Any other point of intersection between C and Af will be called a tangent point.

Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

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

Any linear functional α on tangent vectors can be expanded in terms of the dual basis θ

Any time we choose a point that is rejected, we tighten the envelope with another line segment that is tangent to the curve at the point with the same x-coordinate as the chosen point.

* Any Hilbert space H is a Hilbert manifold with a single global chart given by the identity function on H. Moreover, since H is a vector space, the tangent space T < sub > p </ sub > H to H at any point p ∈ H is canonically isomorphic to H itself, and so has a natural inner product, the " same " as the one on H. Thus, H can be given the structure of a Riemannian manifold with metric

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 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 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 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 non-zero vector v divides the Euclidean space into two half-spaces bounding the hyperplane v < sup >∧</ sup > orthogonal to v, namely v < sup >+</ sup > and v < sup >−</ sup >.

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

* 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.

Any attempt to reconcile this statement of the central issue in the campaign of 1956 with the nature of the man who could not conceive it as the central issue will at least resolve our confusions about the chaotic and misleading results of the earnestness of both doctors and President in a situation which should never have arisen.

Any information we have here in Taiwan is at your disposal ''.

Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.

Any string s has at least one description, namely the program:

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

Any individual alignment could indicate a direction by chance, but he planned to show that together the distribution of alignments was non-random, showing that there was an astronomical intent to the orientation of at least some of the alignments.

Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.

Any player is usually allowed to control or bet in as many boxes as desired at a single table, but it is prohibited for an individual to play on more than one table at a time or to place multiple bets within a single box.

Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.

Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor.

Any young player who has good control will become a successful curve pitcher long before the pitcher who is endeavoring to master both curves and control at the same time.

Any configuration of charges or currents has a ' dipole moment ', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration.

Any byte in the entire file can be owned by at most one section, and there can be orphan bytes which are not owned by any section.

Any Agent or Support staff member can be transferred to any location for any length of time if their skills are deemed necessary at one of the FBI field offices or one of the 400 resident agencies the FBI maintains.

# Any player who actually plays in a Candidates Tournament and scores at least percent.

Any increase in power at the supranational level, he argued, results from a direct decision by governments.

Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart.

Niven demonstrated this, to his own satisfaction, with Safe at Any Speed.

Any policy built into the kernel cannot be overwritten at user level and therefore limits the generality of the microkernel.

Any communication to another system in the galaxy has to be recorded on a physical disc which is transported through the wormhole ; chains of these are referenced in Diplomatic Immunity ( Chapter 9 ) where messages are ' squirted ' to a station on one side of a wormhole, flown ( on a physical medium ) through the wormhole and re-squirted to a similar arrangement at the next wormhole in the sequence.

Any incidence of water is then used by migrating birds who also pass seeds with their droppings which will grow at the water's edge forming an oasis.

When the final episode, " Things Aren't Simple Any More " originally aired on 20 November 2000 at 21: 00, it coincided with the broadcast of the first jackpot winner in the UK version of Who Wants to Be a Millionaire ?, which had been filmed the Sunday before the broadcast.