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.

* 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, during the Battle of Okinawa, a US Marine on the left provides covering fire for the Marine on the right to break cover and move to a different position. A fire and maneuver team is the smallest unit above the individual soldier.

Here R ( r, s ) signifies an integer that depends on both r and s. It is understood to represent the smallest integer for which the theorem holds.

Here is the distance of T from the algebra, namely the smallest norm of an operator T-A where A runs over the algebra.

Here is the size of the largest matching and is the size of the smallest vertex cover.