Consider a ( hyper ) elliptic curve over a finite field where is the power of a prime number.

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

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

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

Consider a curve lying on a submanifold in ambient manifold, parametrized by arclength, with unit tangent vector.

Consider a hyperelliptic curve of genus over the field where is the power of a prime number and define as but now over the field.

* Consider a Bézier curve with control points.

Consider a right angle moving rigidly so that one leg remains on the point P and the other leg is tangent to the curve.

Consider for instance the curve parametrised by where.

Consider the rigid object moving smoothly along the regular curve.

Consider a pointer that in a given interval of the execution is updated several times.

Consider the two endpoints of a rod of length L. The length can be determined from the differences in the three coordinates Δx, Δy and Δz of the two endpoints in a given reference frame

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.

Designer Anthony Ward created a new cobblestone effect for the entire stage while the orchestrations were expanded with new dance arrangements given to Consider Yourself and Who Will Buy?

Consider the following commutative diagram in any abelian category ( such as the category of abelian groups or the category of vector spaces over a given field ) or in the category of groups.

Consider a function that reads the next line of text from a given file:

Consider, for example, this code segment in the Java programming language as given by ( as well as all other Java code segments ):

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

Consider a population of ten individuals and a given locus with two possible alleles, A and a.

Pope Pelagius II ( 578-590 ): " Consider the fact that whoever has not been in the peace and unity of the Church cannot have the Lord … Although given over to flames and fires, they burn, or, thrown to wild beasts, they lay down their lives, there will not be ( for them ) that crown of faith but the punishment of faithlessness … Such a one can be slain, he cannot be crowned … slain outside the Church, he cannot attain the rewards of the Church " ( Denzinger, 469 ).

Suppose S ' is in relative uniform motion to S with velocity v. Consider a point object whose position is given by r

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

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 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 a probabilistic algorithm that, given a formula F ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub >) chooses an assignment x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > uniformly at random.

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 the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set.

Consider the general problem of inferring a distribution for a parameter θ given some datum or data x.

The most straightforward method of calculating a modular exponent is to calculate b < sup > e </ sup > directly, then to take this number modulo m. Consider trying to compute c, given b

Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots.

* Consider an economy with given prices, in which the economy operates below full employment.

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 a domain D in m-dimensional x space, with boundary B.

Consider a list with items and with R1 and R2 being registers containing, respectively, the address of the current ( say C ) list item and a work register containing the XOR of the current address with the previous address ( say C ⊕ D ).

Consider polynomials P ( x ), D ( x ) where degree ( D ) < degree ( P ).

Consider a relation variable ( relvar ) R with attributes ( A, B, C, D ) that has only the following two legal values r1 and r2:

Consider the first-order differential operators D < sub > i </ sub > to be infinitesimal operators on Euclidean space.

Consider an election in which there are 4 candidates A, B, C and D, each voter expresses a top-to-bottom ordering of the candidates, and the voters ' orderings are as follows:

Consider one example of what attracted attention to the style of Hand D.

Consider for example the dihedral group D < sub > 4 </ sub > of symmetries of a square.

Consider region D in the plane: a unit circle or general polygon — the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape.

Consider a triangle ABC Let D be the midpoint of, E be the midpoint of, F be the midpoint of, and O be the centroid.

Among the NCEW ’ s strongest champions for LTEs was Ronald D. Clark of the St. Paul Pioneer Press, who wrote, " Consider letters as a barometer of how well ( you are ) engaging readers or viewers.

Consider, for example, the case where Y is the disc D < sup > 2 </ sup >, and