This conjecture introduced the key idea of bounding various quadratic functions of the coefficients rather than the coefficients themselves, which is equivalent to bounding norms of elements in certain Hilbert spaces of schlicht functions.
32.
If is zero but one of the coefficients,,, or is non-zero, the function is classified as either a quartic function, cubic function, quadratic function or linear function.
33.
This quadratic function is strictly convex when " M " is positive definite, and hence has a unique finite global minimum, if and only if " M " is positive definite.
34.
This means that according to the model using a quadratic function of the exponential function, Wikipedia will never reach so many articles, but will instead start to decrease after a certain " ceiling " size.
35.
However while the description in Leslie's book contains an analogous circle construction, it was presented solely in elementary geometric terms without the notion of a Cartesian coordinate system or a quadratic function and its roots:
36.
Is the resulting approximation for G . More accurate results can be obtained using other methods to quadratic function across pairs of intervals, or building an appropriately smooth approximation to the underlying distribution function that matches the known data.
37.
The tables also capture information about how the Cartesian basis vectors, rotations about them, and quadratic functions of them transform by the symmetry operations of the group, by noting which irreducible representation transforms in the same way.
38.
Note that quadratic functions, such as in the one variable case, are not quadratic forms, as they are typically not homogeneous ( unless " b " and " c " are both 0 ).
39.
If it is applied on a quadratic function, then it yields the trapezoid figure from Carlyle's solution to Leslie's problem ( see graphic ) with one of its sides being the diameter of the Carlyle circle.
40.
When f is a convex quadratic function with positive definite Hessian B, one would expect the matrices H _ k generated by a Quasi-Newton method to converge to the inverse Hessian H = B ^ {-1 }.
