real, dimension (:), allocatable :: points

real :: average_points = 0., positive_average = 0., negative_average = 0.

:: See computer insecurity for an example of the failure of this approach in the real world.

:: When, therefore, this court adjudges, as it does now adjudge, that Congress cannot impose a duty or tax upon personal property, or upon income arising either from rents of real estate or from personal property, including invested personal property, bonds, stocks, and investments of all kinds, except by apportioning the sum to be so raised among the States according to population, it practically decides that, without an amendment of the Constitution — two-thirds of both Houses of Congress and three-fourths of the States concurring — such property and incomes can never be made to contribute to the support of the national government.

:: For any open neighborhood N of A, there is a positive constant T such that f ( t, b ) ∈ N for all real t > T.

:: " My hand feels touched as well as it touches ; real means this, and nothing more "

:: If any person liable to pay any tax neglects or refuses to pay the same after demand, the amount ( including any interest, additional amount, addition to tax, or assessable penalty, together with any costs that may accrue in addition thereto ) shall be a lien in favor of the United States upon all property and rights to property, whether real or personal, belong to such person.

:: Due in part to the sensational death of Reg Calvert and lurid tales depicting real swashbuckling piracy, the British government were finally able to bring in legislation to make offshore broadcasting a part of British criminal law in the United Kingdom.

:: Hot afternoons are real ; afternoons are ; places, things, thoughts, feelings are ; poetry is ;

real :: AP (- kl: ku, n )!

:: One of Dorai's best students, he is now an up-and-coming martial arts movie star whose insistence on " making the fight real " rapidly becomes detrimental to production, due mainly to damaged props and public property as well as injuries to the stunt doubles.

:: Then we'll all live together with a love that is real.

:: so anything real includes it all.

:: Wife: Umm ul-Banin — which means mother of many sons her real name Fatima bint Hizam al-Qilabiyya.

:: The balebast cook promised me a real gedila

functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer N such that for all natural numbers m, n > N

But, even though I disagree with him, his simulation is pretty good, so I ’ m willing to credit him with real thought.

m x + b, for real numbers m and b, and the slope m is given by

If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral

Given m real values t < sub > i </ sub >, called knots, with

It is mostly flat with no real mountains, and the state's highest natural point is Jerimoth Hill, 812 feet ( 247 m ) above sea level.

The government is opening up 5. 5 million ft < sup > 2 </ sup > ( 511, 000 m < sup > 2 </ sup >) of real estate for business.

It was also used by Robert Hooke and Voltaire, the latter of whom remarked: " L ' univers m ' embarrasse, et je ne puis songer Que cette horloge existe, et n ' ait point d ' horloger "; " I'm puzzled by the world ; I cannot dream The timepiece real, its maker but a dream ".

Moreover, in the worst case log ( n ) will approach m. Also, the simple operations tries use during lookup, such as array indexing using a character, are fast on real machines.

Because the total energy must be real, the numerator must also be imaginary: i. e., the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.

< li > If M = ( m < sub > ij </ sub >) ≥ 0 then the diagonal entries m < sub > ii </ sub > are real and non-negative.

where σ is a 3-vector composed of the Pauli matrices ( used here as generators for the Lie group SL ( 2, C )) and n and m are real 3-vectors on the Poincaré sphere corresponding to one of the propagation modes of the medium.

The perceived problems with the portrayal of Lawrence begin with the differences in his physical appearance: the 6-foot 2-inch ( 1. 87 m ) Peter O ' Toole was almost nine inches ( 23 cm ) taller than the real Lawrence.

" " With every particle of matter with mass m and velocity v a real wave must be ' associated '", related to the momentum by the equation:

If f ( x ) is the equation for a straight line, then there are two real numbers m and b such that.

) The singular value decomposition of X is X = WΣV < sup > T </ sup >, where the m × m matrix W is the matrix of eigenvectors of the covariance matrix XX < sup > T </ sup >, the matrix Σ is an m × n rectangular diagonal matrix with nonnegative real numbers on the diagonal, and the n × n matrix V is the matrix of eigenvectors of X < sup > T </ sup > X.

Formally, the singular value decomposition of an m × n real or complex matrix M is a factorization of the form

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

A real number is called computable if there is an algorithm which, given n, returns the first n digits of the number.

In the same way one defines a Cartesian space of any dimension n, whose points can be identified with the tuples ( lists ) of n real numbers, that is, with.

The space R of real numbers and the space C of complex numbers ( with the metric given by the absolute value ) are complete, and so is Euclidean space R < sup > n </ sup >, with the usual distance metric.

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Using the diagonal argument, it is possible to define a real number x, which is not equal to G ( n ) for any n. This means that there is a language L ' that defines x, which is undefinable in L.

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

R < sup > n </ sup > is the prototypical example of a real n-dimensional vector space.

In fact, every real n-dimensional vector space V is isomorphic to R < sup > n </ sup >.

The Euclidean topology turns out to be equivalent to the product topology on R < sup > n </ sup > considered as a product of n copies of the real line R ( with its standard topology ).

The harmonic mean H of the positive real numbers x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > is defined to be the reciprocal of the arithmetic mean of the reciprocals of x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub >:

Let A be the arithmetic mean and H be the harmonic mean of n positive real numbers.

That not everybody considered Jan and Dean's output to be " real " rock ' n roll is illustrated by disc jockey Steve Propes ' calling his early-80s Sunday morning program on KLON Long Beach We Don't Play No Jan And Dean.