Consider the case when we have four layers to blend to produce the final image: F =

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 the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell as in the following diagram.

Consider the case of an airfoil accelerating from rest in a viscous flow.

Consider also the case of a vessel leaving a star system, or heading to the outer planets.

Argument from rarity – Consider this case: a lottery winner is accused of cheating, based on the improbability of winning.

Consider the case when bits are already exchanged between the parties.

Consider the simplest case, a system with one independent variable, time.

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 the special case in which the axis of rotation lies in the xy plane.

Consider the manufacture and sale of any item, which in this case we will call a widget.

Consider the following quote: " How can the fact that, in the case of the brains in a vat, the language is connected by the program with sensory inputs which do not intrinsically or extrinsically represent trees ( or anything external ) possibly bring it about that the whole system of representations, the language in use, does refer to or represent trees or any thing external?

Consider the following theorem ( which is a case of the Pigeonhole Principle ):

Consider the case when a child executes an "" system call ( which is used to execute any executable file from within a C program ) or exits very soon after the.

Consider the Gram – Schmidt process applied to the columns of the full column rank matrix, with inner product ( or for the complex case ).

Consider a case of a level sensing platform on an aircraft flying due North with its three gimbal axes mutually perpendicular ( i. e., roll, pitch and yaw angles each zero ).

Consider the expression: in this case, the dummy variable of the product is not mentioned within the term.

Consider that in the case of the Mount Isa orebody, large amounts of capital are required to sink shafts and associated underground infrastructure, then laboriously drill and blast the ore, crush and process it, to extract the base metals, an activity which requires a large workforce.

Consider the case where ( that is, the jth element is one and all others zero ).

Consider the case when the surfaces are flat and planar cross-sections.

Consider the special case N = 1.

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

Consider the case this way-to a cat, catching and eating mice is perfectly natural and morally sound.

Consider the case of a 2-by-2 matrix

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 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 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 a circuit where R, L and C are all in parallel.

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.