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.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Here, x is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counter clockwise and in radians.

Here Person ( x ) is interpreted to mean x is a person, Time ( y ) to mean that y is a moment of time, and Canfool ( x, y ) to mean that ( person ) x can be fooled at ( time ) y.

Here ( x, y | x ', y ') means that instead of ψ we are writing a different formula, in which x and y are replaced with x ' and y '.

Here, we have < tt >( λx. xx )( λx. xx ) → ( xx ):= λx. xx = ( x := λx. xx )( x := λx. xx ) = ( λx. xx )( λx. xx )</ tt >.

Here the summation is over all prime powers up to x.

Here m is the particle's mass and V ( x ) is the applied potential.

Here x is the node on which the splay operation is performed and root is the root node of the tree.

The Wildhearts song ' 29 x The Pain ', which namedrops the bands major influences, opens with the lyrics ' Here, sitting in my room, with the Replacements and Hüsker Dü '.

Here u ( x ) measures the distance from the equilibrium of the mass situated at x.

Here N < sub > x </ sub > is the number of x atoms per volume, λ the electron escape depth, θ the analyzer angle, T the transmission of the analyzer, I ( t ) the electron excitation flux at depth t, dΩ the solid angle, and δt is the thickness of the layer being probed.

Here e ( x → a ) is the evaluation which gives x the

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 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.

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

< 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 ω < sup > α </ sup >< sub > β </ sub > defines a k × k matrix of one-forms on U. In fact, given any such matrix the above expression defines a connection on E restricted to U. This is because ω < sup > α </ sup >< sub > β </ sub > determines a one-form ω with values in End ( E ) and this expression defines ∇ to be the connection d + ω, where d is the trivial connection on E over U defined by differentiating the components of a section using the local frame.

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:

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 >

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