Consider a physical system that acts as a linear filter, such as a system of springs and masses, or an analog electronic circuit that includes capacitors and / or inductors ( along with other linear components such as resistors and amplifiers ).

Consider the difference that arises in selecting the lumped element view of a circuit rather than the electrodynamic view of the same device.

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 direct-current circuit with a nine-volt DC source ; three resistors of 67 ohms, 100 ohms, and 470 ohms ; and a light bulb -- all connected in series.

Consider a positive going swing: As long as the input is less than the required forward V < sub > BE </ sub > drop (≈ 0. 65 V ) of the upper NPN transistor, it will remain off or conduct very little-this is the same as a diode operation as far as the base circuit is concerned, and the output voltage does not follow the input ( the lower PNP transistor is still off because its base-emitter diode is being reverse biased by the positive going input ).

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

* Consider now L = Q ( ³ √ 2, ω ), where ω is a primitive third root of unity.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

Consider Peter Unger's example of a cloud ( from his famous 1980 paper, " The Problem of the Many "): it's not clear where the boundary of a cloud lies ; for any given bit of water vapor, one can ask whether it's part of the cloud or not, and for many such bits, one won't know how to answer.

Consider, also, that all English speakers often pronounce ' Z ' where ' S ' is spelled, almost always when a noun ending in a voiced consonant or a liquid is pluralized, for example " seasons ", " beams ", " examples ", etc.

Consider the case where the far end of the cable is shorted ( that is, it is terminated into zero ohms impedance ).

Consider the plane spanned by and, where is a ket in the subspace perpendicular to.

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 >

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 database that records customer orders, where an order is for one or more of the items that the enterprise sells.

Consider the simple experiment where a fair coin is tossed four times.

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:

: Example: Consider a scenario where a legitimate party called Alice encrypts messages using the cipher-block chaining mode.

Consider for example, the sharing of food in some hunter-gatherer societies, where food-sharing is a safeguard against the failure of any individual's daily foraging.

Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest ( in any particular frame of reference ).

Consider a 10 year mortgage where the principal amount P is $ 200, 000 and the annual interest rate is 6 %.

Consider a simple banking application where two users have access to the funds in a particular account.

Consider the polynomial ring R, and the irreducible polynomial The quotient space is given by the congruence As a result, the elements ( or equivalence classes ) of are of the form where a and b belong to R. To see this, note that since it follows that,,, etc.

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 a system where the gun and shooter have a combined mass M and the bullet has a mass m. When the gun is fired, the two systems move away from one another with new velocities V and v respectively.

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 for example the same task as above but with an array consisting of 1000 numbers instead of 100, and where all numbers have the value 1.

Consider the physical model of the citizenship of human beings in the early 21st century, where about 30 % are Indian and Chinese citizens, about 5 % are American citizens, about 1 % are French citizens, and so on.

Consider a social network, where the graph ’ s vertices represent people, and the graph ’ s edges represent mutual acquaintance.

Consider the process illustrated in Fig. 2.1, consisting of R distinct stages.

Consider the logarithm function: For any fixed base b, the logarithm function log < sub > b </ sub > maps from the positive real numbers R < sup >+</ sup > onto the real numbers R ; formally:

Consider all the functions φ: G → R such that the set

Consider, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

Consider the solid ball in R < sup > 3 </ sup > of radius π ( that is, all points of R < sup > 3 </ sup > of distance π or less from the origin ).

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

Consider the complex Hilbert space L < sup > 2 </ sup >( R ), and the operator which multiplies a given function by x:

Consider the problem of finding solutions of the form ƒ ( r, θ, φ ) = R ( r ) Y ( θ, φ ).

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

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

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