When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer.

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.

When α is an integer, moreover, as was similarly the case for the functions of the first kind, the following relationship is valid:

When α is an integer, the Bessel functions J are entire functions of x.

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 discussing what complexity classes the integer factorization problem falls into, it's necessary to distinguish two slightly different versions of the problem:

This set, consisting of the integers congruent to a modulo n, is called the congruence class or residue class or simply residue of the integer a, modulo n. When the modulus n is known from the context, that residue may also be denoted.

When the function's argument is 0 ( zero ) it will return the integer 1 ( one ).

When m is chosen so that ( a + bm )/ k is an integer, so are the other two numbers in the triple.

When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency ; these are called harmonics.

# When the balanced equation for a reaction is multiplied by an integer, the corresponding value of ΔH must be multiplied by that integer as well.

When originally developed, for the Intel i860, the use of integer math made sense ( both 2D and 3D calculations required it ), but as graphics cards that did much of this became common, integer SIMD in the CPU became somewhat redundant for graphical applications.

The derivation of de Moivre's formula above involves a complex number to the power n. When the power is not an integer, the result is multiple-valued, for example, when n = ½ then:

Exponentiation is a mathematical operation, written as b < sup > n </ sup >, involving two numbers, the base b and the exponent ( or index or power ) n. When n is a positive integer, exponentiation corresponds to repeated multiplication ; in other words, a product of n factors, each of which is equal to b ( the product itself can also be called power ):

When n is an integer, the solution P < sub > n </ sub >( x ) that is regular at x = 1 is also regular at x = − 1, and the series for this solution terminates ( i. e. is a polynomial ).

When,, denote integer numbers, it can be shown that.

When is a non-negative integer, then gives the number of

When spoken about graph labeling with unique labels, commonly taken from the integer range 1 ,..., n, where n is the number of the vertices of the graph, two labeled graphs are said to be isomorphic if the corresponding underlying unlabeled graphs are isomorphic.

When we want to write functions to make an abstract data type, we wish to write functions to interface with the data type, and thus we want to extract some data from the data type, for example, just the string or just the integer part of.

When a string is bowed or tone in a wind instrument initiated by vibrating reed or lips, a phenomenon called mode-locking counteracts the natural inharmonicity of the string or air column and causes the overtones to lock precisely onto integer multiples of the fundamental pitch, even though these are slightly different than the natural resonance points of the instrument.

When the quotient is not an integer and the division process is extended beyond the decimal point, one of two things can happen.

When a man proves a positive integer to exist, he should show how to find it.

When the overtones are integer multiples ( e. g., 2 ×, 3 × ... 6 × ... ) of the fundamental frequency ( called harmonics ), then the oscillation is periodic, i. e., it vibrates in exactly the same way over and over again.

When it comes to this, I shall prefer emigrating to some country where they make no pretence of loving liberty -- to Russia, for instance, where despotism can be taken pure, without the base alloy of hypocrisy '' ( His emphasis )

When words can be used in a more fresh and primitive way so that they strike with the force of sights and sounds, when tones of sound and colors of paint and the carven shape all strike the sensibilities with an undeniable force of data in and of themselves, compelling the observer into an attitude of attention, all this imitates the way experience itself in its deepest character strikes upon the door of consciousness and clamors for entrance.

When the historian encounters a situation in which he can perceive no visible cause and effect sequence, he should be alert to intuition and unconscious instinct as possible guides.

When she agrees, you can rest assured her position will remain unchanged.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When you start the outdoor performance, you can stay outdoors without a dozen running trips into the kitchen.

When they can take ten seconds to accomplish the descent, they will have the strength to chin-up.

When some thirteen records of newly and recently born individuals are collated, little or no correlation between length and distribution can be detected.

When informed that there were some persons who did not have their arm go up, she commented, `` I don't see how they can prevent it ''.

When the policy has been chosen, the state of the product can be obtained from the state of the feed by repeated application of the transformation ( 1 ) ; ;

When the platform is aligned, the reflected image of the crossed hairs can be seen exactly superimposed upon the original crossed hairs.

`` When the roles of husband and wife are reversed, so that the wife becomes leader and the husband follower '', Dr. Linden says, `` the effects on their whole relationship, sexual and otherwise, can be disastrous ''.

`` When and if it can do so without jeopardizing constitutional and statutory tax-exemption privileges essential to the maintenance of its educational program and facilities, Emory University will consider applications of persons desiring to study or work at the University without regard to race, color or creed, continuing university policy that all applications shall be considered on the basis of intellectual and moral standards and other criteria designed to assure the orderly and effective conduct of the university and the fulfillment of its mission as an institution of Christian higher education ''.

When he attended the Christian Anti-Communist Crusade school here about six months ago, Jim became convinced that an individual can do something constructive in the ideological battle and set out to do it.

In 2009, the American Anthropological Association's Commission on the Engagement of Anthropology with the US Security and Intelligence Communities released its final report concluding, in part, that, " When ethnographic investigation is determined by military missions, not subject to external review, where data collection occurs in the context of war, integrated into the goals of counterinsurgency, and in a potentially coercive environment – all characteristic factors of the HTS concept and its application – it can no longer be considered a legitimate professional exercise of anthropology.

When used in the broader sense, the term can include many different groups.

When the alert is triggered, a message is sent to a caregiver or contact center who can respond appropriately.

When the third car ’ s engine has been mounted, it then can be moved to the hood station ; meanwhile, subsequent cars ( if any ) can be moved to the engine installation station.

When a molten metal is mixed with another substance, there are two mechanisms that can cause an alloy to form, called atom exchange and the interstitial mechanism.

When used with a grammatical qualifier, the adjective American can mean " of or relating to the Americas ", as in Latin American or Indigenous American.

When partially heated, amethyst can result in ametrine.

When used appropriately, opioids and similar narcotic analgesics are otherwise safe and effective, however risks such as addiction and the body becoming used to the drug ( tolerance ) can occur.

When observers or cells are not authorised they can still request fire.

When the price of a stock on the NYSE and its corresponding futures contract on OCX are out of sync, one can buy the less expensive one and sell it to the more expensive market.