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

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

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 symplectic vector space admits a Darboux basis

* Any compact symplectic manifold admits a symplectic Lefschetz pencil ( Donaldson 1999 ).

Any symplectic manifold admits a compatible almost complex structure making it into an almost Kähler manifold.

# 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 smooth manifold is a diffeological space.

Any Calabi – Yau manifold has a finite cover that is the product of a torus and a simply-connected Calabi – Yau manifold.

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 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.

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 open manifold admits a ( non-complete ) Riemannian metric of positive ( or negative ) curvature.

Any “ nice ” space such as a manifold or CW complex is semi-locally simply connected.

Any evolution of spin network provides a spin foam over a manifold of one dimension higher than the dimensions of the corresponding spin network.

* Any manifold with constant sectional curvature is an Einstein manifold — in particular:

Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy.

Any manifold is an n-handlebody, that is, any manifold is the union of handles.

Any handlebody decomposition of a manifold defines a CW complex decomposition of the manifold, since attaching an r-handle is the same, up to homotopy equivalence, as attaching an r-cell.

Any sub-Riemannian manifold carries the natural intrinsic metric, called the metric of Carnot – Carathéodory, defined as

Any compact manifold has isoperimetric dimension 0.

Any classical language can be studied philologically, and indeed describing a language as " classical " is to imply the existence of a philological tradition associated with it.

Any state may be considered as the result of a superposition of two or more other states, and indeed in an infinite number of ways.

Any law passed by the District legislature can be nullified by Congressional action, and indeed the District government could be significantly altered or eliminated entirely by a simple majority vote in Congress.

Any civil disorder is a delicate balance of power, and indeed, a political power struggle of some sort is typically the root cause of any such conflict.

Any foreigner found to be infected with HIV, the virus which causes AIDS ( or, indeed, any other serious medical condition ), is deported to their country of origin.

Any bounded operator L that has finite rank is a compact operator ; indeed, the class of compact operators is a natural generalisation of the class of finite-rank operators in an infinite-dimensional setting.

Any of multiple technical difficulties, while not endangering the patient ( indeed added to protect the patient's interests ) can significantly increase the examination time.

Any thread of execution entering any critical section anywhere in the system will, with this implementation, prevent any other thread, including an interrupt, from getting the CPU and therefore from entering any other critical section or, indeed, any code whatsoever, until the original thread leaves its critical section.

Any two splitting Cartan algebras are conjugate, and they fulfill a similar function to Cartan algebras in semisimple Lie algebras over algebraically closed fields, so split semisimple Lie algebras ( indeed, split reductive Lie algebras ) share many properties with semisimple Lie algebras over algebraically closed fields.

“ As real incomes rose, so public authorities were enabled ( and indeed encouraged ) to raise funds, both from taxation and through borrowing, to accelerate the rate of investment and current spending in projects which are partly immediately productive, partly conducive to the creation of the good life, as seen in Germany .... Any superficial examination of the German townscape, let alone perusal of the statistics, shows that Germany has spent sums on hospitals, libraries, theatres, schools, parks, railway-stations, socially-aided housing, underground railways, airports, museums, and so on which are simply not to be compared with British efforts in this direction .”

Any one, or indeed several in combination, of these factors may result in either lost data and / or compromised data backup attempts.

Any translation will, indeed, be more or less imperfect, and how great the difficulties are to transfer the expressions of a language, especially those of the rich Greek language, into another language, will only those recognize who have attempted to execute a translation.

Any and all payments required to be made by the Secretary of the Treasury under this title pursuant to any award made by the Commission to the Government of the United States shall be covered into the Treasury to the credit of miscellaneous receipts.

Any person who makes application for any such payment shall be held to have consented to all the provisions of this Title.

Any shareholder of any of these funds who finds a mistake in his account certainly should get in touch with the bank.

* Any expression formed using any combination of the basic arithmetic operations and extraction of nth roots gives an algebraic number.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.

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 ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any commutative ring R is an algebra over itself, or any subring of R.

Section 72 says " Any person who takes part in a fight in a public place, or takes part in a fight of such a nature as to alarm the public in any other place to which the public have access, commits a misdemeanour.

Any difference between the hedged positions represents any remaining risk ( such as basis risk ) plus profit ; the belief is that there remains some difference which, even after hedging most risk, represents pure profit.

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 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 non-Jewish slave bought by a Jew will be confiscated by the state ; if a Jew attempts to circumcise a non-Jewish slave, the slave will be freed and the Jew shall face capital punishment ; any Christian slaves owned by a Jew will be taken away and freed ;

Any electric charge that accelerates, or any changing magnetic field, produces electromagnetic radiation.

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 Compatibility Group designator can be assigned to any Hazard Class and Division.

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 qualifying from the Interzonal tournament to play in the Candidates Tournament, even if he did not play in the Candidates for any reason.

Any right action has an equivalent left action, thus only left actions can be considered without any loss of generality.

Any client can use any method that they want and the server can choose to support any method it wants.

Any customer who opted to keep theirs was required to sign a waiver indicating their understanding that no more software would be written for the system and which absolved Intellivision of any future responsibility for technical support.

Any member may make accusations of any crime.