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 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, a vertical line ( black ) is drawn perpendicular to the plane of each planet's orbit.

Here, the horizontal axis gives the position and vertical axis the velocity.

Here the vertical bars denote the absolute value.

Here erosion has created vertical channels giving the characteristic jagged shapes for which the mountain is named ( Montserrat literally means " jagged mountain ").

Here, the wave is said to be ducted or trapped, and a vertically standing wave may form, where the vertical component of group velocity approaches zero.

To reach the water in the cave one has either to abseil or to descend an ancient, hand-forged ladder that hangs free of the vertical dolomite walls of the cave for over 50 m. Here, too, SCUBA divers have descended as deep as they have dared ( 80 m ) in the crystal-clear waters and have reported nothing but deep blue below them from one ledge of dolomite to the next with nothing discernible in the depths.

Here is an image for which the alt attribute is " In the sky flies a red flag with a white cross whose vertical bar is shifted toward the flagpole.

" Here the Goums more than proved their value as light, highly mobile mountain troops who could penetrate the most vertical terrain in fighting order and with a minimum of logistical requirements.

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.

The album's second single, " Now I'm Here ", a more traditional hard rock composition, was a number eleven hit in Britain, while the high speed rocker " Stone Cold Crazy " featuring May's uptempo riffs is a precursor to speed metal.

Here composition of morphisms is just ring multiplication and the unique hom-set is the underlying abelian group.

Here the composition for orchestra, using the ideas of the tautology, gives a completely new aspect to the memorized sound.

Autry also sang the classic Ray Whitley hit " Back In The Saddle Again ," as well as many Christmas holiday songs, including " Santa Claus Is Coming to Town ," his own composition " Here Comes Santa Claus ," " Frosty the Snowman ," and his biggest hit, " Rudolph the Red-Nosed Reindeer.

Here, with his fellow students ( who included Carl Maria von Weber ), he learnt not only the craft of composition but also the business of music ( organising concerts and dealing with publishers ).

Here the algebra multiplication is given by the composition of operators.

Jazz musician, Charles Mingus, recites a variation on the poem in the introduction to his composition “ Don't Let it Happen Here ”.

Here we might divide into sub genres: epic singing, containing not only historical facts, but as well the tribe's genealogy, love songs, didactic verses ; and as a special form the composition of two or more singers in public ( Aitys ), of dialogue character and usually unexpectedly frankly in content.

Here Gance's mastery of lighting, composition and editing was accompanied by a range of literary and artistic references which some critics found pretentious and alienating.

Here he won prizes for piano accompaniment, harmony, counterpoint, fugue and composition ( studying under Olivier Messiaen from 1968 to 1972 ).

Here, in addition to schillerization, the original enstatite has been altered by hydration and the product has the approximate composition of serpentine.

He was born in Philadelphia, Pennsylvania, and is best known for his role as sideman in Art Blakey's Jazz Messengers ( 1958 – 1961 ) and the composition of " Moanin '", " Dat Dere ", and " This Here ", each of which are typical of his distinctive gospel soul-jazz style.

It contained the hit singles " Still of the Night ", " Is This Love ", " Give Me All Your Love ", and " Here I Go Again " ( the last was not a Sykes composition ).

Also in 1964, she auditioned for producer Chet Atkins, the architect of the Nashville sound, who agreed to produce her composition " Here Comes My Baby ".

Ralph Rainger and Leo Robin wrote six songs that appear in the film: “ This Little Ripple Had Rhythm ” ( an instrumental composition ); “ Don ’ t Tell a Secret to a Rose ;” “ You Took the Words Right Out of My Heart ;” “ Thanks for the Memory ;” “ Mama, That Moon is Here Again ;” and “ The Waltz Lives On .”

McCartney later described in Beat Instrumental how he went about the song's composition: " Here ’ s one example of a bit I pinched from someone: I used the bass riff from ' Talkin ’ About You ' by Chuck Berry in ' I Saw Her Standing There '.

Part of the song appears mixed alongside another Harrison composition, " Here Comes the Sun ", on the 2006 Cirque du Soleil album, Love.

Here he developed his computer composition programs Project 1 ( 1964 ) and Project 2 ( 1966 ), designed to formalise the composition of musical structure-variants.