affine space


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affine space

[ə′fīn ‚spās]
(mathematics)
An n-dimensional vector space which has an affine connection defined on it.
References in periodicals archive ?
The topics include Schwartz space of parabolic basic affine space and asymptotic Hecke algebras, generalized and degenerate Whittaker quotients and Fourier coefficients, on the support of matrix coefficients of super-cuspidal representations of the general linear group over a local non-Archimedean field, limiting cycles and periods of Maass forms.
The affine space is created by 0,1 and 16 operators.
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.
Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2 + 1.
Affine space. Let A = [F.sub.1][[X.sub.1], ..., [X.sub.n]].
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. Other topics include optimal control of a dynamical biological system, algebraic and analytic properties of quasimetric space with dilations, the Schwarz kernel in Clifford analysis, and global holomorphic approximations of Cauchy-Riemann functions.
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][[??].sup.0*] relative to the intrinsic affine space coordinates of the symmetry-partner observers' frames [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and -[phi][[??].sup.0*] respectively in the context of the intrinsic special theory of relativity ([phi]SR), as developed in [1], implied by item 3, are valid relative to every one of the four symmetry-partner observers in the four proper Euclidean 3-spaces (or universes).
Friedman [1983] showed how to do this in the modern language of geometrical objects on differentiable manifolds: more simply stated, we supplement 'Leibnizian spacetime' with a four-dimensional affine structure, and we further stipulate (by means of a preferred timelike vector field) that one particular family of parallel straight lines of the affine space represents 'immobile space'.
The end of the foregoing paragraph is so since the affine space coordinates [??]' and [??]' of the particle's frame are not rotated along with the affine space coordinate [??]' from affine 3space [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of the particle's frame (as a hyper-surface) along the horizontal towards the time dimension ct along the vertical.
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.
In other words, our considerations take place in an arbitrary affine space.
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).