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equipping distributions; linear distribution; affine space
In this paper there are discussed the three-component distributions of affine space $A_{n+1}$. Functions $\lbrace \mathcal{M}^\sigma \rbrace $, which are introduced in the neighborhood of the second order, determine the normal of the first kind of $\mathcal{H}$-distribution in every center of $\mathcal{H}$-distribution. There are discussed too normals $\lbrace \mathcal{Z}^\sigma \rbrace $ and quasi-tensor of the second order $\lbrace \mathcal{S}^\sigma \rbrace $. In the same way bunches of the projective normals of the first kind of the $\mathcal{M}$-distributions were determined in the differential neighborhood of the second and third order.
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