Consider the ring of formal power series

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 the ring Z of integers.

Consider the following ring environment ( for example, running at OC-48c Gbit / s ) with 6 routers ( A through F sequentially ) on it.

Consider now the ring R defined as the intersection

Consider a sample space generated by two random variables and.

Consider this example based on Ohm's law: A voltage of 10 mV is generated by passing 10 nanoamperes of current across 1 MΩ of resistance.

A fundamental part of ` Abdul-Bahá's teachings on evolution is the belief that all life came from the same origin: " the origin of all material life is one ..." He states that from this sole origin, the complete diversity of life was generated: " Consider the world of created beings, how varied and diverse they are in species, yet with one sole origin " He explains that a slow, gradual process led to the development of complex entities:

Consider, for example, the group generated by 2 modulo ( the order of the group is, 2

Consider the timelike congruence generated by some timelike unit vector field X, which we should think of as a first order linear partial differential operator.

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

Consider on K the metric induced by the uniform distance.

Consider a car's cruise control, which is a device designed to maintain vehicle speed at a constant desired or reference speed provided by the driver.

* Consider Phlebas, a novel by Iain M Banks, contains depictions of a tribe known as the Eaters, who repeatedly engage in coprophagia.

Consider for instance the sequence defined by and.

Consider, friend, as you pass by: As you are now, so once was I.

Consider a rectangular area a by b, and any common divisor c that divides both a and b exactly.

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 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, for example, the claim that the extinction of the dinosaurs was probably caused by a large meteorite hitting the earth.

Consider two ISPs, A and B, which each have a presence in New York, connected by a fast link with latency 5 ms ; and which each have a presence in London connected by a 5 ms link.

* Chapter 7 divides humility into twelve degrees, or steps in the ladder that leads to heaven :( 1 ) Fear God ; ( 2 ) Substitute one's will to the will of God ; ( 3 ) Be obedient to one's superior ; ( 4 ) Be patient amid hardships ; ( 5 ) Confess one's sins ; ( 6 ) Accept oneself as a " worthless workman "; ( 7 ) Consider oneself " inferior to all "; ( 8 ) Follow examples set by superiors ; ( 9 ) Do not speak until spoken to ; ( 10 ) Do not laugh ; ( 11 ) Speak simply and modestly ; and ( 12 ) Be humble in bodily posture.

Consider three things being pulled by the moon: the oceans nearest the moon, the solid earth, and the oceans farthest from the moon.

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 the first claim, that God is a spirit, by itself.

Consider the following URL as it would be requested by a client:

Consider the algorithm described by the pseudocode:

Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, vary sinusoidally in time and are out of phase by one quarter of a cycle.

Consider " Oh that I had a Thousand Voices " (" O daß ich tausend Zungen hätte ") by German, Johann Mentzer Verse 2: " Ye forest leaves so green and tender, that dance for joy in summer air …" or " O Day Full of Grace " (" Den signede Dag ") by Dane, Nikolai Grundtvig verse 3: " Yea were every tree endowed with speech and every leaflet singing …".

Consider these pairs of Modern English words.

From the Szemerédi – Trotter theorem, the number of such lines is, as follows: Consider the set P of n points, and the set L of all those lines spanned by pairs of points of P that contain at least points of P. Note that, since no two points can lie on two distinct lines.

Consider two rays emanating from an external homothetic center E. Let the antihomologous pairs of intersection points of these rays with the two given circles be denoted as P and Q, and S and T, respectively.

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

Consider the relation involving three roles that people might play, expressed in a statement of the form " X thinks that Y likes Z ".

Suppose that U: D → C is a functor from a category D to a category C, and let X be an object of C. Consider the following dual ( opposite ) notions:

Consider for instance the following elements of Q < nowiki ></ nowiki > X < nowiki ></ nowiki >:

Consider a random variable X whose probability distribution belongs to a parametric family of probability distributions P < sub > θ </ sub > parametrized by θ.

Consider T to be a differentiable multilinear map of smooth sections α < sup > 1 </ sup >, α < sup > 2 </ sup >, ..., α < sup > q </ sup > of the cotangent bundle T * M and of sections X < sub > 1 </ sub >, X < sub > 2 </ sub >, ... X < sub > p </ sub > of the tangent bundle TM, written T ( α < sup > 1 </ sup >, α < sup > 2 </ sup >, ..., X < sub > 1 </ sub >, X < sub > 2 </ sub >, ...) into R. Define the Lie derivative of T along Y by the formula

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

Consider first the set of all possible singular n-simplices on a topological space X.

* Consider the Riesz space C < sub > c </ sub >( X ) of all continuous complex-valued functions of compact support on a locally compact Hausdorff space X.

Consider a Borel regular measure μ on X, and a functional ψ defined by

Consider any topological space X.

Consider a partially ordered set ( X, ≤).

Consider a scheme X and a cover by affine open subschemes Spec A < sub > i </ sub >.

Consider a finitely presented monoid where X is a finite set of generators and R is a set of defining relations on X.

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

Consider the Hilbert space X = L < sup > 2 </ sup > 3 of complex-valued square integrable functions on the interval 3.