A structure is deemed to satisfy the ultimate limit state criteria if all factored bending, shear and tensile or compressive stresses are below the factored resistances calculated for the section under consideration.

There is an analogous result, also referred to as the Weierstrass preparation theorem, for power series rings over the ring of integers in a p-adic field ; namely, a power series f ( z ) can always be uniquely factored as π < sup > n </ sup >· u ( z )· p ( z ), where u ( z ) is a unit in the ring of power series, p ( z ) is a distinguished polynomial ( monic, with the coefficients of the non-leading term each in the maximal ideal ), and π is a fixed uniformizer.

At this stage in the algorithm, it is required that terms with zero-valued coefficients are dropped, so that only binary coefficients equal to one are counted, thus the problem of multiplication or division by zero is not an issue, despite this implication in the factored equation:

When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known ; an effort concluded in 2009 by several researchers factored a 232-digit number ( RSA-768 ), utilizing hundreds of machines over a span of 2 years.

When they are both large, for instance more than 2000 bits long, randomly chosen, and about the same size ( but not too close, e. g. to avoid efficient factorization by Fermat's factorization method ), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical ; that is, as the number of digits of the primes being factored increases, the number of operations required to perform the factorization on any computer increases drastically.

There are fast algorithms for computing the GCD that do not require the numbers to be factored, such as the Euclidean algorithm.

The saleability of the item and the amount that the customer wants for it are also factored into the pawnbroker's assessment ; if a customer offers a very salable item at a low price, the pawnbroker may accept it even if it is unlikely that the customer will return, because the pawnshop can turn around a quick profit on the item.

Daley inherited a city with revenue-generating assets, manageable debt and pension funds so flush with cash that he was able to use some of the money to provide a one-time property tax break, but he left behind a city literally on the brink of bankruptcy, with a structural deficit that Mayor-elect Rahm Emanuel said could approach $ 1. 2 billion when unfunded pension funds are factored in.

For example, stronger strings can discharge through weaker strings until voltage imbalances are equalized, and this must be factored into the individual inter-cell measurements within each string.

For instance we might follow the statement " an integer can be factored as a product of prime numbers " with " the product is unique up to ordering ", meaning the order of the operands is irrelevant, integers and their prime factorization are ; or we might say " the solution to an indefinite integral is, up to addition by a constant ", meaning that the constant is not the focus here, the solution is, and that the addition of a constant is to be regarded as a background, of secondary focus.

Altered life situations including death of a partner, relationship breakdown, children starting school or leaving home, death of a child, re-partnering and re-marriage, increased wealth ( which previously factored against having more children ), mean that the psychological associations and effects of vasectomy are not only those which immediately follow the vasectomy, but may be ongoing throughout a person's life history.

Battling Jim, who died during Spanish influenza epidemic of 1918, ended with a career record of 30 wins against 31 losses and six draws when his newspaper decisions are factored in.

But the lower rows of zeros in R are superfluous in the product, which is thus already in lower-triangular upper-triangular factored form, as in Gaussian elimination ( Cholesky decomposition ).

When the same roots occur multiple times, the terms in this formula corresponding to the second and later occurrences of the same root are multiplied by increasing powers of n. For instance, if the characteristic polynomial can be factored as ( x − r )< sup > 3 </ sup >, with the same root r occurring three times, then the solution would take the form

By the fundamental theorem of algebra, this can be factored into mn linear factors so there are mn solutions to the system of equations.

When " Role-Informative " and " Role-Directive " ( corresponding to orientation to people or to task ), and finally E / I are factored in, you attain the 16 types.

* is called the factored form, where and are the roots of the quadratic equation, it is used in logistic map

In mathematics, a polynomial is said to be irreducible if it cannot be factored into the product of two or more non-trivial polynomials whose coefficients are of a specified type.

Therefore, a more accurate fix can be made if the time of year and approximate latitude are factored in.

But a component of the illusion remains even when all optical and retinal components are factored out.

In the development of the RBRVS, the physician work ( including the physician's time, mental effort, technical skill, judgment, stress and an amortization of the physician's education ), the practice expense and the malpractice expense are factored into the result.

Reduction Factors are applied to determine the various factored resistances of the section.

The polynomials can be factored into linear factors of the form ( a < sub > j </ sub > + n ) and ( b < sub > k </ sub > + n ) respectively, where the a < sub > j </ sub > and b < sub > k </ sub > are complex numbers.

Now suppose that we have found the roots of g ( x ), i. e. we have factored it.

A complex or large database migration may be a complicated and costly ( one-time ) project by itself, which should be factored into the decision to migrate.

The GCD of two numbers a and b is the product of the prime factors shared by the two numbers, where a same prime factor can be used multiple times, but only as long as the product of these factors divides both a and b. For example, since 1386 can be factored into 2 × 3 × 3 × 7 × 11, and 3213 can be factored into 3 × 3 × 3 × 7 × 17, the greatest common divisor of 1386 and 3213 equals 63 = 3 × 3 × 7, the product of their shared prime factors.

The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L < sup > 2 </ sup >, where L is the number of bits in the number to be factored ; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 10 < sup > 4 </ sup > qubits without error correction.

One writer in the Huffington Post looked at FBI statistics on robbery, fraud, and crime and concluded that Wall Street was the " most dangerous neighborhood in the United States " if one factored in the $ 50 billion fraud perpetrated by Bernie Madoff.

A cone to the empty diagram is essentially just an object of C. The limit of F is any object that is uniquely factored through by every other object.

In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits.

Now is an integer, and so can be factored as a product of prime numbers, by the fundamental theorem of arithmetic.

Quadratic polynomials can sometimes be factored into two binomials with simple integer coefficients by use of Vieta's formulas, without the need to use the quadratic formula.

According to Carbide, " in designing the plant's safety systems, a chemical reaction of this magnitude was not factored in " because " the tank's gas storage system was designed to automatically prevent such a large amount of water from being inadvertently introduced into the system " and " process safety systems — in place and operational — would have prevented water from entering the tank by accident ".

, it is still the best algorithm for divisors not greatly exceeding 20 to 25 digits ( 64 to 83 bits or so ), as its running time is dominated by the size of the smallest factor p rather than by the size of the number n to be factored.

" This became known as Jevons ' Number and was factored by Derrick Norman Lehmer in 1903 and later on a pocket calculator by Solomon W. Golomb.

The first episode was watched by approximately 1 million viewers, though the figure rose by 25 % when BBC iPlayer viewings were factored in and, uncharacteristically, viewing figures rose over the series.

While the latter can be priced easily by taking into account the raw material costs, in case of services attendant costs-such as labor and overhead costs-also need to be factored in.

It was represented by a macroscopic factored component ( a macroscopic eigenvalue ) in the first-order reduced density matrix.

At the same time they should not be too close together, or else the number can be quickly factored by Fermat's factorization method.

It is stated under factored loads and factored resistances.

While working on the design Bandel also factored in the loads upon the 630 foot arch caused by the wind and worked out that if he added more weight to the first 300 feet of the arch and placed 25, 980 tons of concrete in the arch's foundation the center of gravity would be lowered to a stable location.