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

Here the ( pc )< sup > 2 </ sup > term represents the square of the Euclidean norm ( total vector length ) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered.

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, with respect to identity diffusion for example, an optimal level is interpreted as the norm, as it is unrealistic to expect an individual to resolve all their conflicted identifications with others ; therefore we should be alert to individuals with levels which are much higher or lower than the norm – highly diffused individuals are classified as diffused, and those with low levels as foreclosed or defensive.

Here to be a global norm means to be an element k of K such that there is an element l of L with ; in other words k is a relative norm of some element of the extension field L. To be a local norm means that for some prime p of K and some prime P of L lying over K, then k is a norm from L < sub > P </ sub >; here the " prime " p can be an archimedean valuation, and the theorem is a statement about completions in all valuations, archimedean and non-archimedean.

Here, is the Euclidean norm ( denoted customarily by single bars in PDEs ), and is time.

Here, ||·||< sub > p </ sub > refers to the matrix norm induced by the vector p-norm.

Here, the norm on the left-hand side denotes the maximum value of f in the closed disc:

Here, cattle leases to local ranchers as well as timber harvesting are the norm.

( Here N is the field norm of an ideal.

Here, she dropped the keys on a small table beside the door and went upstairs to her bedroom.

Here, on the hottest day, it is cool beneath the stone and fresh from the water flowing in the sluices at the bottom of the vaults.

Here, on a desk, is a stack of pamphlets representing the efforts of some of the best men of the day to penetrate these questions.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here in the cool darkness Mr. Podger could still feel the warmth of midday, could still see the yellow butterflies dancing over the road, could still see the friendly grin on the young, sun-browned face as the driver looked back over his shoulder for a moment before the car streaked out of sight.

Here, as in all sectors of the economy, quality and justice are both dependent on the right of the individual to deal directly with his employer if he so chooses.

Here are some key areas to examine to make sure your pricing strategy will be on target:

Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

Here no attempt is made, first to determine out-of-pocket or marginal costs and then to superimpose on these costs `` reasonably distributed '' residues of total costs.

Here, at the Ravine Lodge, President Dickey acts as host every year to about a hundred freshmen who are being introduced by the Dartmouth Outing Club to life on the trails.

Here is the world of the chauffeured limousine and the gossip reporter, of caviar on stale crackers and the warm martini, of the poseur, the spy, the party crasher, and the patriot, of the rented tails, the double cross, and the tired Lothario.

And, Here, I'll take this, I was before her, you wait on me now or I don't bother with it, see!!

Here '' -- She thrust a bundle of keys strung on a thick red cord into Sarah's hand.

Here and there on work table or pedestal stood a shape with a sheet or a tarpaulin draped over it.

Or have a sign on his car that says, ' Here Comes the Paxton Kidnapper ' ''??

Here I took my leave of my learned friends to step out on another path, to which we might give the modern name of Pragmatism, or the thing that works.

Here the peoples spoke the tongue of Iceland because that island had gotten the jump on the Hawaiian-Americans who were busy resettling North America and the western half of South America after the Apocalyptic War.

Here, souls rest, recuperate from life, and reflect on the experiences they had during their lives.

Here, the lord Krishna says that just as a man discards his old clothes and wears new ones ; similarly the soul discards the old body and takes on a new one.

The slab on top carries the inscription (" Here lies a French soldier who died for the fatherland 1914 – 1918 ").

Here, Steiner developed a concept of free will based on inner experiences, especially those that occur in the creative activity of independent thought.

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, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.

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

Here are found the Little Office of the Blessed Virgin Mary, the Office of the Dead ( obligatory on All Souls ' Day ), and offices peculiar to each diocese.