Note that sometimes the elliptic integral of the third kind is defined with an inverse sign for the characteristic,

Note that, as with multiplexers, links are almost always bi-directional and, at either end of the link, an inverse mux will be combined with its reverse ( an inverse demux ) and still be called an inverse mux.

Note that the axioms are given in terms of the maps ( binary product, unary inverse, and nullary identity ), hence are categorical definitions.

Note that three independent values are given, so it is possible to calculate the inverse tree ( see figure above ).

Note that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying " elements " of group – categories in general do not have elements to their objects.

Note however that a right inverse of F ( i. e. a functor G such that FG is naturally isomorphic to 1 < sub > D </ sub >) need not be a right ( or left ) adjoint of F. Adjoints generalize two-sided inverses.

A principal fractional ideal is one of the form for some nonzero x in K. Note that each principal fractional ideal is invertible, the inverse of being simply.

Note that Ω has determinant + 1 and has an inverse given by Ω < sup >− 1 </ sup >

w / MPL Since the wage rate is assumed constant marginal cost and marginal product of labor have an inverse relationship-if marginal cost is increasing ( decreasing ) the marginal product of labor is decreasing ( increasing ).< ref > Note also that AVC

Note that when a transformation decreases symmetry, a transformation of the same kind ( the inverse ) obviously for some patterns increases the symmetry.

:: Note that the notation does not denote the modular multiplication of times the modular multiplicative inverse of but rather the quotient of divided by, i. e., the largest integer value to satisfy the relation.

Note that this inverse system is not unique.

Note that, for, this becomes precisely the definition of the continuous Fourier transform, and for it is the definition of the inverse continuous Fourier transform.

Note that since, the inverse is equal to the complex conjugate.

* According to the inverse function theorem, a smooth map f: M → N is a local diffeomorphism if and only if the derivative Df < sub > p </ sub >: T < sub > p </ sub > M → T < sub > f ( p )</ sub > N is a linear isomorphism for all points p in M. Note that this implies that M and N must have the same dimension.

Note that the multiplicative inverse of < tt > 0x00 </ tt > is defined as itself.

Note: Data is plotted on an inverse vertical axis approaching 1.

Note that the requirement that the maps be continuous is essential ; if X is infinite-dimensional, there exist linear maps which are not continuous, and therefore not bounded.

Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.

Note that using a hierarchical system like this ( assuming it is done carefully ) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence.

Note that the tensor rank of a matrix can also mean the minimum number of simple tensors necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed.

Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).

Note that, in a linear time-invariant system, the input frequency has not changed, only the amplitude and the phase angle of the sinusoid has been changed by the system.

Note, however, that unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time.

Note that a queen can only ever be partially pinned, as it can move in any linear direction.

Note that u can only be given if linear, nondispersive and uniform materials are involved, i. e., if the constitutive relations can be written as

Note that in this special case where the consumer demand curve is linear, consumer surplus is the area of a triangle.

Note that by definition, a linear combination involves only finitely many vectors ( except as described in Generalizations below ).

Note that this usage of the term linear is not the same as the above, because linear polynomials over the real numbers do not in general satisfy either additivity or homogeneity.

Note that the scale on this chart is NOT linear.

Note that if the u < sup > 2 </ sup > term were replaced with u, the problem would be linear ( the exponential decay problem ).

( Note that the leading zeros of the linear address, segmented addresses, and the segment and offset fields, which are usually neglected, were shown here for clarity.

Note that the correlation reflects the noisiness and direction of a linear relationship ( top row ), but not the slope of that relationship ( middle ), nor many aspects of nonlinear relationships ( bottom ).

In this case, the orthonormal basis is sometimes called a Hilbert basis for H. Note that an orthonormal basis in this sense is not generally a Hamel basis, since infinite linear combinations are required.

Note that LineString objects, along with LinearRing objects, assume linear interpolation between the specified points.

Note that the correlation reflects the non-linearity and direction of a linear relationship ( top row ), but not the slope of that relationship ( middle ), nor many aspects of nonlinear relationships ( bottom ).

Note that more general linear transformations do change the correlation: see a later section for an application of this.

Note that not all elastic materials undergo linear elastic deformation ; some, such as concrete, gray cast iron, and many polymers, respond nonlinearly.

Note that this means that algebraic group is narrower than Lie group, when working over the field of real numbers: there are examples such as the universal cover of the 2 × 2 special linear group that are Lie groups, but have no faithful linear representation.

Note that the examples are sometimes said to demonstrate that the Pearson correlation assumes that the data follow a normal distribution, but this is not correct.

Note that this definition of entropy can even be viewed as equivalent to the previous one ( unknown information ) if we take a meta-perspective, and say that for observer A to " know " the state of system B means simply that there is a definite correlation between the state of observer A and the state of system B ; this correlation could thus be used by a meta-observer ( that is, whoever is discussing the overall situation regarding A's state of knowledge about B ) to compress his own description of the joint system AB.

Note: the pyramids have been Rotation ( mathematics ) | rotated and Scaling ( geometry ) | scaled to facilitate correlation.

Note also that the correlation suggested here between the Athenian months and those of the modern ( Gregorian ) calendar is only loose, and, in some years, might have been out by over a month.

Note, however, that decreased temporal correlation between activity in STS and V3 would be expected simply from the lack of an evoked response in STS to intent-laden animations in subjects with autism ; a more informative analysis would be to compute functional connectivity after regressing out evoked responses from all time series.

Note: Percentage indicates correlation to the total number of seats in the city council which is 50.

Note that if for all t, then the cross correlation function is simply the autocorrelation function.

Note: The correlation between some fruit characters of pili.