In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Here n is the refractive index of the medium in which the measurement is made ; and f is the measured frequency of the source.

Harefield enters recorded history through the Domesday Book ( 1086 ) as Herefelle, comprising the Anglo-Saxon words Here " army " ( c. f.

Here we denote a pair of corresponding lower and upper adjoints by f < sup > ∗</ sup > and f < sub > ∗</ sub >, respectively.

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 it is customary to speak of the domain of f ( z ) as lying in the z-plane, while referring to the range or image of f ( z ) as a set of points in the w-plane.

Here < u > n </ u > is the numeral corresponding to the natural number n, which is defined to be the closed term 1 + ··· + 1 ( n ones ), and < u > f ( n )</ u > is the numeral corresponding to f ( n ).

Here by an arc from x to y we mean the image in M of a topological embedding f from an interval to M such that f ( a )= x and f ( b )= y.

for any torsion sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S ( with f = gj ), and as before the definition does not depend on the choice of j and Y. Cohomology with compact support is the special case of this with S a point.

Here if f, g: X → Y are group homomorphisms, their coequalizer is the quotient of Y by the normal closure of the set

Here, the asterisk indicates the complex conjugate of f.

Here K < sub > f </ sub > is the cryoscopic constant, equal to 1. 86 ° C kg / mol for the freezing point of water.

Here ω = 2πf is the angular frequency ( and f the frequency ), and i = is the imaginary unit, so that I is a phasor.

Here ' restriction ' is interpreted by means of fiber product, applied to f and the inclusion map of Y ′ into Y.

Here f is the resonant frequency.

Here to be precise, f would have to be replaced by its natural hyperreal extension usually denoted f < sup >*</ sup > ( see discussion of Transfer principle in main article at non-standard analysis ).

Here the point x ' is assumed to be in the domain of ( the natural extension of ) f.

Here, g and g ′ are SU ( 2 ) and U ( 1 ) gauge couplings and tanθ < sub > W </ sub > =

Here, the prime ′ symbols mean gamma correction is being used ; thus R ′, G ′ and B ′ nominally range from 0 to 1, with 0 representing the minimum intensity ( e. g., for display of the color black ) and 1 the maximum ( e. g., for display of the color white ).

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 C and C ′ are given conics.

Here U is the same as before and P ′ is given by

" Here Norwegian forces stopped the enemy ′ s attempt at capturing the King, Crown Prince, parliament and cabinet ".

Here a ′ and b ′ are in the duals of A and B,

Here A ′ and B ′ mean the topological duals of

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.