# Any non-zero real number can divide both sides.

Any non-zero change of direction is possible: if this distance is zero the velocities are reversed in the collision ; if it is close to the sum of the radii of the spheres the two bodies are only slightly deflected.

Any non-zero number with magnitude smaller than the smallest normal number is ' sub-normal '.

Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the pressure on the bottom being greater.

Any non-zero vector of an irreducible representation is cyclic.

Any linear time-invariant operation on s ( t ) produces a new spectrum of the form H ( f )• S ( f ), which changes the relative magnitudes and / or angles ( phase ) of the non-zero values of S ( f ).

Any practical implementation of an LC circuit will always include loss resulting from small but non-zero resistance in the wires connecting the circuit elements, as well as series and shunt resistances within the elements themselves.

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

* Any vector space V endowed with the identically zero Lie bracket becomes a Lie algebra.

# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.

Any point on a ray starting from point with direction ( here is a unit vector ) can be written as

Any force directed parallel to the particle's position vector does not produce a torque.

Any particular vector file format supports only some kinds of primitive objects.

Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal

Any vector that rotates around an axis with an angular speed vector ( as defined before ) satisfies:

Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:

Any element in the direct sum of two vector spaces of matrices can be represented as a direct sum of two matrices.

* Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space.

Any rotation in three-dimensions can be represented as an axis vector and an angle of rotation.

Any tangent vector at a point of the parametric surface M can be written in the form

Any covector field α has components in the basis of vector fields f. These are determined by

Any kind of animal that often visits or encounters flowers is likely to be a pollen vector to some extent.

# Any mental state can be described as an ( N )- dimensional vector of numeric activation values over neural units in a network.

Any vector bundle V over a manifold may be realized as the pullback of a universal bundle over the classifying space, and the Chern classes of V can therefore be defined as the pullback of the Chern classes of the universal bundle ; these universal Chern classes in turn can be explicitly written down in terms of Schubert cycles.

* Any coset of a subspace of a vector space is an affine space over that subspace.

Any smooth function on a symplectic manifold gives rise, by definition, to a Hamiltonian vector field and the set of all such form a subalgebra of the Lie Algebra of symplectic vector fields.

( vi ) Any compound, mixture, or preparation which contains any quantity of any of the substances referred to in paragraphs ( b )( 31 )( i ) through ( v ) of this section.

Last version VAD was working fine is 1. 1. 12, since v 1. 2 it has been replaced with simple Any Activity Detection.

Any consideration which relates to the use or development of land is capable of being a material consideration, but other circumstances such as personal hardship and fears of affected residents can be considered in exceptional cases ( the House of Lords in Great Portland Estates v. Westminster City Council ).

Any continuous valuation v on K < sup > n </ sup > that is invariant under rigid motions can be represented as

Any continuous valuation v on K < sup > n </ sup > that is invariant under rigid motions and homogeneous of degree j is a multiple of W < sub > n-j </ sub >.

Let now v and w be two vertices in G. Any spanning tree contains precisely one simple path between v and w. Taking this path in the uniform spanning tree gives a random simple path.

Any residual concern about the efficacy of such charges were comprehensively ousted by the House of Lords in Salomon v A Salomon & Co Ltd AC 22.

Any conformal map on a portion of Euclidean space of dimension greater than 2 can be composed from three types of transformation: a homothetic transformation, an isometry, and a special conformal transformation.

* Any square matrix with unit Euclidean norm is the average of two unitary matrices.

* Any reflection, translation and rotation is a global isometry on Euclidean spaces.

Any geometry found inside the square representing the Manhattan distance from the corner undergoes an additional check to see if the same geometry lies outside the quarter-circle radius representing the Euclidean distance.

Any discrete subset of Euclidean space is countable, since the isolation of each of its points ( together with the fact the rationals are dense in the reals ) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many.

Any finite set of lines in the Euclidean plane has a combinatorially equivalent arrangement in the hyperbolic plane ( e. g. by enclosing the vertices of the arrangement by a large circle and interpreting the interior of the circle as a Klein model of the hyperbolic plane ).

* Any Euclidean space is contractible, as is any star domain on a Euclidean space.