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

* Any analytic function is smooth, that is, infinitely differentiable.

* Any smooth manifold is a diffeological space.

Any smooth manifold admits a Riemannian metric, which often helps to solve problems of differential topology.

# Any smooth manifold of dimension n ≥ 3 admits a Riemannian metric with negative Ricci curvature.

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 smooth function of one variable approximates a quadratic function when examined near enough to its minimum point ; and therefore the force — which is the derivative of energy with respect to displacement — will approximate a linear function.

Any splices narrow enough to maintain smooth running would be less able to support the required weight.

The Bureau of Alcohol, Tobacco, Firearms & Explosives recognizes these firearms as being a smooth bore handgun which is an Any Other Weapon ( AOW ).

Any deviations from a smooth curve will cause the airflow over the leeward side of the sail to separate causing a reduction in lift and reduced performance.

Any such surface is the Kummer variety of the Jacobian of a smooth hyperelliptic curve of genus 2 ; i. e. a quotient of the Jacobian by the Kummer involution x ↦ − x.

Any number of caenophidian snakes can be induced to sidewind on artificial smooth surfaces, though difficulty in getting them to do so and their proficiency at it vary greatly.

The article continues: " Any lady must be as great an Infidel as the Grand Sultan himself, who, after receiving such authority can doubt that her skin will become as superlatively smooth, soft, white and delicate, as that of the lovely Fatima, whatever may have been its feel or its appearance before.

The canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism between the respective canonical rings.

Any real-valued differentiable function, H, on a symplectic manifold can serve as an energy function or Hamiltonian.

Any function itself defines an equivalence relation on according to which if and only if.

Any cryptographic hash function, such as MD5 or SHA-1, may be used in the calculation of an HMAC ; the resulting MAC algorithm is termed HMAC-MD5 or HMAC-SHA1 accordingly.

Any compression algorithm can be viewed as a function that maps sequences of units ( normally octets ) into other sequences of the same units.

The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.

Any non-constant algebraic function of a single variable yields a transcendental value when applied to a transcendental argument.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.

Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.

Any building requires a certain amount of internal infrastructure to function, which includes such elements like heating / cooling, power and telecommunications, water and wastewater etc.

Any such function is called a Urysohn function for A and B.

Any function can be restricted to a subset of its domain.

Any such K is referred to as a Lipschitz constant for the function ƒ.

Any impairment which limits the physical function of limbs or fine or gross motor ability is a physical disability.

* Any polynomial ( real or complex ) is an analytic function.

Any Taylor series for this function converges not only for x close enough to x < sub > 0 </ sub > ( as in the definition ) but for all values of x ( real or complex ).

Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

" Any sequence of numbers that may be modeled by a mathematical function can be considered a pattern.

Any such satisficing problem can be formulated as an ( equivalent ) optimization problem using the Indicator function of the satisficing requirements as an objective function.

Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms.

:: Theorem ( Lefschetz theorem on ( 1, 1 )- classes ) Any element of H < sup > 2 </ sup >( X, Z ) ∩ H < sup > 1, 1 </ sup >( X ) is the cohomology class of a divisor on X.

Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where ( in units where c = 1 ) E is equal to H at any point in space.

Any ξ ∈ gives rise to a canonical vertical vector field X < sub > ξ </ sub > by taking the derivative of the right action of the 1-parameter subgroup of H associated to ξ.

Any steps ( other than the conclusion ) which do not actually depend on H should be moved up before the hypothesis step and unindented one level.

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 of the extinct members ( or in works of fiction, living members ) of the clade Hominina other than Homo or alternatively just H. sapiens sapiens.

Any friction would result in a pressure build-up in the syringe and would lead to an inaccurate measurement, that is, a lower amount of gas would be determined, than really obtained .< ref > Schmid, H. P. " Pressure and Gas Laws.

#" Cape Feare ": " Any Last Requests ?/ H. M. S.

Any unitary operator on H is a partial isometry with initial and final subspaces being all of H.

** Any parabolic element of G fixing a boundary point of D is in H.

The state of the composite system is given by a density operator on H. Any density operator σ on H is a sum of the form:

* Any irreducible representation R of H gives an irreducible representation of G using the quotient map from G to H ( that is, as a restricted representation ).

* 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