Consider a planar pendulum with natural frequency ω in the small angle approximation.

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

# Consider a planar projection of each knot and suppose these projections are disjoint.

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 the projection π: S < sup > 1 </ sup > → S < sup > 1 </ sup > given by z ↦ z < sup > 2 </ sup >.

Consider for instance the projection p < sub > 1 </ sub >: R < sup > 2 </ sup > → R on the first component ; A =

Consider the context of evaluating each one of a class of events A < sub > 1 </ sub >, A < sub > 2 </ sub >, A < sub > 3 </ sub >,..., A < sub > n </ sub > ( for example, is the occurrence of the event harmful or not ?).

Consider two observers O and O ', each using their own Cartesian coordinate system to measure space and time intervals.

Consider the closed intervals for all integers k ; there are countably many such intervals, each has measure 1, and their union is the entire real line.

Consider as above systems and each with a Hilbert space,.

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.

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 an n × m array of nodes, each of which contains a weight vector and is aware of its location in the array.

Consider two variables said to be " inversely proportional " to each other.

" Consider each person's auricular "

Consider an equilateral triangle with three spins, one on each vertex.

Consider Thomas Hood's " Bridge of Sighs :", in which the lines are of two feet, each composed of three syllables:

Consider a system of K wire loops, each with one or several wire turns.

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 space for a maze being a large grid of cells ( like a large chess board ), each cell starting with four walls.

Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time.

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 two objects, A and B, which each refer to two memory blocks x < sub > i </ sub > and y < sub > i </ sub > ( i

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 language of set theory with extra constant symbols c < sub > 1 </ sub >, c < sub > 2 </ sub >, ... for each positive integer.

Consider an assignment to each curve γ in the manifold a collection of mappings

Consider a dataset represented as a matrix ( or a database table ), such that each row represents a set of attributes ( or features or dimensions ) that describe a particular instance of something.

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.

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, 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 the Alexander module to be the first homology group of the universal abelian cover of the knot complement:.

Consider the EPR thought experiment, and suppose quantum states could be cloned.

Consider a system in which voters can vote for any candidate from any one of many parties ; suppose further that if a party gets 15 % of votes, then that party will win 15 % of the seats in the legislature.

Consider a non-interacting fermion system ( a Fermi gas ), and suppose we " turn on " the interaction slowly.

Consider the previous example with men's heights and suppose we have a random sample of n people.

Consider two inconsistent statements, “ All lemons are yellow ” and " Not all lemons are yellow ", and suppose for the sake of argument that both are simultaneously true.

Consider a system composed by cascaded non interacting blocks, each having a rise time and no overshoot in their step response: suppose also that the input signal of the first block has a rise time whose value is.

Consider a two-body system consisting of a central body of mass M and a much smaller, orbiting body of mass m, and suppose the two bodies interact via a central, inverse-square law force ( such as gravitation ).

Consider the assembly of a car: assume that certain steps in the assembly line are to install the engine, install the hood, and install the wheels ( in that order, with arbitrary interstitial steps ); only one of these steps can be done at a time.

Consider roim ‘ crime ’ versus English crime or taunima ‘ to condemn, disapprove ’ versus Finnish tuomita ‘ to condemn, to judge ’ ( these Aavikisms appear in Aavik ’ s 1921 dictionary ).

Consider these examples:

Consider a problem that has these four properties:

Consider these three things we say about God: first, God is a spirit ; second, God is the creator of the world ; and third, God exists apart from space and time.

Consider these pairs of Modern English words.

Consider code that adds two numbers and then multiplies by a third ; in the Cray, these would all be fetched at once, and both added and multiplied in a single operation.

Consider, for instance, these remarks in the introduction to Hegel's Lectures on the Philosophy of History:

Consider further that there is an adversary called Eve that can observe these encryptions and is able to forward plaintext messages to Alice for encryption ( in other words, Eve is capable of a chosen-plaintext attack ).

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 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 the ring generated by pairs ( X, V ) where V is a smooth vector bundle on the compact smooth oriented manifold X, with relations that the sum and product of the ring on these generators are given by disjoint union and product of manifolds ( with the obvious operations on the vector bundles ), and any boundary of a manifold with vector bundle is 0.

Consider the category C of algebraic structures ; these can be thought of as sets plus operations, obeying some laws.

The first of these three identities says that the 0 form a representation of the ordinary Lie algebra spanned by E ( Consider the 0 as vectors on which the E act.

Consider a case where these two ions have equal concentration gradients directed in opposite directions, and that the membrane permeabilities to both ions are equal.

During the course of this study, Derrida not only divulges the exact instances Socrates or his interlocutors make use of this concept, but also reveals the relationship between Plato and Socrates which scholars have kept in secret by questioning the validity of authorship in Plato's letters, where in the second letter Socrates writes: " Consider these fact and take care lest you sometimes come to repent of having now unwisely published your views.

Consider these examples.

They are maps from flat 3-space into the Lie group G. Consider now glueing these two balls together at their boundary S².

Consider that a perpetuity growth rate exceeding the annualized growth of the S & P 500 and / or the U. S. GDP implies that the company's cash flow will outpace and eventually absorb these rather large values.

Consider how you would access and search through digital media catalogs from these same devices or set top boxes.

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.

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Jesus Christ also said: " Consider the lilies, how they grow ; they neither toil nor spin ; yet I tell you, even Solomon in all his glory was not arrayed like one of these. But if God so clothes the grass which is alive in the field today and tomorrow is thrown into the oven, how much more will he clothe you, O men of little faith!