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 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 unification of matter is even more complete, since the irreducible spinor representation 16 contains both the and 10 of SU ( 5 ) and a right-handed neutrino, and thus the complete particle content of one generation of the extended standard model with neutrino masses.

Here is the standard form of the conjecture:

( Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams )

Here, with von Neumann's inspiration, Richard Clippinger suggested that it could be configured in a jury rigged version of the stored-program architecture that has become standard on most computers.

Here, is the standard complex-valued wavefunction known from quantum theory, which evolves according to Schrödinger's equation

Here the contestants had been asked to modify their weapons so that they could use the standard size of cartridge used by the Austrian infantry.

Here a is constant acceleration, or in the case of bodies moving under the influence of gravity, the standard gravity g is used.

Here follows the operatic tenor fächer, with examples of the roles from the standard repertory that they commonly sing.

They had three chart hits, " Baby, Please Don't Go " ( 1964 ), " Here Comes the Night " ( 1965 ), and " Mystic Eyes " ( 1965 ), though it was the b-side of " Baby, Please Don't Go ", the garage band classic, " Gloria ", that went on to become a rock standard covered by Patti Smith, The Doors, Shadows of Knight, Jimi Hendrix and many others.

Here, volunteer vessels record position, depth and time data using their standard navigation instruments, and then the d ata is processed on the server for speed of sound, tidal and other corrections.

Here, a primary standard is typically a reagent which can be weighed easily, and which is so pure that its weight is truly representative of the number of moles of substance contained.

Here are some examples of usages often regarded as solecisms in standard English:

Here for an n-cell σ in T and for g in G the cell g σ is exactly the translate of σ by a covering transformation of T corresponding to g. Moreover, C < sub > n </ sub >( T ) is a free ZG-module with free ZG-basis given by representatives of G-orbits of n-cells in T. In this case the standard topological chain complex

( Here the velocity and position axes have been reversed from the standard convention in order to align the two diagrams )

** Kentucky — Here, " Independent " districts are separate from county districts, the standard form of school district in the state.

Here the restricted divine command theory is commonly combined with a view reminiscent of Plato: God is identical to the ultimate standard for goodness.

Here is the grand standard deviation ( or pooled standard deviation ), 1

Here it is legally known as Greenwich Mean Time and has been in standard use in England, Scotland and Wales since 1847, and Northern Ireland since 1922.

Here, the vast majority of the railway system standardised on the standard gauge of.

Here, the vast majority of the railway system standardised on the standard gauge of.

Here, the special nanori reading of (, ii ) and a standard kun ' yomi reading of (, da ) are combined.

Here he introduced quite a few innovations that were to remain standard procedure for many decades to come. The most notable was the formula for conversion of barometric readings taken at different temperatures to 32 degrees Fahrenheit.