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 π < sub > n </ sub > is a homotopy group, GL ( R ) is the direct limit of the general linear groups over R for the size of the matrix tending to infinity, B is the classifying space construction of homotopy theory, and the < sup >+</ sup > is Quillen's plus construction.

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 >.

Here a cut is a subset U of A < sup >+</ sup > ( the non-zero elements of A ) such that if q is in U and p ≤ q then p is in U, and is called regular if whenever p is not in U there is some r ≤ p such that U has no elements ≤ r.

Here in an evening Persians enjoy many of the things which are important to them: poetry, water, the moon, a beautiful face.

Here are the two Preambles: Federal Constitution, 1789

Here artistic realism involves the audience in an impassioned participation in events whose overtones and implications are transcendent.

Here, in two nations alone, are almost five hundred million people, all working, and working hard, to raise their standards, and in doing so, to make of themselves a strong bulwark against the spread of an ideology that would destroy liberty.

Here we may observe that at least one modern philosophy of history is built on the assumption that ideas are the primary objectives of the historian's research.

Here, as in all sectors of the economy, quality and justice are both dependent on the right of the individual to deal directly with his employer if he so chooses.

Here then is our problem: aircraft are vital to winning a war today because they can perform those missions which a missile is totally incapable of performing ; ;

Here they are, with my comments and judgments.

Here are the brands ( in alphabetical order ) and the new models.

Here are a couple of the latest, highly styled ways to fix skinless franks in your own back yard!!

Here are suggestions for the frankfurter trimmings: 1.

Here are some key areas to examine to make sure your pricing strategy will be on target:

Here are some of the newer items currently available:

Here a variety of meanings and emotions are concentrated, or reduced, in their communicative expression, to some comparatively simple-seeming verbal or nonverbal statement.

Here again laboratory approaches are being evolved, for it is recognized how `` elastic '' these readings can be, how they can apply to many people, and are often stated in general terms all too easily applied to any individual's own case.

Here I do not speak of military power where our advantage is obvious and overwhelming but of political power -- of influence, if you will -- about which the relevant questions are: Is Soviet influence throughout the world greater or less than it was ten years ago??

Here, at the Ravine Lodge, President Dickey acts as host every year to about a hundred freshmen who are being introduced by the Dartmouth Outing Club to life on the trails.

Here are hatched plans for getting a share of the American bounty, the secret of the anti-missile missile, or an invitation to dinner.

`` Here are two old men, mad at each other and too proud to pick up the phone '', said a House Democratic leader.

Here are several:

Here are a few facts and figures I've assembled.

Here are some examples:

Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC ( ZF plus AC ).

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 | u | and | v | denote the length of the strings respectively.

Here, a single twist is illustrated, with left-plaited and right-plaited stitches on the left and right, respectively.

Here, there are four energy levels, energies E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, E < sub > 4 </ sub >, and populations N < sub > 1 </ sub >, N < sub > 2 </ sub >, N < sub > 3 </ sub >, N < sub > 4 </ sub >, respectively.

He reported: Here there is the great church called St. Abram, and this was a Jewish place of worship at the time of the Mohammedan rule, but the Gentiles have erected there six tombs, respectively called those of Abraham and Sarah, Isaac and Rebekah, Jacob and Leah.

Here T, ΔS and ΔH are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting.

Here is the time-domain impulse response of the LTI system and,,, are the Laplace transforms of the input, output, and impulse response, respectively.

( Here, we think of the DFT or DCT as approximations for the Fourier series or cosine series of a function, respectively, in order to talk about its " smoothness ".

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 we denote a pair of corresponding lower and upper adjoints by f < sup > ∗</ sup > and f < sub > ∗</ sub >, respectively.

Here, B < sub > V </ sub > and B < sub > W </ sub > are the bilinear forms on V and W respectively.

Alexakis has also dabbled in songwriting with other artists, including co-writing the song " At the End of the Day " released on Marion Raven's 2005 and 2007 albums, Here I Am and Set Me Free, respectively.

Here he wrote his Geschichte des Volkes Israel ( 1869 – 1870 ), in two parts, extending respectively to the end of the Persian domination and to the fall of Masada, 72 AD, as well as a work on the Pauline epistles, Zur Kritik Paulinischer Briefe ( 1870 ), on the Moabite Stone, Die Inschrift des Mescha ( 1870 ), and on Assyrian, Sprache und Sprachen Assyriens ( 1871 ), besides revising the commentary on Job by Ludwig Hirzel, first published in 1839.

Here, ran and dom denote the range and the domain, respectively.

Here is called a spherical harmonic function of degree ℓ and order m, is an associated Legendre polynomial, N is a normalization constant, and θ and φ represent colatitude and longitude, respectively.

Here and are called the amplitude and phase of the state, respectively.

Writer Tim Footman suggested that these images are borrowed from Pink Floyd, respectively corresponding to the Pink Floyd pigs and Wish You Were Here cover.

Here players with initial capital dollars, respectively,

Released in the US as Hear Here and Beat Group, respectively, they failed to crack the top 100.

Here d < sub > X </ sub > and d < sub > Y </ sub > denote the metrics on X and Y respectively.

Here refers to the final amount of good 2 allocated to person 1, etc., and refer to the final levels of utility experienced by person 1 and person 2 respectively, refers to the level of utility that person 2 would receive from the initial allocation without trading at all, and and refer to the fixed total quantities available of goods 1 and 2 respectively.

Here is the time and,, and, and are respectively an electron's momentum, charge, number density, mass, and mean free time between ionic collisions.

In 2001, the album was remastered and reissued on CD with three additional bonus tracks, two of which (" Julie Don't Live Here " and " When Time Stood Still ") had already been released as B-sides of singles (" Twilight " and " Hold On Tight " respectively ) from the original album, while the other (" The Bouncer ") was originally released as the UK B-side of the 1983 single " Four Little Diamonds " from the follow-up album Secret Messages.

Here and represent the changes in and, respectively, while and are the partial derivatives of with respect to and