Intuitively, W ( t ) is a process that " wiggles up and down " in such a random way that its expected change over any time interval is 0.

Intuitively, the spectral density measures the frequency content of a stochastic process and helps identify periodicities.

Intuitively, the distinction says merely that there is no canonical choice of where the origin should go in the space, because it can be translated anywhere.

Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.

Intuitively then, the oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle for an answer to a specific question of the form " is x in A?

Intuitively, this means there are computational limits on what can be proven by computer programs.

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, the reasoning is that, as web crawlers have a limit to how many pages they can crawl in a given time frame, ( 1 ) they will allocate too many new crawls to rapidly changing pages at the expense of less frequently updating pages, and ( 2 ) the freshness of rapidly changing pages lasts for shorter period than that of less frequently changing pages.

Intuitively, a Lipschitz continuous function is limited in how fast it can change: for every pair of points on the graph of this function, the absolute value of the slope of the line connecting them is no greater than a definite real number ; this bound is called the function's " Lipschitz constant " ( or " modulus of uniform continuity ").

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, this finds the filter that is as close as you can get to the desired response given that you can use only N coefficients.

Intuitively this seems to mean that the number of inputs and the number of outputs can always be equal in each subswitch, but intuition does not prove this can be done nor does it tell us how to do so.

Intuitively, one can view a unit as the smallest testable part of an application.

Intuitively, represents a small perturbation in the index of T. By noting that and that is always between 0 and 1, can be used to ignore the floor function in the index.

Intuitively, we can think of this as being all meromorphic functions whose poles at every point are no worse than the corresponding coefficient in D ; if the coefficient in D at z is negative, then we require that h has a zero of at least that multiplicity at z – if the coefficient in D is positive, h can have a pole of at most that order.

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, this is allowed in the antecedent because we can always restrict the scope of our proof ( if all cars have wheels, then it's safe to say that all black cars have wheels ); and in the succedent because we can always allow for alternative conclusions ( if all cars have wheels, then it's safe to say that all cars have either wheels or wings ).

If, for example, we simply look at a curve in the real affine plane there might be singular P modulo the stalk, or alternatively as the sum of m ( m − 1 )/ 2, where m is the multiplicity, over all infinitely near singular points Q lying over the singular point P. Intuitively, a singular point with delta invariant δ concentrates δ ordinary double points at P. For an irreducible and reduced curve and a point P we can define δ algebraically as the length of where is the local ring at P and is its integral closure.

Intuitively, the first Betti number of a space counts the maximum number of cuts that can be made without dividing the space into two pieces.

Intuitively, a continuous curve in 2 or 3 ( or higher ) dimensions can be thought of as the path of a continuously moving point.

Intuitively, a system simulates another system if it can match all of its moves.

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.

Intuitively, it should be

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, theories of value must be important to ethics.

Intuitively this would seem to be folly because it would cool the iron.

Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e. g. the value assigned to " 1 or 2 " in a throw of a die should be the sum of the values assigned to " 1 " and " 2 ".

Intuitively, it seems clear that the answer should be more than a half, since there are more plain cookies in bowl # 1.

Intuitively, the divergence ( denoted ∇•) of a vector field is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point, hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region ( see main article for details ).

Schubert wrote, " Intuitively, iterated limiting identification might be regarded as higher-order inductive inference performed collectively by an ever-growing community of lower order inductive inference machines.

Intuitively we would expect it to be even more unlikely for all 5 marbles to be white.

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 HJB can be " derived " as follows.

Intuitively, it may be constructed as follows: Roll a 2-dimensional rectangle into a cylinder, so that its top and bottom edges meet.

Intuitively, this can be understood as follows: In quantum mechanics, the entropy of the joint system can be less than the sum of the entropy of its components because the components may be entangled.

Intuitively, partial function application says " if you fix the first arguments of the function, you get a function of the remaining arguments ".

The quantity ds in () is called the line element, while ds < sup > 2 </ sup > is called the first fundamental form of M. Intuitively, it represents the principal part of the square of the displacement undergone by when u is increased by du units, and v is increased by dv units.

Intuitively, if both coins are tossed the same number of times, the first coin should turn up fewer heads than the second one.

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, 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, we can think of each characteristic line implying a solution to along itself.

Intuitively, a ray consists of those points on a line passing through A and proceeding indefinitely, starting at A, in one direction only along the line.