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Intuitively, one would expect systems which collect more than one type of data to be more useful than systems which collect only one type of information ( such as single-purpose laboratory or 911 call-center based systems ), and be less prone to false alarms, and this appears to be the case.
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Intuitively and one
Intuitively, for two sets S and T to have the same cardinality means that it is possible to " pair off " elements of S with elements of T in such a fashion that every element of S is paired off with exactly one element of T and vice versa.
Intuitively, the process can be pictured as follows: first shrink the real line to the open interval (- π, π ) on the x-axis ; then bend the ends of this interval upwards ( in positive y-direction ) and move them towards each other, until you get a circle with one point ( the topmost one ) missing.
Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).
Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.
Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree.
Intuitively, multiplying by a scalar r stretches a vector out by a factor of r. Geometrically, this can be visualized ( at least in the case when r is an integer ) as placing r copies of the vector in a line where the endpoint of one vector is the initial point of the next vector.
Intuitively, one would not expect this pattern from firing a single particle at the slits, because the particle should pass through one slit or the other, not a complex overlap of both.
Intuitively, one can understand this second formulation by noting that an elastic band stretched between two points will contract its length, and in so doing will minimize its energy.
Intuitively, one should think of a + b as the " union " or the " least upper bound " of a and b and of ab as some multiplication which is monotonic, in the sense that a ≤ b implies ax ≤ bx.
Intuitively, one can view a unit as the smallest testable part of an application.
Intuitively, this reflects the fact that reliability involves freedom from random error and random errors do not correlate with one another.
Intuitively, one can think of the radical of I as obtained by taking all the possible roots of elements of I. Rad ( I ) turns out to be an ideal itself, containing I.
Intuitively, given an equation that one is seeking to solve,
Intuitively one expects that the waves in the system return to the initial state, as characterized by the amplitudes and phases ( and accounting for the passage of time ).
Intuitively, one can think of the m constraints as reducing the problem to one with n-m free variables.
Intuitively, mutual information measures the information that X and Y share: it measures how much knowing one of these variables reduces uncertainty about the other.
Intuitively, this is caused by the storm simply blowing the water towards one side of the basin in the direction of its winds.
Intuitively, the algorithm follows all chains of inference after making each of its choices ; this either leads to a contradiction and a backtracking step, or, if no contradiction is derived, it follows that the choice was a correct one that leads to a satisfying assignment.
Intuitively, one may think that the larger the weight for a criterion is, the more critical that criterion should be.
Intuitively and would
Intuitively, if we placed a small paddle wheel there, the larger " current " on its right side would cause the paddlewheel to rotate clockwise, which corresponds to a curl in the negative z direction.
Intuitively this would seem to be folly because it would cool the iron.
Intuitively we would expect it to be even more unlikely for all 5 marbles to be white.
Intuitively, a stochastic matrix represents a Markov chain with no sink states, this implies that the application of the stochastic matrix to a probability distribution would redistribute the probability mass of the original distribution while preserving its total mass.
Intuitively, if you have a tensor field and a vector field Y, then is the infinitesimal change you would see when you flow using the vector field-Y, which is the same thing as the infinitesimal change you would see in if you yourself flowed along the vector field Y.
Intuitively, since propellant is by far the largest part of a rocket, propellant costs would be expected to be significant, but it turns out that with hydrocarbon fuel these costs can be under $ 50 per kg of payload.
Intuitively, in a forward flow problem, it would be fastest if all
Intuitively, if the leader was no better off than the follower, it would simply adopt a Cournot competition strategy.
Intuitively and systems
Intuitively two systems are bisimilar if they match each other's moves.
Intuitively and which
Intuitively, an expander is a finite, undirected multigraph in which every subset of the vertices " which is not too large " has a " large " boundary.
Intuitively, NP is the set of all decision problems for which the instances where the answer is " yes " have efficiently verifiable proofs of the fact that the answer is indeed " yes ".
In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are " near " S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context.
Intuitively, as the name suggests, what a subobject classifier does is to identify / classify subobjects of a given object according to which elements belong to the subobject in question.
Intuitively, this has the consequence that all points of the space are " lumped together " and cannot be distinguished by topological means ; it belongs to a pseudometric space in which the distance between any two points is zero.
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a " vertex " of S.
Intuitively, this says that if one writes a function which is polynomial-time assuming that function calls are constant-time, and if those called functions themselves require polynomial time, then the entire algorithm takes polynomial time.
Intuitively, it helps determine what part of an absolute homology group comes from which subspace.
In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it represents the smallest subgroup which " controls " the structure of G when G is solvable.
Intuitively, given a function which is rather irregular, by convolving it with a mollifier the function gets " mollified ", that is, its sharp features are smoothed, while still remaining close to the original nonsmooth ( generalized ) function.
Intuitively, as an example, consider a function ƒ whose singular support is concentrated on a smooth curve in the plane at which the function has a jump discontinuity.
Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time ; its significance is that giving the initial conditions on this plane determines the future ( and the past ) uniquely.
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