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 refractive index of the medium in which the measurement is made ; and f is the measured frequency of the source.

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 no attempt is made, first to determine out-of-pocket or marginal costs and then to superimpose on these costs `` reasonably distributed '' residues of total costs.

Here, an apportionment, say, of $5,000,000 of the total costs to residential service as a class would include an allowance of perhaps 6 per cent as the cost of whatever capital is deemed to have been devoted to the service of the residential consumers.

Here he produced a little over a third of his total published work, and lived with his wife, daughters, and two grandchildren until dying of natural causes in 1967.

The Beatles performed for fifty-two BBC Radio programmes, beginning with an appearance on the series Teenager's Turn — Here We Go, recorded on 7 March 1962, and ending with the special The Beatles Invite You to Take a Ticket to Ride, recorded on 26 May 1965 ; in total, 275 performances of 88 different songs were broadcast.

Here, dq < sub > k </ sub >/ T represents a very small exchange of heat energy at temperature T. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.

Here, the explanation of the effect requires that the total energy of all of the virtual particles in a vacuum can be added together.

Here is a comparison of two total solar eclipses one exeligmos apart:

When we specify the internal energy to be U, what we really mean is that the total energy of the gas lies somewhere in an interval of length around U. Here is taken to be very small, it turns out that the entropy doesn't depend strongly on the choice of for large N. This means that the above " area " must be extended to a shell of a thickness equal to an uncertainty in momentum, so the entropy is given by:

Here, N is the total number of particles and n is the number density of particles-the number of particles per unit volume, or the density divided by the mass of individual particles.

Here the ( pc )< sup > 2 </ sup > term represents the square of the Euclidean norm ( total vector length ) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered.

Here the unpowered kite is tethered to a pilot who arranges to have a harness to which is attached a thrusting prime moving engine or motor ; the total system is a

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, the widths of the individual metal structures in between the slots lie within the area of a bamboo structure, while the resulting total width of all the metal structures meets power requirements.

Here χ ″( G ) is the total chromatic number ; Δ ( G ), maximum degree ; and δ ( G ), minimum degree.

Here, it is seven lanes total with three travel lanes in each direction and two reversible high-occupancy vehicle lanes in the center.

Here a new set of six X-10 vehicles would complete the testing of the N-6 inertial navigation system out to supersonic speeds, reach 49, 000 feet altitude, a total flight distance of and a peak speed of Mach 2. 05.

Here, the regulation of local production of wheat was rationally related to Congress's goal: to stabilize prices by limiting the total supply of wheat produced and consumed.

Here, the tri-corner intersections show that the phase wraps around three times, for a total of, indicating that the zeros are of the third power:.

Here, J is the total electronic angular momentum, L is the orbital angular momentum, and S is the spin angular momentum.

Very popular in Germany, where the band holds the record of most total weeks ( 25 ) at number one on the German singles chart over the past 30 years — scoring such hits as " Old Pop in an Oak ", " The Spirit of the Hawk ” and " Wish You Were Here ".

Here p is a vector of prices, and X is a vector of quantities demanded so that the sum of all p < sub > i </ sub > x < sub > i </ sub >, is the total expense on goods X.

Here he was able to finish 5th in the feature race which resulted in Pakistan scoring a total of 10 points.

As Charles Schultze, Chairman of the Council of Economic Advisors and a member of the Committee, said, “ Here is a project that is 95 % complete, and if one takes the cost of finishing it against the total project benefits, and does it properly, it doesn ’ t pay, which says something about the original design .”

Here a cadet has to undergo training for a total of six terms before he passes out from NDA.