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

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 idea was to map mathematical notation to a natural number ( using a Gödel numbering ).

Here and there a few natural islands permit slightly larger clusters.

Here n is the number of digits of precision at which the natural logarithm is to be evaluated and M ( n ) is the computational complexity of multiplying two n-digit numbers.

Here Spengler received a classical education at the local Gymnasium ( academically oriented secondary school ), studying Greek, Latin, mathematics and natural sciences.

Here, the concept of adherence tradition is embodied by the political philosophy of traditionalist conservatism ( or simply traditionalism ), which emphasizes the need for the principles of natural law and transcendent moral order, hierarchy and organic unity, agrarianism, classicism and high culture, and the intersecting spheres of loyalty.

which is natural in the variable N. Here the functor Hom ( N, F –) is the composition of the Hom functor Hom ( N, –) with F. This isomorphism is the unique one which respects the limiting cones.

Here he produced a little over a third of his total published work, and lived with his wife, daughters, and two grandchildren until dying of natural causes in 1967.

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

Here he showed a natural aptitude for mathematics.

Here permaculture principles would be applied in terms of aiming to reduce energy and water needs, harnessing natural resources such as sunlight, and generally creating a harmonious, sustainable environment in which to live and work.

Here, the basin becomes the natural setting to experience the lives and traditions of the people of the region.

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, he made it explicit that the generality of the laws whereby God regulated His behaviour extended not only to His activity in the natural world but also applied to His gift of grace to human beings.

Here, if one exponentiates 1, the product is 2. 71828 ; thus, the exponential function is the reciprocal of the natural logarithm.

Here it considers how local natural geography and local history gave rise to cultural truths.

Here, Hobbes stands upon his presumptions over the state of nature, within which he describes the hypothetical condition that preceded governments and details that within natural world, life is " solitary, poor, nasty, brutish, and short " ( loc.

Here, hundreds of Dawn redwoods have been planted in a natural state where they can be observed and recorded in the wild, without having to travel to China.

Here < u > n </ u > is the numeral corresponding to the natural number n, which is defined to be the closed term 1 + ··· + 1 ( n ones ), and < u > f ( n )</ u > is the numeral corresponding to f ( n ).

Here too, infrastructures followed the natural assets, and tourists can now stay in themed resorts, featuring of course hot baths perfumed with bamboo.

Here he developed the arithmetic of the natural numbers by first defining objects by primitive recursion, then devising another system to prove properties of the objects defined by the first system.

Here he established a natural history museum and wrote a textbook for his students, the Zoologiae fundamenta.

Here the natural forests are mainly broadleaf evergreen in lower elevations and deciduous in higher elevations.

Here, n is a natural number ; if n > 1, then B < sub > n </ sub > is an infinite group.