IV) Usefulness of this new method in problem solving and related to polyhedral and

affine space.

Another perspective, which may be more natural to some readers, is to consider the

affine space {x' + N(A)} consisting of solutions to Az = b, where, x' is the solution of minimal norm.

The 21 papers propose an algorithm for continuous piecewise affine maps of compact support, investigate the stability of cycles in gene networks with variable feedbacks, and describe polynomial maps of the

affine space.

We will treat these points as elements of

affine space, and use [t.

Consequently the simultaneous rotations by equal intrinsic angle [phi][psi] of the intrinsic

affine space coordinates of the symmetry-partner particles' frames [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and -[phi][[?

which shows that the set of the functions h(t) is a vector space and the set of the functions x(t) + [epsilon]h(t) is an

affine space.

L] is an

affine space whose dimension is equal to the number of "+" entries in L, which we denote by [absolute value of L].

k] minimizes [phi] over the entire

affine space [x.

that contains the one-dimensional intrinsic rest mass pm0 of the particle in the intrinsic

affine space coordinate [phi][?

The extended three-dimensional

affine space constituted by the affine coordinates [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] cannot hold matter (or mass of particles and objects).

One aspect that we stress more explicitly than Sonneveld and van Gijzen is that IDR(s) is a Krylov space method, and therefore the residuals lie in an

affine space that is embedded in a Krylov subspace.

It is quite obvious for a mathematician that the authors confuse a vector space with an

affine space.