Conclusion: Any light beam moving vertically downwards in the concavity of the parabola ( parallel to the axis of symmetry ) will bounce off the parabola moving directly towards the focus.

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

Any planar cross section passing through the center of an ellipsoid forms an ellipse on its surface: this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution ( or all sections when the ellipsoid degenerates to a sphere.

Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite.

* Any baryon net excess existing before the electroweak symmetry breaking was wiped off because sphalerons were abundant due to the high temperatures existing in the universe.

Any conserved quantum number is a symmetry of the Hamiltonian of the system ( see Noether's theorem ).

* Any member of the genus Eunectes, a group of large, aquatic snakes found in South America

Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.

Any formal or informal group — a family, a church, a club, a business, a trade union — may be said to have government.

* Any Lie group G defines an associated real Lie algebra.

* Any topologically closed subgroup of a Lie group is a Lie group.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.

# 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 attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.

However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).

* Any subgroup of a free group is free.

Any group of four students may run for office, but there must always be four students.

Any group that managed to find ways of reasoning effectively would reap benefits for all its members, increasing their fitness.

Any time during a triad conversation, group members can switch seats and one of the co-pilots can sit in the pilot ’ s seat.

Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

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 algebra whose elements are idempotent is also power-associative.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

Any class can be viewed as a category whose only morphisms are the identity morphisms.

: Any magistrate, or in the absence of any magistrate any commissioned officer in Her Majesty's Naval, Military or Air Force Service or any police officer above the rank of inspector, in whose view a riot is being committed, or who apprehends that a riot is about to be committed by persons being assembled within his view, may make or cause to be made a proclamation in the Queen's name, in such form as he thinks fit, commanding the rioters or persons so assembled to disperse peaceably.

Any sort of radio transmitter whose presence is suspected is detectable with suitable equipment.

Any source whose appearance or behavior indicates that he is willing to talk should be noted by the screeners.

Any conjectures are largely based on the date of her father's death ( 1006 ), the approximate date of her betrothal to Cnut ( 1004 × 1016, see below ) and the time by which she had borne him sons, whose ages are themselves difficult to establish.

Any timelike curve admits a comoving observer whose " time axis " corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis.

Any oscillator whose oscillations are driven by a system that almost always is dissipating energy may be called a relaxation oscillator.

Any misuse of the arm by the employee of the company in whose custody the arm is placed is the responsibility of the company / agency.

" The Amerasian Foundation ( AF ) and Amerasian Family Finder ( AFF ) define an Amerasian as: " Any person who was fathered by a citizen of the United States ( an American servicemen, American expatriate, or U. S. Government Employee ( Regular or Contract )) and whose mother is, or was, an Asian National Asian.

Any physical object whose radius R becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become a black hole.

** " Common variation ": Any player whose score hits exactly " 45 " is set back to Zero — The dreaded Forty-Five Rule.

Any man whose name appeared on the list was ipso facto stripped of his citizenship and excluded from all protection under law ; reward money was given to any informer who gave information leading to the death of a proscribed man, and any person who killed a proscribed man was entitled to keep part of his estate ( the remainder went to the state ).

-- Any attempt to access a member whose existence depends

Any node whose lower bound is greater than can be discarded.

Any human with courage and presence of mind can outwit a troll, and those whose faith is strong can even challenge them to mortal combat.

Any Iraqi whose citizenship was withdrawn for political, religious, racial, or sectarian reasons has the right to reclaim his Iraqi citizenship, and each Iraqi is guaranteed the right to carry more than one citizenship.

An introductory title screen – repeated as the Foreword to the 1946 novelization by Eric Warman – contains an explicit statement: " This is the story of two worlds, the one we know and another which exists only in the mind of a young airman whose life and imagination have been violently shaped by war ", adding " Any resemblance to any other world known or unknown is purely coincidental ".

Any skew semistandard tableau of shape / with positive integer entries gives rise to a sequence of partitions ( or Young diagrams ), by starting with, and taking for the partition places further in the sequence the one whose diagram is obtained from that of by adding all the boxes that contain a value ≤ in ; this partition eventually becomes equal to.

Any pair of successive shapes in such a sequence is a skew shape whose diagram contains at most one box in each column ; such shapes are called horizontal strips.