a
-matrix, then so is its matrix inverse (if exists).Comment: 7 pages, 1 figur
Conditions implying regularity of the three dimensional Navier-Stokes equation
We obtain logarithmic improvements for conditions for regularity of the
Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda.
Some of the proofs make use of a stochastic approach involving Feynman-Kac like
inequalities. As part of the our methods, we give a different approach to a
priori estimates of Foias, Guillope and Temam.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints/
(Changes: this is a substantial rewrite of the previous version.
Two kinds of hook length formulas for complete -ary trees
In this paper, we define two kinds of hook length for internal vertices of
complete -ary trees, and deduce their corresponding hook length formulas,
which generalize the main results obtained by Du and Liu.Comment: 6 pages, 1 figure. To appear in Discrete Mathematic
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