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 December 2004 Joe Pasquale, winner of the fourth series of ITV's I'm a Celebrity ... Get Me Out of Here !, became well known for his frequent use of the term " Jacobs ", for Jacob's Crackers, a rhyming slang term for knackers i. e. testicles.

Here, i is the complex number whose square is the real number − 1 and is identified with the point with coordinates ( 0, 1 ), so it is not the unit vector in the direction of the x-axis ( this confusion is just an unfortunate historical accident ).

Here, indexes i, j are related to the various components and not to the space coordinates.

Here, sgn ( p ) is the signature of each permutation ( i. e. + 1 if p is composed of an even number of transpositions, and − 1 if odd.

Here the most regular of irregularities, i. e., archaisms, will be delineated:

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

Here, an " event " is a set of zero or more outcomes, i. e., a subset of the sample space.

( Here, e is the base of the natural logarithm, about 2. 71828 ..., and i is the imaginary unit, a square root of − 1.

Here the generalized coordinates q < sub > i </ sub > for i

A decade-and-a-half later, the reggae-rock band 311's hit single " I'll Be Here Awhile " " borrowed " several lines from " The Lust ..." ( i. e., " And if a person, place, or thing can deliver / I will quiver with delight ").

Here and are the i < sup > th </ sup > columns of the corresponding SVD matrices, are the ordered singular values, and each is separable.

Here Saadia controverts the Mutakallamin, who considered the soul an " accident " arad ( compare Guide for the Perplexed i. 74 ), and employs the following one of their premises to justify his position: " Only a substance can be the substratum of an accident " ( that is, of a non-essential property of things ).

Here, is density, u, v, and are the components of wind velocity, and is the 2-dimensional ( i. e. horizontal-component-only ) del.

Here the X < sub > i </ sub > are the generalized forces corresponding to the external variables x < sub > i </ sub >.

Here Saadia controverts the Mutakallamin, who considered the soul an " accident " arad ( compare Guide for the Perplexed i. 74 ), and employs the following one of their premises to justify his position: " Only a substance can be the substratum of an accident " ( that is, of a non-essential property of things ).

Here there is the idea that God's heritage ( the created world ) is largely under the dominion of evil – i. e., it is " shared with Azazel " ( Abr.

Here, each vector Y < sub > j </ sub > of the f ' basis is a linear combination of the vectors X < sub > i </ sub > of the f basis, so that

Here is a known vector, and is an unknown vector of numbers x < sub > i </ sub > yet to be determined.

Here if the null hypothesis weren't rejected ( i. e. there is no reason to reject the hypothesis that A is at least as good as B ), the conclusion would be that treatment A should continue to be used.

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

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 Wright gave a slight sigh of weariness, and continued, `` It means more long years lived across the social grain of the life of our people, making shift to live in the face of popular disrespect and misunderstanding as I best can for myself and those dependent upon me ''.

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Here, ' simple ' means an appearance of the factor of the form.

Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.

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 '.

The first question was answered in the negative when in 1963, Eggan gave examples of regular languages of star height n for every n. Here, the star height h ( L ) of a regular language L is defined as the minimum star height among all regular expressions representing L. The first few languages found by are described in the following, by means of giving a regular expression for each language:

Here, the Chinese character 至 means " extreme ", so the terms for the solstices directly signify the summits of summer and winter.

( Here, formalizing accurately and completely means that all true propositions — and only true propositions — are derivable within the mathematical system.

Here, F means " draw forward ", + means " turn right 60 °", and − means " turn left 60 °".

( Here, means that.

Here means “ divides ”; that is, if is a divisor of.

Here " immediately " means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale.

Here the phrase " due use of the ordinary means " includes appeals to pastors and teachers

Here, I only want my dispositions to be known: it is a means to avoid further ills.

Here, M2 is adjusted for inflation by means of the deflator published by the federal government in the GDP report.

Here " validation " means that the object in question has been validated as evidence of technological developments that were present in an ancient society and which were previously unknown to us.

Here empty pride means a fake pride, in the sense of vainglory, unjustified by one's own achievements and actions, but sought by pretense and appeals to superficial characteristics.

The grace of God means something like: Here is your life.

" Here the propagandists is dealing with a foreign adversary whose morale he seeks to destroy by psychological means so that the opponent begins to doubt the validity of his beliefs and actions.

( Here the notation ( a ) means the principal ideal of R consisting of all the multiples of a.

Here, the maiden falls in love with Achilles, and accepts to be sacrificed on the pyre as a means to ensure both her lover's happiness ( as predicted by an oracle ) and her father Agamemnon's victory in the Trojan War.