Consider a particular collision ( an elementary reaction ) between molecules A and B.

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 two systems ; S < sub > 1 </ sub > and S < sub > 2 </ sub > at the same temperature and capable of exchanging particles.

* Consider the modulo 2 equivalence relation on the set of integers: if and only if their difference is an even number.

* Consider the field K = Q ( ³ √ 2 ).

* Consider now L = Q ( ³ √ 2, ω ), where ω is a primitive third root of unity.

Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.

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 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.

* 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, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).

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 the vectors e < sub > 1 </ sub > = ( 1, 0, 0 ), e < sub > 2 </ sub > = ( 0, 1, 0 ) and e < sub > 3 </ sub > = ( 0, 0, 1 ).

Consider the vectors ( polynomials ) p < sub > 1 </ sub > := 1, p < sub > 2 </ sub > := x + 1, and p < sub > 3 </ sub > := x < sup > 2 </ sup > + x + 1.

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 >

Consider two particles, denoted by subscripts 1 and 2.

Consider for example 2x < sup > 2 </ sup > − 5x + 2

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:

Consider a set of functions f < sub > 1 </ sub >, f < sub > 2 </ sub >,..., f < sub > n </ sub >.

Consider the two equilibria, in aqueous solution, between the copper ( II ) ion, Cu < sup > 2 +</ sup > and ethylenediamine ( en ) on the one hand and methylamine, MeNH < sub > 2 </ sub > on the other.

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 plate with dimensions containing a crack of length.

Consider for example the natural representation of the symmetric group S < sub > n </ sub > in n dimensions by permutation matrices, which is certainly faithful.

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

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:

Consider the following examples, created using animated GIFs, wherein a key frame defines the starting and ending points of any smooth transition:

#: 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 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 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 the open balls centered upon a common point, with any radius.

Consider this example: reality for people who believe in any particular God is different from reality for those who believe that science is sufficient for explaining life and the universe.

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 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 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 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 promptly any significant areas of deficiency in financial reporting that might be improved through standard setting.

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

Consider any object of arbitrary shape and volume V surrounded by a liquid.

Consider any node x somewhere in the heap ( x need not be the root of one of the main trees ).

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 cumulative impact-minimize number of boats at any one time / per day

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.

He told Hall: " Consider, here are 2000 people sitting still, absolutely declining to give me any indication of where they belong to ; they will sit still where they are and do nothing else.

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 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 Ferrers graph of any partition of n into distinct parts.