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 G is final average grain size, G < sub > 0 </ sub > is the initial average grain size, t is time, m is a factor between 2 and 4, and K is a factor given by:

Here Q is the molar activation energy, R is the ideal gas constant, T is absolute temperature, and K < sub > 0 </ sub > is a material dependent factor.

The third single was a double a-side, features new versions of " Here I go impossible again " and " All this time still falling out of love " It maded the U. K. Top 20.

( Here K ( a ) denotes the smallest subfield of L containing K and a )

* the algebra of all n-by-n matrices over the field ( or commutative ring ) K. Here the multiplication is ordinary matrix multiplication.

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

Here, the very low temperature is held constant at 77 K by slow boiling of the liquid, resulting in the evolution of nitrogen gas.

( Here ⊗ refers to the tensor product over K and id is the identity function.

Here C is either empty or Prikry generic over K ( so it has order type ω and is cofinal in κ ) and unique except up to a finite initial segment.

Here SZ is the center of SL, and is naturally identified with the group of nth roots of unity in K ( where n is the dimension of V and K is the base field ).

Here j is the injection of the generic point, i < sub > x </ sub > is the injection of a closed point x, G < sub > m, K </ sub > is the sheaf G < sub > m </ sub > on ( the generic point of X ), and Z < sub > x </ sub > is a copy of Z for each closed point of X.

Here i is the van't Hoff factor as above, K < sub > b </ sub > is the ebullioscopic constant of the solvent ( equal to 0. 512 ° C kg / mol for water ), and m is the molality of the solution.

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

Here permeability to Na is high and K permeability is relatively low.

In mathematics, an arithmetic group ( arithmetic subgroup ) in a linear algebraic group G defined over a number field K is a subgroup Γ of G ( K ) that is commensurable with G ( O ), where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them.

( Here F < sub > q </ sub > ⊂ K is the finite field of order q.

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

The main recent sense of the word “ art ” is roughly as an abbreviation for creative art or “ fine art .” Here we mean that skill is being used to express the artist ’ s creativity, or to engage the audience ’ s aesthetic sensibilities, or to draw the audience towards consideration of the “ finer ” things.

Here, Jesus plays on the imagery of Sheol found in Jonah ’ s prayer.

Here he found the first pirate of his voyage, Robert Culliford, ( the same man who had stolen Kidd ’ s ship years before ) and his crew aboard the Mocha Frigate.

Here, the cogito has already assumed the " I "' s existence as that which thinks.

Here is Schleicher ’ s explanation of why he offered reconstructed forms:

Here are some simple but useful commutator identities, true for any elements s, g, h of a group G:

beautiful whelks, a penny a lot .” “ Here ‘ s ha ‘ p ‘ orths ,” shouts the perambulating confectioner.

Here the Jose Abad Santos Falls present one of the nation ’ s scenic wonders at the gateway to a 200-hectare national park development.

Here, he apparently discontinued Leo III ’ s policies of favouring clergy over lay aristocracy.

Tillie Olsen ’ s I Stand Here Ironing ( 1961 ) adopted a consciously feminist perspective.

Here the notion of causality is one of contributory causality as discussed above: If the true value, then a change in will result in a change in y unless some other causative variable ( s ), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect ; thus a change in is not sufficient to change y.

Here, she created her own moves, imitated the famous dancers she watched in the movies, and taught “ Sister ’ s ” waltz clog.

* Note: Here P ( s ) is any polynomial in s.

" Minimal Deterrence Makes Minimal Sense ( And Here ’ s Why ).

*" Sweet 16: A-list Cinematographers Say the Emulsion ’ s Never Looked So Good, Here ’ s Why ...", written February 1, 2005 and accessed December 29, 2005.

Gene Green ’ s 1917 " From Here to Shanghai ", which featured faux-Chinese scatting, and Gene Rodemich's 1924 " Scissor Grinder Joe " and " Some of These Days " also pre-date Armstrong.

Here he participated in the shambolic acts that crippled the empire ’ s eastern provinces, including his strategic retreat when Caesar John Doukas was confronting Norman mercenary rebels, resulting in the humiliating defeat of the Byzantine army, and the capture of John Doukas.

Bert Berns, Them ’ s producer and composer of their 1965 hit, " Here Comes the Night ", persuaded Morrison to return to New York to record solo for his new label, Bang Records.

Here, Route 28 heads east through residential and commercial areas before turning northeast to closely parallel New Jersey Transit ’ s Raritan Valley Line ( which runs to the south of the route ) as North Avenue.

Here he was seduced by the king Chitravahana ’ s daughter, Chitrangadaa.

Shaffer's memoir, We'll Be Here for the Rest of Our Lives: A Swingin ' Show-biz Saga ( co-authored by David Ritz ) was published by Flying Dolphin Press ( an imprint of Random House Inc .' s Doubleday Broadway Publishing Group ) on October 6, 2009.