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

When a ligand activates the G protein-coupled receptor, it induces a conformational change in the receptor that allows the receptor to function as a guanine nucleotide exchange factor ( GEF ) that exchanges GDP for GTP on the G < sub > α </ sub > subunit.

When perturbation theory is applied to quantum electrodynamics, the resulting perturbative expansions for physical results are expressed as sets of power series in α.

When α is very small ( α < π / 6 ), the following approximations can be done:

When viewed through a telescope, this system is resolved into two components designated α < sup > 1 </ sup > and α < sup > 2 </ sup >.

When P is chosen as the centroid G, then α = − 1 / 3.

When P is chosen as the circumcenter O, then α = − 1 and the generated orthocentric system is congruent to the original system as well as being a reflection of it about the nine-point center.

When both parameters are less than one ( α < 1 and β < 1 ), this is the anti-mode: the lowest point of the probability density curve.

When α < sub > TC </ sub >( μ ) becomes strong at scale Λ < sub > TC </ sub > ≅ F < sub > EW </ sub >, the fermionic condensate forms.

When metarhodopsin activates transducin, the GDP bound to the α subunit ( T < sub > α </ sub >) is exchanged for GTP from the cytoplasm.

When I is a principal ideal αO < sub > K </ sub > then N ( I ) is equal to the absolute value of the norm to Q of α, for α an algebraic integer.

When the method of least squares is used to estimate α < sub > 0 </ sub > and α < sub > 1 </ sub >, then the residuals, unlike the errors, cannot be independent since they satisfy the two constraints

When the vector spaces involved are over the real numbers, a slightly more general form of homogeneity is often used, requiring only that () hold for all α > 0.

When prodynorphin is cleaved during processing by proprotein convertase 2 ( PC2 ), multiple active peptides are released: dynorphin A, dynorphin B, and α / β-neo-endorphin.

When the measure μ is associated to a mass distribution on a sufficiently smooth hypersurface S ( a Lyapunov surface of Hölder class C < sup > 1, α </ sup >) that divides R < sup > d </ sup > into two regions D < sub >+</ sub > and D < sub >−</ sub >, then the Newtonian potential of μ is referred to as a simple layer potential.

: When α = 1 / 2, the equation reduces to the Legendre equation, and the Gegenbauer polynomials reduce to the Legendre polynomials.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

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

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 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.