Here variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds.

Here, the coefficients χ < sup >( n )</ sup > are the n-th order susceptibilities of the medium and the presence of such a term is generally referred to as an n-th order nonlinearity.

( Here primitive is used in the sense that the highest common factor of the set of coefficients of P is 1 ; this is weaker than requiring the coefficients to be pairwise relatively prime.

Here are the unknowns, are the coefficients of the system, and are the constant terms.

Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of N coefficients that minimize the maximum deviation from the ideal.

Here the vectors are elements of a given vector space V over a field K, and the coefficients are scalars in K.

Here is an image showing the Chebyshev filters next to other common kind of filters obtained with the same number of coefficients ( all filters are fifth order ):

Here, as in the earlier example of, the coefficients 1 prevent Eisenstein's criterion from applying directly.

Here Z < sub > l </ sub > denotes the ℓ-adic integers, but the definition is by means of the system of ' constant ' sheaves with the finite coefficients Z / l < sup > k </ sup > Z.

Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of coefficients that minimize the maximum deviation from the ideal.

( Here, homology and cohomology is taken with coefficients in the ring of integers, but the isomorphism holds for any coefficient ring.

Here the ratio of coefficients of y is same as that of the constant terms.

Here it is easy to see that if some linear combination of the x < sub > i </ sub > and 1 with non-zero rational number coefficients is zero, then the coefficients may be taken as integers, and a character χ of the group T other than the trivial character takes the value 1 on P. By Pontryagin duality we have T ′ contained in the kernel of χ, and therefore not equal to T.

Here, the for are coefficients fully determined by the data, being defined as

Here, are the standard spherical harmonics, and are constant coefficients which depend on the function.

Here is an image showing the elliptic filter next to other common kind of filters obtained with the same number of coefficients:

( Here, are symbols of components or states, are coefficients ).

Here phrase structures are not derived from rules that combine words, but from the specification or instantiation of syntactic schemata or configurations, often expressing some kind of semantic content independently of the specific words that appear in them.

Here he states that the Christian moral doctrine provides people with intrinsic value, belief in God ( which justifies the evil in the world ) and a basis for objective knowledge.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

Here alone exists a broad basis for " a new passionate sense of brotherhood, and a new scale of human values.

Here Petruchio is specifically attacking the very function of Katherina's language, vowing that no matter what she says, he will purposely misinterpret it, thus undermining the very basis of the linguistic sign, and disrupting the relationship between signifier and signified.

The topic of divorce became a major topic that centered around the Here, My Dear album, while Gaye's concerns of the world in the context of his religious beliefs and his conflict with " good " and " evil " formed the basis of the In Our Lifetime album.

Here, rather than defining a social group based on expressions of cohesive social relationships between individuals, the social identity model assumes that “ psychological group membership has primarily a perceptual or cognitive basis ”.

Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that

Here Saadia refutes the objections made, on the basis of nature, reason, and the Bible, to the doctrine of the resurrection of the dead, and presents the proof for it contained in tradition.

" Here the argument expresses the fact that the Mohawk nation has a more legitimate claim to distinct nationhood on the basis of traditional lands and a constitution predating confederation ( and the creation of Quebec and a Québécois identity ) and thus should be afforded the right of self-determination.

Hit it Here Café tickets are only sold on an individual game basis.

Here Hervás attempts to investigate the origin and ethnological relationship of different nations on the basis of language.

Here he also published, in 1531, his most important work, the Chronica, Zeitbuch und Geschichtsbibel, largely a compilation on the basis of the Nuremberg Chronicle ( 1493 ), and in its treatment of social and religious questions connected with the Reformation.

Here we're saying it's okay to separate two people on the basis of their religious beliefs.

* Heaven Can Wait ( play ), a stage play by Harry Segall ; basis for Here Comes Mr. Jordan

::" Here, as in that case, the injunction operates, not to redress alleged private wrongs, but to suppress, on the basis of previous publications, distribution of literature ' of any kind ' in a city of 18, 000.

Lyricist to the album ; Clint Boge, has commented that the themes throughout Begins Here are complex, ambiguous and deeply diverse, and has hinted that his own life experiences have formed the basis for numerous lyrics within the album, such as Without Wings.

These events formed the basis of the television series Here Come the Brides.

Here the court allowed the statement to be admitted on the basis that the statement was reliable, as it was partially corroborated by Mr. Crawford's statement to police.

Here x and t are spacetime coordinates, (,) is the Killing form of a real r-dimensional Cartan algebra of a Kac-Moody algebra over, α < sub > i </ sub > is the i < sup > th </ sup > simple root in some root basis, n < sub > i </ sub > is the Coxeter number, m is the mass ( or bare mass in the quantum field theory version ) and β is the coupling constant.

Here a non-trivial coordinate subspace means a linear subspace spanned by any proper subset of basis vectors.

Here, the Lorentz transformation is no longer a mere collection of auxiliary hypotheses but reflects a fundamental Lorentz symmetry and forms the basis of successful theories such as Quantum electrodynamics.

Here again, UE's progressive position was used against it by its foes ; in several instances the IUE openly appealed for the votes of white workers on the basis of racial bigotry and by attacking UE's support for racial equality.

Here the manuscripts were handed over to the grammarian Tyrannion of Amisus, who took copies of them, on the basis of which the peripatetic philosopher Andronicus of Rhodes prepared an edition of Aristotle's works.