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Consider the process illustrated in Fig. 2.1, consisting of R distinct stages.
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Consider and process
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 the Gram – Schmidt process applied to the columns of the full column rank matrix, with inner product ( or for the complex case ).
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 that in the case of the Mount Isa orebody, large amounts of capital are required to sink shafts and associated underground infrastructure, then laboriously drill and blast the ore, crush and process it, to extract the base metals, an activity which requires a large workforce.
Consider any process involving an incoming particle with momentum p. For the particle to give a measurable contribution to the amplitude, it has to interact with a number of different particles with momenta via a vertex.
Consider the management of a process with cash earnings or savings for a company or government: potentially £ 100, 000 but aiming to make £ 60, 000.
Consider and illustrated
Consider finding a shortest path for travelling between two cities by car, as illustrated in Figure 1.
Consider and consisting
Consider a test apparatus consisting of a closed and well insulated cylinder equipped with a piston.
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.
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 a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time.
Consider for example the same task as above but with an array consisting of 1000 numbers instead of 100, and where all numbers have the value 1.
Consider the subset C of B, consisting of those B elements, which satisfy monic polynomial equations over A:
Consider an-dimensional space, foliated as a product by subspaces consisting of points whose first co-ordinates are constant.
Consider a portfolio P consisting of C < sub > i </ sub > amount of each Arrow security A < sub > i </ sub >.
Consider a neutral plasma, consisting of a gas of positively charged ions and negatively charged electrons.
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 an election consisting of five voters and three alternatives, in which three voters prefer A to B and B to C, while two of the voters prefer B to C and C to A.
Consider a discrete charge distribution consisting of N point charges q < sub > i </ sub > with position vectors r < sub > i </ sub >.
Let p be a point of M. Consider the space consisting of smooth maps defined in some neighborhood of p. We define an equivalence relation on as follows.
Consider a trader who has bought a unit portfolio consisting of one contract each for the Red Party, the Blue Party, and the Green Party, at a cost of $ 1.
Consider and R
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 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, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).
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 solid ball in R < sup > 3 </ sup > of radius π ( that is, all points of R < sup > 3 </ sup > of distance π or less from the origin ).
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 the set of all nilpotent elements of R, which will be called the nilradical of R ( and will be denoted by N ( R )).
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