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Any and real-valued

Any smooth real-valued function H on a symplectic manifold can be used to define a Hamiltonian system.

Any and differentiable

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

* Noether's theorem: Any quantity which has a continuous differentiable symmetry in the action has an associated conservation law.

Any covering space of a differentiable manifold may be equipped with a ( natural ) differentiable structure that turns p ( the covering map in question ) into a local diffeomorphism – a map with constant rank n.

1 ) Any non-diagonalizable intersection form gives rise to a four-dimensional topological manifold with no differentiable structure ( so cannot be smoothed ).

Any and function

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 0 ( 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.

Any and H

:: Theorem ( Lefschetz theorem on ( 1, 1 )- classes ) Any element of H 2 ( X, Z ) ∩ H 1, 1 ( 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 ξ 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 p 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 and on

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced by the piston heads cannot be readily computed.

Any free elections that were to be held in Poland would have to produce a government in which Moscow had complete confidence, and all pressure from the West for free voting by anti-Soviet elements in Poland would be met by restrictions on voting by these elements.

Any adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.

Any decline in amphibian numbers will have an impact on the patterns of predation.

Any historical material on anagrams must always be interpreted in terms of the assumptions and spellings that were current for the language in question.

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.

Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.

Any alcohol ( beer, wine, spirits ) cannot be bought on Sundays before noon.

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 measure μ defined on the σ-algebra of Borel sets is called a Borel measure.

Any desired arbitration logic is placed on the daughter cards.

Any attempt to impose an organization on them is bound to be somewhat arbitrary.

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

The Environmental Modification Convention ( ENMOD ), formally the Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques is an international treaty prohibiting the military or other hostile use of environmental modification techniques.

One episode in Series 5 of Steptoe and Son was entitled " Any Old Iron ", for the same reason, when Albert thinks that Harold is ' on the turn '.

Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.

Any person who felt himself wronged might lay an information before the Council of Areopagus, on declaring what law was broken by the wrong done to him.

Any elected or appointed board, committee, town officer or ten voters, may place an article on the warrant.

Any rain falling on the above-water rim quickly percolates through the surface sand and encounters the salt water underneath.

* 1976 – The United Nations General Assembly adopts the Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques.

Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.

:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;

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