The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.

We have just observed that we can write Af where D is diagonalizable and N is nilpotent, and where D and N not only commute but are polynomials in T.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Each performance of an n-trial binomial experiment results in some whole number from 0 through N as the value of the random variable X, where Af.

or under ' Four Stems ', I set off by asterisks cases where the combined N of stems Af was Af.

1 / N, where N is the scale or magnification of the image.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

The route has to be changed, which will require it to go through Rock Ridge, a frontier town where everyone has the last name of " Johnson " ( including a " Howard Johnson ", a " Dr. Samuel Johnson ", a " Van Johnson " and an " Olson N. Johnson ").

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

Under the administration of Félix Éboué, France's first black colonial governor, a military column, commanded by Colonel Philippe Leclerc de Hauteclocque, and including two battalions of Sara troops, moved north from N ' Djamena ( then Fort Lamy ) to engage Axis forces in Libya, where, in partnership with the British Army's Long Range Desert Group, they captured Kufra.

( V, T, P, S ), where N / V is the Non-terminal Variable, and Σ / T is the Terminal ) is context-sensitive if all rules in P are of the form

where A ∈ N ( i. e., A is a single nonterminal ), α, β ∈ ( N U Σ )* ( i. e., α and β are strings of nonterminals and terminals ) and γ ∈ ( N U Σ )< sup >+</ sup > ( i. e., γ is a nonempty string of nonterminals and terminals ).

The highest point is just east of where Connecticut, Massachusetts, and New York meet ( 42 ° 3 ' N ; 73 ° 29 ' W ), on the southern slope of Mount Frissell, whose peak lies nearby in Massachusetts.

where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.

But California is where we're goin ''.

He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.

Now I wish to enter the American market, where the competition is very strong.

from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.

The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.

Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.

Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.

A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.

In a society where everything is for sale, Marlowe is the only man who cannot be bought.

This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.

As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.

`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.

She was exposing herself to temptation which it is best to avoid where it can consistently be done.

Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.

but it is perennially restructured in situations where anchors are dragged or lost.

`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.

Finally we may note that the idea appears in educational theory where its influence is at present widespread.

All numbers which can be obtained from the integers using a finite number of integer additions, subtractions, multiplications, divisions, and taking nth roots ( where n is a positive integer ) are algebraic.

Within a shell where n is some integer n < sub > 0 </ sub >, ranges across all ( integer ) values satisfying the relation.

Within a subshell where is some integer, ranges thus:.

The AA compiler generated range-checking for array accesses, and allowed an array to have dimensions that were determined at run-time ( i. e. you could declare an array as < code >< u > integer </ u > < u > array </ u > Thing ( i: j )</ code >, where and were calculated values ).

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.

where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

where each is a specific positive integer known as binomial coefficient.

Many later CPU designs use similar mixed bit width, especially when the processor is meant for general-purpose usage where a reasonable balance of integer and floating point capability is required.

For example, intervals, where takes all integer values in Z, cover R but there is no finite subcover.

: Theorem ( A. Korselt 1899 ): A positive composite integer is a Carmichael number if and only if is square-free, and for all prime divisors of, it is true that ( where means that divides ).

: where l is a non-negative integer and is the reduced Planck constant.

Multiplying by a linear phase for some integer m corresponds to a circular shift of the output: is replaced by, where the subscript is interpreted modulo N ( i. e., periodically ).

Today Diophantine analysis is the area of study where integer ( whole number ) solutions are sought for equations, and Diophantine equations are polynomial equations with integer coefficients to which only integer solutions are sought.

where denotes the largest integer that

where denotes the largest integer that is not greater than x.

The set of all integral linear combinations of a and b is actually the same as the set of all multiples of g ( mg, where m is an integer ).

where s here means the integer value of the entire significand, ignoring any implied decimal point, and p is the precision — the number of digits in the significand.

Various reasons have been suggested for the resistance to the Celsius system in the U. S., including the larger size of each degree Celsius ( resulting in the need for decimals where integer Fahrenheit degrees were adequate for much non-technical work ), the lower zero point in the Fahrenheit system ( which reduces the number of negative signs when measurements such as weather data were averaged ), and the more intuitive alignment of its 0-100 scale to the ordinary range of outdoor temperatures seen in most of the U. S. ( e. g., 0 ° F