Consider also the grade point average.

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

Consider a function from a metric space M to a topological space V, and a point c of M. We direct the set M

Consider a point, P, such that light that is initially travelling parallel to the axis of symmetry is reflected from P along a line that is perpendicular to the axis of symmetry.

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider the system at the point it has reached equilibrium.

Consider a point charge q with position ( x, y, z ).

Consider a particular bundle and take the total derivative of about this point:

Consider the class of all regular paths from a point p to another point q.

If S is compact but not closed, then it has an accumulation point a not in S. Consider a collection consisting of an open neighborhood N ( x ) for each x ∈ S, chosen small enough to not intersect some neighborhood V < sub > x </ sub > of a.

Consider the open balls centered upon a common point, with any radius.

Consider as an example the interaction between a star and a distant galaxy: The error arising from combining all the stars in the distant galaxy into one point mass is negligible.

Consider the space of real-valued functions together with a special point.

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider a massless rigid rod of length l with a point mass m at one end and rotating about the other end.

Consider first one mole of gas which is composed of non-interacting point particles

Consider the point 1 ∈ R < sup >+</ sup >, and x ∈ R an element of the tangent space at 1.

Suppose S ' is in relative uniform motion to S with velocity v. Consider a point object whose position is given by r

Consider a valid line to be one where every point is within distance w / 2 of the line ( that is, lies on a track of width w, where w << d ).

Consider, for purposes of illustration, a mountainous landscape M. If f is the function sending each point to its elevation, then the inverse image of a point in ( a level set ) is simply a contour line.

Consider climbing up the connectivity ladder — assume X is a simply-connected CW-complex whose 0-skeleton consists of a point.

Consider a sphere S ( r ) with radius r. A point on the sphere is identified by its latitude φ and longitude λ, for which we introduce the random variables Φ and Λ that take values in Ω < sub > 1 </ sub > = respectively Ω < sub > 2 </ sub > =.

Consider a Lagrangian which does not depend on an (" ignorable ", as above ) coordinate q < sub > k </ sub >; so it is invariant ( symmetric ) under changes q < sub > k </ sub > → q < sub > k </ sub > + δq < sub > k </ sub >.

Consider the positive real numbers R < sup >+</ sup >, a Lie group under the usual multiplication.

Consider the comparison to its RCOOH acid analogue: the chloride ion is an excellent leaving group while the hydroxide is not under normal conditions ; i. e. even weak nucleophiles attack the carbonyl.

Consider the hierarchy shown below, which has several Subcriteria under each Criterion.

Consider a smooth velocity field and the family of transformations of the initial domain under the velocity field:

Consider a particle under the action of a non-uniform oscillating field.

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Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.

Consider a binary electrolyte AB which dissociates into A + and B-ions and the equilibrium state is represented by the equation:

Consider a qubit in a pure state.

Consider a dissident in a totalitarian state who wishes to share a modified bit of software with fellow dissidents, but does not wish to reveal the identity of the modifier, or directly reveal the modifications themselves, or even possession of the program, to the government.

Consider the circuit minimization problem: given a circuit A computing a Boolean function f and a number n, determine if there is a circuit with at most n gates that computes the same function f. An alternating Turing machine, with one alternation, starting in an existential state, can solve this problem in polynomial time ( by guessing a circuit B with at most n gates, then switching to a universal state, guessing an input, and checking that the output of B on that input matches the output of A on that input ).

Consider a quantum mechanical system whose state space is the tensor product of Hilbert spaces.

Consider a SISO system with states ( see state space for details about MIMO systems ), if the row rank of the following observability matrix

Consider a system with state space X for which evolution is deterministic and reversible.

Consider a maximally entangled state such as a Bell state.

Consider a composite quantum system with state space For a state

1 ) Consider a system of two photons which at time t are located, respectively, in the spatially distant regions A and B and which are also in the entangled state of polarization described below:

Consider the example of a one dimensional nonrelativistic particle with a 2D ( i. e. two state ) internal degree of freedom called " spin " ( it's not really spin because " real " spin is for particles in three-dimensional space ).

Consider a state.