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 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 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 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 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, (( 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.

Here we define the distance in B ( X, M ) in terms of the distance in M as

Here n is the number of digits of precision at which the natural logarithm is to be evaluated and M ( n ) is the computational complexity of multiplying two n-digit numbers.

Here he met his first mentor M. Rost.

Notable story arcs of this decade are " Revolution " ( 2000 ), " Eve of Destruction ," " E Is For Extinction " ( 2001 ), " Planet X ," " Here Comes Tomorrow ," " Gifted ," ( 2004 ) X-Men: Phoenix-Endsong, " House of M ," " Decimation " ( 2005 ), Deadly Genesis ( 2005 – 2006 ), " Endangered Species " ( 2007 ), " Messiah Complex " ( 2007 – 2008 ), " Divided We Stand " ( 2008 ), " Manifest Destiny " ( 2008 – 2009 ), X-Infernus, " Messiah War ," " Utopia ," " Nation X " and " Necrosha " ( 2009 ).

* Kennedy, David M., Over Here: The First World War and American Society ( New York: Oxford University Press, 1980 )

Here, under the supervision of Kazimierz Kuratowski, he received his M. A. degree in 1932 and his D. Sc.

The Culture novel Excession by Iain M. Banks features a ship called Not Invented Here.

The book No Quitters Here: Quest for the Dome by B. M.

where dA is the element of area of the surface, and ds is the line element along the boundary of M. Here, is the Euler characteristic of.

One of Mayfield's most successful funk-disco meldings was the 1977 hit " Do Do Wap is Strong in Here " from his soundtrack to the Robert M. Young film of Miguel Piñero's play Short Eyes.

Here, just short of the Scottish border it becomes the A74 ( M ) which continues to Glasgow as the M74.

Here, M is a deterministic Turing machine, and x is its input ( the initial contents of its tape ).

Here Ellis touches upon the often paradoxical nature of widely reported consensual S & M practices.

Here " Reprinted in McCann " refers to McCann, M., ed.

Here Graeme ( 126 ) and Peter Pollock ( 10 / 87 ) won the match and Snow ( 1 / 63 & 3 / 83 ) was dropped both for the last Test and the M. C. C.

* Kennedy, David M. Over Here: The First World War and American Society ( 1982 ), covers politics & economics & society

Here M < sup > T </ sup > denotes the transpose of the matrix M. One can easily verify that the set of all such matrices forms a group.

Here the fiber over a point x in M is the set of all frames ( i. e. ordered bases ) for the tangent space T < sub > x </ sub > M.

* Kennedy, David M. Over Here: The First World War and American Society ( 1982 )

Here by an arc from x to y we mean the image in M of a topological embedding f from an interval to M such that f ( a )= x and f ( b )= y.