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, K < sup > s </ sup > is the separable closure of K, which coincides with the algebraic closure when K is a perfect field.

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.

Here the term yoga denotes a kind of " meta-theory " that can be used heuristically ; Michel Raynaud writes the other terms " Ariadne's thread " and " philosophy " as effective equivalents.

Here highbit ( S ) denotes the most significant bit of S ; the '< tt >*</ tt >' operator denotes unsigned integer multiplication with lost overflow ; '< tt >^</ tt >' is the bitwise exclusive or operation applied to words ; and P is a suitable fixed word.

# 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 is the particle's velocity and × denotes the cross product.

Let ρ, θ, and φ be spherical coordinates for the source point P. Here θ denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice.

Here denotes the maximum-likelihood estimate, and is the sample mean of the observations.

Here, denotes the natural logarithm.

Here C < sub > b </ sub >( X ) denotes the C *- algebra of all continuous bounded functions on X with sup-norm.

Here denotes vertical composition of natural transformations, and denotes horizontal composition.

Here the t denotes the matrix transpose.

( Here V0, V1, and V2 denote verbs and Ny denotes a noun.

Here y *( w ) denotes the value of the linear functional y * ( which is an element of the dual space of W ) when evaluated at the element w ∈ W. This scalar in turn is multiplied by x to give as the final result an element of the space V.

Here, || ||< sub > 2 </ sup > is the matrix 2-norm, c < sub > n </ sub > is a small constant depending on n, and ε denotes the unit round-off.

Here 0 denotes the trivial abelian group with a single element, the map from Z to Z is multiplication by 2, and the map from Z to the factor group Z / 2Z is given by reducing integers modulo 2.

Here, denotes the radical of J and I ( U ) is the ideal of all polynomials which vanish on the set U.

Here, " prequel " denotes status as a " franchise-renewing original " that depicts events earlier in the ( internally inconsistent ) narrative cycle than those of a previous installment.

Here N < sub > m </ sub > denotes the number of turns in loop m, Φ < sub > m </ sub > the magnetic flux through this loop, and L < sub > m, n </ sub > are some constants.

Here denotes the standard complex inner product on and.

Here it also denotes a hand gesture, now linked to three other hand mudrās — the action ( karma ), pledge ( samaya ), and dharma mudrās — but also involves " mantra recitations and visualizations that symbolize and help to effect one ’ s complete identification with a deity ’ s divine form or awakening mind ( bodhicitta ).

Here, denotes the resolution limit in arcseconds and is in millimeters.

Here, the Nebel was less of an obstacle, but the great battery positioned on the edge of the village enjoyed a good field of fire across the open ground stretching to the hamlet of Schwennenbach.

Here the server, 192. 168. 1. 1, specifies the IP address in the YIADDR ( Your IP Address ) field.

Here the scattering is due to the molecular polarizability α, which describes how much the electrical charges on the molecule will move in an electric field.

Here is also worth noting what Tacitus stated in his work Germania about capital punishment amongst the Germanic folk ; that none could be flogged, imprisoned or executed, not even on order of the warlord, without the consent of the priest ; who was himself required to render his judgement in accordance with the will of the god they believe accompanies them to the field of battle In the same source this god is stated being the chief deity.

Here is an ASP example using ADO to select the " Name " field, from a table called " Phonebook ", where a " PhoneNumber " was equal to " 555-5555 ".

Here A and φ represent the electromagnetic field, and the three sigmas are the Pauli matrices.

Here is the amplitude of the field and

Here u might describe the displacement of a stretched string from equilibrium, or the difference in air pressure in a tube, or the magnitude of an electromagnetic field in a tube, and c is a number that corresponds to the velocity of the wave.

Here the temperature field within the object begins to change as a function of time, as the heat is removed from the metal, and the interest lies in analyzing this spatial change of temperature within the object over time, until all gradients disappear entirely ( the ball has reached the same temperature as the oil ).

Here Δk is the field-dependent difference between LCP and RCP absorption, α is the electric permeability, n is the index of refraction, H is the applied magnetic field, k is the Boltzmann constant and T is the temperature.

Here lay the strength and advantage of Saxe's choice: the descent in many places along the position formed a natural glacis, and throughout the whole length, from Antoing to the wood, the prolonged slope offered an even and deadly field for cannon and musketry fire.

Here is a variable which parametrizes the curve Streamlines are calculated instantaneously, meaning that at one instance of time they are calculated throughout the fluid from the instantaneous flow velocity field.

Here he found a fruitful field for his activity.

Here he spent time cultivating the tribesmen as well indulging his enjoyment of field sports.

Here + is addition either in the field or in the vector space, as appropriate ; and 0 is the additive identity in either.

Here the coherent state of a field describes an oscillating field, the closest quantum state to a classical sinusoidal wave such as a continuous laser wave.

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 one considers a modification of the directional derivative by a certain linear operator, whose components are called the Christoffel symbols, which involves no derivatives on the vector field itself.

Here he distinguished himself in the field and in the cabinet.

* The Hit it Here Café is located in right field, on the same level as the Terrace Club.

* The dimension of the – vector space is the same for all prime ideals of R .< ref > Here, is the residue field of the local ring .</ ref >