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 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 ).

( Here, e is the base of the natural logarithm, about 2. 71828 ..., and i is the imaginary unit, a square root of − 1.

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, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

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 K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

Here k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.

Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here, R < sub > ij </ sub > is the Ricci tensor.

# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

Here the last product means that a first electron, r < sub > 1 </ sub >, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus.

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 the notion of convergence corresponds to the norm on L < sup > 2 </ sup >.

" Here, take her, sir " ( Sir Joseph, Josephine, Ralph, Cousin Hebe and Chorus )< sup > 1 </ sup >

< center >< span style = " font-variant: small-caps "> Here were buried the remains of

( Here, we have used the fact that N < sub > 1 </ sub >< sup >− 1 </ sup > N < sub > 1 </ sub > is unity when evaluated modulo N < sub > 2 </ sub > in the inner sum's exponent, and vice-versa for the outer sum's exponent.

Lorne stated of the hall: " Here we are settling down in this big and comfortable House < nowiki >< nowiki ></ nowiki >, which I tell Louise is much superior to Kensington, for the walls are thick, the rooms are lathed and plastered ( which they are not at Kensington ) and there is an abundant supply of heat and light.

Here is an example showing the use of with < code >< nowiki >< pre ></ pre ></ nowiki ></ code > tags.

Here ω < sup > α </ sup >< sub > β </ sub > defines a k × k matrix of one-forms on U. In fact, given any such matrix the above expression defines a connection on E restricted to U. This is because ω < sup > α </ sup >< sub > β </ sub > determines a one-form ω with values in End ( E ) and this expression defines ∇ to be the connection d + ω, where d is the trivial connection on E over U defined by differentiating the components of a section using the local frame.

Here the rank of Q < sub > i </ sub > should be interpreted as meaning the rank of the matrix B < sup >( i )</ sup >, with elements B < sub > j, k </ sub >< sup >( i )</ sup >, in the representation of Q < sub > i </ sub > as a quadratic form:

Here D < sup > J </ sup >< sub > MK </ sub > is an element of the Wigner D-matrix.

Here, another electron reacts with sulfur to form S < sub > n </ sub >< sup > 2 −</ sup >, sodium polysulfide.

Here is the character table of C < sub > 3 </ sub > = < nowiki >< u ></ nowiki >, the cyclic group with three elements and generator u:

Here Diff < sub > x </ sub >< sup > n </ sup >( M ) is a normal subgroup of Diff < sub > x </ sub >< sup > 1 </ sup >( M ), which means we can look at the quotient group

She's A Friend Of Mine / The Train Don't Stop Here No More / Black Cat Moan / Rainy Night In Paris ( Memphis Reject )/ When I Lay My Burden Down / Sweet Sweet Surrender / We Gotta Move ( Keep On Rolling )/ Miss Eleana / I Need You / Look What The Years Have Done ( personnel: Don Nix: vcl / gtr, Pete Carr / Eddie Hinton / Larry Rasberry / Bobby Manuel / Furry Lewis: gtr, George Harrison slide gtr, Wayne Perkins: gtr / bcgr. vcls, Barry Beckett / Chris Stainton: keys, Steve Smith: keys / gtr, Tim Smith: gtr / pno, David Hood / Klaus Voormann: bs, Roger Hawkins: dms, Lon Price: sax, Jay Pruitt: strings, Jeanie Green / Claudia Lennear: bcgr. vcls + The Dallas-Ft. Worth Symphony Orchestra ) ( recorded at Apple Studio, London & Muscle Shoals Sound Studio etc., produced by Don Nix ) ( reissue: P-Vine PCD-5175, 1997 JAP )</ TD >< TD >< font size =" 2 "> 1973 US </ TD ></ TR >

Here the iodinating agent is the tri-iodine cation I < sub > 3 </ sub >< sup >+</ sup > and the base is HSO < sub > 4 </ sub >< sup >-</ sup >.

< u > New York Times </ u > 25 Oct. 1941 </ ref >< ref >" 2 Texas Merchants Held With Thieves ; Supposedly Reputable Men Seized Here, Accused of Buying Stolen Goods Linked to Ex-Convicts ".

Here in this case D < sub > U </ sub > = k TBP < sup > 2 </ sup > NO < sub > 3 </ sub >< sup > 2 </ sup >