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.

In December 2004 Joe Pasquale, winner of the fourth series of ITV's I'm a Celebrity ... Get Me Out of Here !, became well known for his frequent use of the term " Jacobs ", for Jacob's Crackers, a rhyming slang term for knackers i. e. testicles.

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, the battery acts as a temporary energy store, allowing e. g. the implementation of regenerative braking and switching off the hydrocarbon engine when idling or stationary ( as used in automobiles such as the Toyota Prius ).

* Interactional: Here language is used to make contact with others and form relationships ( e. g. ' Love you, mummy ')

Here the most regular of irregularities, i. e., archaisms, will be delineated:

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 e < sub > a </ sup >< sup > μ </ sup > is the vierbein and D < sub > μ </ sub > is the covariant derivative for fermion fields, defined as follows

Here D is a traceless matrix such that αDe gives the derivative of e with respect to z.

Here, an " event " is a set of zero or more outcomes, i. e., a subset of the sample space.

Here, in each step of the XPath, the axis ( e. g. or ) is explicitly specified, followed by and then the node test, such as or in the examples above

Here e ( x → a ) is the evaluation which gives x the

Here, a number of its constituent sovereign nations have legalized traditional authority as manifested in the recognized hereditary transmission of chieftaincy in historically relevant regions of the continent ( e. g. the Asantehene of Ghana ).

A decade-and-a-half later, the reggae-rock band 311's hit single " I'll Be Here Awhile " " borrowed " several lines from " The Lust ..." ( i. e., " And if a person, place, or thing can deliver / I will quiver with delight ").

Here the coefficient A is an approximation of the short-wavelength ( e. g., ultraviolet ) absorption contributions to the refractive index at longer wavelengths.

Here, is density, u, v, and are the components of wind velocity, and is the 2-dimensional ( i. e. horizontal-component-only ) del.

Here the U ( 1 ) subgroup of U ( n ) consists of matrices of the form diag ( e < sup > iθ </ sup >, 1, 1, ..., 1 ).

Here there is the idea that God's heritage ( the created world ) is largely under the dominion of evil – i. e., it is " shared with Azazel " ( Abr.

Here | z | is the absolute value or modulus of the complex number z ; θ, the argument of z, is usually taken on the interval 0 ≤ θ < 2π ; and the last equality ( to | z | e < sup > iθ </ sup >) is taken from Euler's formula.

Here if the null hypothesis weren't rejected ( i. e. there is no reason to reject the hypothesis that A is at least as good as B ), the conclusion would be that treatment A should continue to be used.

Here, the real-life cast members were superimposed over pictures hanging in an art gallery and interacted with them in different ways ( e. g., spinning the canvas to put it right-side up, swinging the frame out as if it were a door, etc .).

Here h is the zero-field height ( or unreduced height ) of the barrier, e is the elementary positive charge, F is the barrier field, and ε < sub > 0 </ sub > is the electric constant.

Here the fiber over a point x in M is the set of all frames ( i. e. ordered bases ) for the tangent space T < sub > x </ sub > M.

Here R plays the role of im T and U is ker T, i. e.

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.