Here A < sub >–</ sub > and A < sub >+</ sub > are the absorbances of LCP or RCP, respectively ; ω is the modulator frequency – usually a high acoustic frequency such as 50 kHz ; t is time ; and δ < sub > 0 </ sub > is the time-dependent wavelength shift.

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 ω = 2πf is the angular frequency ( and f the frequency ), and i = is the imaginary unit, so that I is a phasor.

Here the Hilbert space is L < sup > 2 </ sup >( R ), the space of square integrable functions on R, and the energy operator H is defined by ( assuming the units are chosen such that &# 8463 ; = m = ω = 1 )

Here n ( G ) is the order of G, α ( G ) is the independence number, ω ( G ) is the clique number, and χ ( G ) is the chromatic number.

Here ω < sub > d </ sub > is the volume of the unit d-ball, and sometimes sign conventions may vary ; compare and.

Here ω ( Y ) is the-valued function obtained by duality from pairing the one-form ω with the vector field Y, and X ( ω ( Y )) is the Lie derivative of this function along X.

Here, d < sub > F </ sub > is called the degree ( or dimension ) of F. It is given by < ref > While the ω < sub > i </ sub > are not uniquely defined by F, Selberg's result shows that their sum is well-defined .</ ref >

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.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

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 k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.

Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.

The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:

Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.

Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion

Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.

Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.

Here, R < sub > ij </ sub > is the Ricci tensor.

# 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, the coefficients χ < sup >( n )</ sup > are the n-th order susceptibilities of the medium and the presence of such a term is generally referred to as an n-th order nonlinearity.

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

Here e < sub > a </ sup >< sup > μ </ sup > is the vierbein and D < sub > μ </ sub > is the covariant derivative for fermion fields, defined as follows

" Here, take her, sir " ( Sir Joseph, Josephine, Ralph, Cousin Hebe and Chorus )< sup > 1 </ sup >

Here constant α quantifies the strength of the interaction between adjacent molecules.

Here the scattering is due to the molecular polarizability α, which describes how much the electrical charges on the molecule will move in an electric field.

Here u ( x, t ) is the temperature of the rod at position x and time t and α is a constant that depends on how fast heat diffuses through the rod.

Here Δk is the field-dependent difference between LCP and RCP absorption, α is the electric permeability, n is the index of refraction, H is the applied magnetic field, k is the Boltzmann constant and T is the temperature.

Here, α, β, and γ are the angles at the center of the sphere subtended by the three arcs of the spherical surface triangle a, b, and c, respectively.

( Here the term κ-additive means that, for any sequence A < sub > α </ sub >, α < λ of cardinality λ < κ, A < sub > α </ sub > being pairwise disjoint sets of ordinals less than κ, the measure of the union of the A < sub > α </ sub > equals the sum of the measures of the individual A < sub > α </ sub >.

Here, < sup > α </ sup > M is the class of all sequences of length α whose elements are in M.

( Here α and β are real and i represents the imaginary unit.

Here, glycogen phosphorylase cleaves the bond linking a terminal glucose residue to a glycogen branch by substitution of a phosphoryl group for the α linkage.

Here satisfies α² = α − 41.

Here F ( s ) denotes the Laplace transform of ƒ, and this property expresses that I < sup > α </ sup > is a Fourier multiplier.

: Here, α is √ 2 < sup >√ 2 </ sup > which ( as proved by the theorem itself ) is transcedental rather than algebraic.

Here, a, b, and c are the angles at the centre of the sphere subtended by the three sides of the triangle, and α, β, and γ are the angles between the sides, where angle α is opposite the side which subtends angle a, and so forth.

Here we have c < sup > a </ sup > for the ghost field while α fixes the gauge's choice for the quantization.

Here, (( α → β ) → α ) is the type of the function f, which can either return a value of type α directly or apply an argument to the continuation of type ( α → β ).

Here the last product means that a first electron, r < sub > 1 </ sub >, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus.

< center >< span style = " font-variant: small-caps "> Here were buried the remains of

( Here, we have used the fact that N < sub > 1 </ sub >< sup >− 1 </ sup > N < sub > 1 </ sub > is unity when evaluated modulo N < sub > 2 </ sub > in the inner sum's exponent, and vice-versa for the outer sum's exponent.

Lorne stated of the hall: " Here we are settling down in this big and comfortable House < nowiki >< nowiki ></ nowiki >, which I tell Louise is much superior to Kensington, for the walls are thick, the rooms are lathed and plastered ( which they are not at Kensington ) and there is an abundant supply of heat and light.

Here is an example showing the use of with < code >< nowiki >< pre ></ pre ></ nowiki ></ code > tags.

Here the rank of Q < sub > i </ sub > should be interpreted as meaning the rank of the matrix B < sup >( i )</ sup >, with elements B < sub > j, k </ sub >< sup >( i )</ sup >, in the representation of Q < sub > i </ sub > as a quadratic form:

Here D < sup > J </ sup >< sub > MK </ sub > is an element of the Wigner D-matrix.

Here, another electron reacts with sulfur to form S < sub > n </ sub >< sup > 2 −</ sup >, sodium polysulfide.

Here is the character table of C < sub > 3 </ sub > = < nowiki >< u ></ nowiki >, the cyclic group with three elements and generator u:

Here Diff < sub > x </ sub >< sup > n </ sup >( M ) is a normal subgroup of Diff < sub > x </ sub >< sup > 1 </ sup >( M ), which means we can look at the quotient group

She's A Friend Of Mine / The Train Don't Stop Here No More / Black Cat Moan / Rainy Night In Paris ( Memphis Reject )/ When I Lay My Burden Down / Sweet Sweet Surrender / We Gotta Move ( Keep On Rolling )/ Miss Eleana / I Need You / Look What The Years Have Done ( personnel: Don Nix: vcl / gtr, Pete Carr / Eddie Hinton / Larry Rasberry / Bobby Manuel / Furry Lewis: gtr, George Harrison slide gtr, Wayne Perkins: gtr / bcgr. vcls, Barry Beckett / Chris Stainton: keys, Steve Smith: keys / gtr, Tim Smith: gtr / pno, David Hood / Klaus Voormann: bs, Roger Hawkins: dms, Lon Price: sax, Jay Pruitt: strings, Jeanie Green / Claudia Lennear: bcgr. vcls + The Dallas-Ft. Worth Symphony Orchestra ) ( recorded at Apple Studio, London & Muscle Shoals Sound Studio etc., produced by Don Nix ) ( reissue: P-Vine PCD-5175, 1997 JAP )</ TD >< TD >< font size =" 2 "> 1973 US </ TD ></ TR >

Here the iodinating agent is the tri-iodine cation I < sub > 3 </ sub >< sup >+</ sup > and the base is HSO < sub > 4 </ sub >< sup >-</ sup >.

< u > New York Times </ u > 25 Oct. 1941 </ ref >< ref >" 2 Texas Merchants Held With Thieves ; Supposedly Reputable Men Seized Here, Accused of Buying Stolen Goods Linked to Ex-Convicts ".

Here in this case D < sub > U </ sub > = k TBP < sup > 2 </ sup > NO < sub > 3 </ sub >< sup > 2 </ sup >