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Page "Differential topology" ¶ 7
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Some Related Sentences

Consider and example
Consider the following example.
Consider for example the compound ( 3Z, 6E )- 3, 5, 7-trimethylnona-3, 6-diene.
Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.
Consider the example< big >×</ big > < big >×</ big > F.
Consider, for example,
Consider for example determining which of the following are to be considered diseases ( i. e., abnormal states requiring cure ): alcoholism, homosexuality, and chronic fatigue syndrome.
Consider for example workers who take coffee beans, use a roaster to roast them, and then use a brewer to brew and dispense a fresh cup of coffee.
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 the Lake Sturgeon as but one example.
Consider an example:
Consider, for example, a reference frame moving relative to another at velocity in the direction.
Consider the following example ( in Kwakw ' ala, sentences begin with what corresponds to an English verb ):
Consider, for example, what happens when an object in the periphery of the visual field moves, and a person looks toward it.
Consider for example a particular oak tree.
Consider, for example, the claim that the extinction of the dinosaurs was probably caused by a large meteorite hitting the earth.
Consider for example songbirds.
For example: Consider first a classical computer that operates on a three-bit register.
Consider an audio DSP example: if a process requires 2. 01 seconds to analyze, synthesize, or process 2. 00 seconds of sound, it is not real-time.
Consider for example the 4-by-4 matrix
Consider, for example, the implication this has for plane rotations.
Consider, for example, that when the bride says " I do " at the appropriate time in a wedding, she is performing the act of taking this man to be her lawful wedded husband.
Consider the classic example of the human body.
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 and see
#: Consider a unit sphere placed at the origin, a rotation around the x, y or z axis will map the sphere onto itself, indeed any rotation about a line through the origin can be expressed as a combination of rotations around the three-coordinate axis, see Euler angles.
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 COX-2 inhibitory capacity of the 4-methyl and 4-ethyl modifications: 4-methyl can inhibit COX-2 such that the IC50 is 0. 040μM while that of the 4-ethyl is 0. 86μM which means that the 4-methyl substituent is at least 20-fold more potent ( see structures 22 and 23 ).
Consider a SISO system with states ( see state space for details about MIMO systems ), if the row rank of the following observability matrix
Consider particles described by f, each experiencing an external force F not due to other particles ( see the collision term for the latter treatment ).

Consider and <
Consider the following reactions of acetic acid ( CH < sub > 3 </ sub > COOH ), the organic acid that gives vinegar its characteristic taste:
Consider two systems ; S < sub > 1 </ sub > and S < sub > 2 </ sub > at the same temperature and capable of exchanging particles.
Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.
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 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:
< li > Consider the group ( Z < sub > 6 </ sub >, +), the integers from 0 to 5 with addition modulo 6.
Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.
< p > Consider an interesting and revealing incident that occurred during the Quasi War.
Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.
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 that 700 < 738, yet 700²
Consider an elastic collision in 2 dimensions of any 2 masses m < sub > 1 </ sub > and m < sub > 2 </ sub >, with respective initial velocities u < sub > 1 </ sub > and u < sub > 2 </ sub >

Consider and class
Consider the class of all regular paths from a point p to another point q.
Consider the ( possibly proper ) class B defined such for every set y, y is in B if and only if there is an x in A with F < sub > P </ sub >( x ) = y.
Consider a simple example: a class of students takes a 100-item true / false test on a subject.
Consider an ontology for tea based on a Tea class.
By the time of the events of the novel Look to Windward, Minds of the class described within Consider Phlebas are referred to as minds, with a small'm '.
Consider this simple Python class:
Consider the following class declarations in C ++ syntax:
Consider a set of observations ( also called features, attributes, variables or measurements ) for each sample of an object or event with known class y.
Consider the following class hierarchy.

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