Expand all Collapse all | Results 1 - 3 of 3 |
1. CMB 2011 (vol 54 pp. 566)
Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows We consider approximation of multivariate functions in Sobolev
spaces by high order Parzen windows in a non-uniform sampling
setting. Sampling points are neither i.i.d. nor regular, but are
noised from regular grids by non-uniform shifts of a probability
density function. Sample function values at sampling points are
drawn according to probability measures with expected values being
values of the approximated function. The approximation orders are
estimated by means of regularity of the approximated function, the
density function, and the order of the Parzen windows, under
suitable choices of the scaling parameter.
Keywords:multivariate approximation, Sobolev spaces, non-uniform randomized sampling, high order Parzen windows, convergence rates Categories:68T05, 62J02 |
2. CMB 2011 (vol 54 pp. 288)
The Resultant of Chebyshev Polynomials Let $T_{n}$ denote the $n$-th
Chebyshev polynomial of the first kind,
and let $U_{n}$ denote the $n$-th
Chebyshev polynomial of the second kind.
We give an explicit formula for the resultant
$\operatorname{res}( T_{m}, T_{n} )$.
Similarly, we give a formula for
$\operatorname{res}( U_{m}, U_{n} )$.
Keywords:resultant, Chebyshev polynomial Categories:11Y11, 68W20 |
3. CMB 2004 (vol 47 pp. 343)
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras We construct new examples of non-nil algebras with any number of
generators, which are direct sums of two
locally nilpotent subalgebras. Like all previously known examples, our examples
are contracted semigroup algebras and the underlying semigroups are unions
of locally nilpotent subsemigroups.
In our constructions we make more
transparent
than in the past the close relationship between the considered problem
and combinatorics of words.
Keywords:locally nilpotent rings,, nil rings, locally nilpotent semigroups,, semigroup algebras, monomial algebras, infinite words Categories:16N40, 16S15, 20M05, 20M25, 68R15 |