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 n is the number of electrons / mole product, F is the Faraday constant ( coulombs / mole ), and ΔE is cell potential.

As explained above, Gaussian elimination writes a given m × n matrix A uniquely as a product of an invertible m × m matrix S and a row-echelon matrix T. Here, S is the product of the matrices corresponding to the row operations performed.

# 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 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, 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 Z is atomic number and n is a number which varies between 4 and 5.

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 d is the spacing between diffracting planes, is the incident angle, n is any integer, and λ is the wavelength of the beam.

Here are the concrete instances of these equations for n = 2 and n = 3:

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, on the hottest day, it is cool beneath the stone and fresh from the water flowing in the sluices at the bottom of the vaults.

Here in these little rooms -- or stages arched open to the sky and river -- they choose a few lines out of the hundreds they may know and sing them according to one of the modes into which Persian music is divided.

Here, on a desk, is a stack of pamphlets representing the efforts of some of the best men of the day to penetrate these questions.

Here, if anywhere, it is not wholly incontrovertible.

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 an important caveat is in order.

Here, then, is what Swift would have called a modest proposal by way of a beginning.

But this we know: Here is a great life that in every area of American politics gives the American people occasion for pride and that has invested the democratic process with the most decent qualities of honor, decency, and self-respect.

Here is a word of advice when you go shopping for your pansy seeds.

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 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 is an original kedgeree recipe from the Family Club's kitchen:

Here is the promise of a vacation trip they can afford.

Here is where things stand today:

Here the Af distance is 2.44 Aj.

Here the pulmonary vein, as in type 2,, is noted to draw away from the bronchus, and to follow a more direct, independent course to the hilum ( figs. 23, 24 ).

Here the number of trials is a random variable, not a fixed number.

Here there is a specific preventive component which applies in a more generalized sense to any casework situation.

( Here an entry is a form plus the information that pertains to it.

Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

Here is the best short explanation of the origins of the Cold War that has been written.

Here the coefficient A is an approximation of the short-wavelength ( e. g., ultraviolet ) absorption contributions to the refractive index at longer wavelengths.

Here, the effect is caused by free electrons and can be characterized as a difference in the refractive index seen by the two circularly polarized propagation modes.

Here we denote with the Bernoulli number of the second kind ( only because the historical reason of formation of this article ) which differ from the first kind only for the index 1.

Here is a link to their website: http :// www. twinoakspark. com / index. html

This pre-occupation in ordering his oeuvre is reflected in an index to MS A entitled " Vesci l ' ordenance que G. de Machau wet qu ' il ait en son livre " (" Here is the order that G. de Machaut wants his book to have ").

Here is a simple example of index register use in assembly language pseudo-code that sums a 100 entry array of 4-byte words:

Here, both contain N-particle state-kets completely symmetric in the single-particle state index.

Here, both contain N-particle state-kets completely anti-symmetric in the single-particle state index in accordance with Pauli exclusion principle.

Here, is a shorthand notation to mean the index runs over either the left or right Weyl spinors.

Here the Hoover index and the Theil are equal at a value of around 0. 46.

* For low inequalities the Theil index is smaller than the Hoover index. Here, on the path to reaching equilibrium, a planned and optimized reallocation of resources would contribute more to the dynamics of redistribution than stochastic redistribution.

In mathematics, an arithmetic group ( arithmetic subgroup ) in a linear algebraic group G defined over a number field K is a subgroup Γ of G ( K ) that is commensurable with G ( O ), where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them.

Here χ < sup >′</ sup >( G ) is the chromatic index of G ; and K < sub > n, n </ sub >, the complete bipartite graph with equal partite sets.

Here P serves as a price index, and Q serves as a quantity index of real value.

Here, a index file points to a directory of loose files somewhere else on the system.

Here, d is the exterior derivative of the a < sup > th </ sup > component of x, which is a scalar field ( so this isn't a pure abstract index notation ).

where I < sub > ad </ sub > is the Dynkin index of the adjoint representation of g. Here

Here is a reformulation for the Laspeyres index:

Here are the entries in the index that warrant two lines of page references or more :"