Consider a wave packet as a function of position x and time t: α ( x, t ).

Consider the vectors ( functions ) f and g defined by f ( t ) := e < sup > it </ sup > and g ( t ) := e < sup >− it </ sup >.

Proof of claim: Consider a graph on t vertices and colour its edges with c colours.

Consider for instance the map f: ( 0, 1 ) → R < sup > 2 </ sup > with f ( t )

" Consider also Rabbinic Hebrew תרמ √ trm ‘ donate, contribute ’ ( Mishnah: T ’ rumoth 1: 2: ‘ separate priestly dues ’), which derives from Biblical Hebrew תרומה t ' rūmå ‘ contribution ’, whose root is רומ √ rwm ‘ raise ’; cf.

Consider solutions in which a fixed wave form ( given by f ( X )) maintains its shape as it travels to the right at phase speed c. Such a solution is given by ( x, t )

Consider the example of moving along a curve γ ( t ) in the Euclidean plane.

Consider the cubic polynomial equation 4t < sup > 3 </ sup > − g < sub > 2 </ sub > t − g < sub > 3 </ sub > =

Consider the following test case: The field f has been on for infinite time and is switched off at t = 0

Consider a scalar quantity φ = φ ( x, t ), where t is understood as time and x as position.

Consider a nominal value ( say of an hourly wage rate ) in each different year t. To derive a real-value series from a series of nominal values in different years, divide nominal value in each year by P < sup > t </ sup >, the price index in that year.

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 an unemployed person who will be able to work for ten more years t = 1, 2 ,..., 10.

Consider a line of atoms A-O-B, separated by distance t. Rotate the entire row by + 2π / n and − 2π / n, with point O kept fixed.

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

Consider the vectors ( polynomials ) p < sub > 1 </ sub > := 1, p < sub > 2 </ sub > := x + 1, and p < sub > 3 </ sub > := x < sup > 2 </ sup > + x + 1.

Consider for example 2x < sup > 2 </ sup > − 5x + 2

Consider a number n > 0 in base b ≥ 2, where it is written in standard notation with k + 1 digits a < sub > i </ sub > as:

Consider a capacitor of capacitance C, holding a charge + q on one plate and − q on the other.

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 a complete graph on R ( r − 1, s ) + R ( r, s − 1 ) vertices.

Consider a random walk on the number line where, at each step, the position ( call it x ) may change by + 1 ( to the right ) or-1 ( to the left ) with probabilities:

Consider the direct system composed of the groups Z / p < sup > n </ sup > Z and the homomorphisms Z / p < sup > n </ sup > Z → Z / p < sup > n + 1 </ sup > Z which are induced by multiplication by p. The direct limit of this system consists of all the roots of unity of order some power of p, and is called the Prüfer group Z ( p < sup >∞</ sup >).

Consider the following swap in which Party A agrees to pay Party B periodic fixed interest rate payments of 8. 65 %, in exchange for periodic variable interest rate payments of LIBOR + 70 bps ( 0. 70 %) in the same currency.

Consider the C expression ( 4 + 9 ).

Consider the expression < tt > 7 − 4 + 2 </ tt >.

Consider an ensemble of systems described by a Hamiltonian H with average energy E. If H has pure-point spectrum and the eigenvalues of H go to + ∞ sufficiently fast, e < sup >- r H </ sup > will be a non-negative trace-class operator for every positive r.

Consider again the illustration to the right, where it is known that c, e, b + d, and the triangle area A are integers.

Consider the polynomial x < sup > 5 </ sup > − 3x < sup > 4 </ sup > + 3x < sup > 3 </ sup > − 9x < sup > 2 </ sup > + 2x − 6.

Consider any set of d + 2 points in d-dimensional space.

Consider the following expressions from first order logic over a signature containing a constant symbol 0 for the number 0, a unary function symbol s for the successor function and a binary function symbol + for addition.

Consider, for instance, the top half of the unit circle, x < sup > 2 </ sup > + y < sup > 2 </ sup > = 1, where the y-coordinate is positive ( indicated by the yellow arc in Figure 1 ).

Consider forming a permutation of n + 1 objects from a permutation of n objects by adding a distinguished object.

Consider the linear probing hash function h ( k, i ): ( h `( k ) + i ) mod N. With k being the key, i the probing-iteration, N being the number of slots in the hash-table and h `( k ) being the secondary-hash function.

Consider the unitary form defined above for the DFT of length N, where

Consider the number N ( r ) of balls of radius at most r required to cover X completely.

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

Consider a jar containing N lottery tickets numbered from 1 through N. If you pick a ticket randomly then you get positive integer n, with probability 1 / N if n ≤ N and with probability zero if n > N. This can be written

Consider an unsorted database with N entries.

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 a quantum ensemble of size N with occupancy numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >,..., n < sub > k </ sub > corresponding to the orthonormal states, respectively, where n < sub > 1 </ sub >+...+ n < sub > k </ sub >

Consider a rigid regular, crystalline, i. e. not amorphous, lattice composed of N particles.

Consider a system of N qubits that is coupled to a bath symmetrically.

Consider a graph G with vertices V, each numbered 1 through N. Further consider a function shortestPath ( i, j, k ) that returns the shortest possible path from i to j using vertices only from the set

Consider an MDCT with 2N inputs and N outputs, where we divide the inputs into four blocks ( a, b, c, d ) each of size N / 2.

Consider the set of all nilpotent elements of R, which will be called the nilradical of R ( and will be denoted by N ( R )).

Consider N systems in adiabatic isolation from the rest of the universe, i. e. no heat exchange is possible outside of these N systems, all of which have a constant volume and composition, and which can only exchange heat with one another.

Consider a sphere B < sub > 2 </ sub > of radius 2 centered at N. The inversion with respect to B < sub > 2 </ sub > transforms B into its stereographic projection P.

Consider a linear polymer to be a freely-jointed chain with N subunits, each of length, that occupy zero volume, so that no part of the chain excludes another from any location.

# Quadratic residue code: Consider the set N of quadratic non-residues ( mod 23 ).

Consider the special case N = 1.

Consider an integer N and a non-negative monotone decreasing function f defined on the unbounded interval < nowiki >