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So, the determinant is zero only if all of its random variables take on values that make the polynomial zero.
Then, standard methods to compute the volume of polytopes are applied to get a symbolic cost in polynomial form.
We have also made no further progress on deciding how well the constant term f0 of the flow polynomial can be approximated.
We will refer to such sequences as bounded sequences of polynomials or, where the context is clear, simply as bounded sequences.
We examine the possibilities for a polynomial version.
Because they use a numerical algorithm to optimize the cubic polynomial joint interpolator, it is not a real-time algorithm.
We now apply our main theorem and the previous results to show that polynomial rank-one transformations having restricted growth are mixing transformations.
The fluctuating velocity component a t each downstream location was curve fit up to the tenth degree polynomial.
In fact, we are easily able to reject a fourth-order polynomial against the cubic (likelihood ratio test 2 3.712).
The explicit forms of these polynomial equations have been found.
The trajectories of the body and its feet are modeled by piecewise cubic polynomials.
The interface between combinatorics and statistical mechanics provided by these polynomials has yielded progress in both areas.
This notion includes many regressions, polynomial fitting and supervised learning problems.
After this step, traditional formulae of symbolic summation can be applied and polytope volumes are expressed by polynomials whose variables are symbolic sizes.
A linear irreducible characteristic set, when its polynomials are arranged ascendingly according to the order of the leading variables, can be explained geometrically.
