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 χ is a Dirichlet character and s a complex variable with real part greater than 1.

Here we wrote τ ( χ ) for the Gauss sum

Here is the Legendre symbol, which is a quadratic character mod p. An analogous formula with a general character χ in place of the Legendre symbol defines the Gauss sum G ( χ ).

Here χ is the quadratic residue symbol modulo D, where − D is the discriminant of an imaginary quadratic field.

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, χ is the character.

Here χ ″( G ) is the total chromatic number ; Δ ( G ), maximum degree ; and δ ( G ), minimum degree.

Here χ < sup >′</ sup >( G ) is the chromatic index of G ; and K < sub > n, n </ sub >, the complete bipartite graph with equal partite sets.

Here n ( G ) is the order of G, α ( G ) is the independence number, ω ( G ) is the clique number, and χ ( G ) is the chromatic number.

Here, C, χ, M and N are

Here, on the hottest day, it is cool beneath the stone and fresh from the water flowing in the sluices at the bottom of the vaults.

Here in these little rooms -- or stages arched open to the sky and river -- they choose a few lines out of the hundreds they may know and sing them according to one of the modes into which Persian music is divided.

Here, on a desk, is a stack of pamphlets representing the efforts of some of the best men of the day to penetrate these questions.

Here, if anywhere, it is not wholly incontrovertible.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here an important caveat is in order.

Here, then, is what Swift would have called a modest proposal by way of a beginning.

But this we know: Here is a great life that in every area of American politics gives the American people occasion for pride and that has invested the democratic process with the most decent qualities of honor, decency, and self-respect.

Here is a word of advice when you go shopping for your pansy seeds.

Here then is our problem: aircraft are vital to winning a war today because they can perform those missions which a missile is totally incapable of performing ; ;

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Here is an original kedgeree recipe from the Family Club's kitchen:

Here is the promise of a vacation trip they can afford.

Here is where things stand today:

Here the Af distance is 2.44 Aj.

Here the pulmonary vein, as in type 2,, is noted to draw away from the bronchus, and to follow a more direct, independent course to the hilum ( figs. 23, 24 ).

Here the number of trials is a random variable, not a fixed number.

Here there is a specific preventive component which applies in a more generalized sense to any casework situation.

( Here an entry is a form plus the information that pertains to it.

Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

Here is the best short explanation of the origins of the Cold War that has been written.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Here, the idea was to map mathematical notation to a natural number ( using a Gödel numbering ).

Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).

The result, 1977's Here You Come Again, became her first million-seller, topping the country albums chart and reaching No. 20 on the pop albums chart ; the Barry Mann-Cynthia Weil-penned title track topped the country singles chart, and became Parton's first top-ten single on the pop charts ( reaching number three ).

Here n is the number of electrons / mole product, F is the Faraday constant ( coulombs / mole ), and ΔE is cell potential.

Here we denote with the Bernoulli number of the second kind ( only because the historical reason of formation of this article ) which differ from the first kind only for the index 1.

The piece has enjoyed a number of major revivals, and several of its songs have become standards, including " Broadway Baby ", " I'm Still Here ", " Too Many Mornings ", " Could I Leave You?

Carlotta amuses everyone with a tale of how her dramatic solo was cut from the Follies because the audience found it humorous, but somehow the number works when she sings it today (" I'm Still Here ").

Here he composed a large number of motets and other sacred music, which, being brought to the notice of Pope Urban VIII, obtained for him an appointment in the choir of the Sistine Chapel at Rome with the contralto role.

Here, sgn ( p ) is the signature of each permutation ( i. e. + 1 if p is composed of an even number of transpositions, and − 1 if odd.

Here we have the composite number 90 made up of one atom of the prime number 2, two atoms of the prime number 3 and one atom of the prime number 5.

Here they are combined with a number of peripheral interfaces to reduce the overall complexity and power requirements of a design.

Here n is the number of digits of precision at which the natural logarithm is to be evaluated and M ( n ) is the computational complexity of multiplying two n-digit numbers.

Here Z is atomic number and n is a number which varies between 4 and 5.

Here represents the reflexive and transitive closure of the step relation meaning any number of consecutive steps ( zero, one or more ).

" Here Comes the Judge " peaked at number 19 on the Billboard charts.

During this period in London he also collaborated on a number of songs with Bruce Woodley of the Seekers, including " I Wish You Could Be Here ", " Cloudy ", and " Red Rubber Ball ", which would be a U. S. No. 1 hit for the Cyrkle in 1966.

The album opened to sales of 185, 000 and has since been certified platinum in the U. S. The first single " Right Here " has been the biggest success from the album thus far, garnering much mainstream radio play and peaking at number 1 on the mainstream rock chart.