Plot of Bessel function of the second kind, Y < sub > α </ sub >( x ), for integer orders α = 0, 1, 2.

Y < sub > α </ sub >( x ) is necessary as the second linearly independent solution of the Bessel's equation when α is an integer.

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

; Assumes input format is 3 integers separated by a space with the first integer smaller than the second.

* Mainframes are measured in millions of instructions per second ( MIPS ) while assuming typical instructions are integer operations, but supercomputers are measured in floating point operations per second ( FLOPS ) and more recently by traversed edges per second or TEPS.

For example, is a polynomial, but is not, because its second term involves division by the variable x ( 4 / x ), and also because its third term contains an exponent that is not a non-negative integer ( 3 / 2 ).

Use the integer part, 2, as an approximation for the reciprocal, to get a second approximation of ;.

The integer 2 factors as as a Gaussian integer, the second factorisation ( in which i is a unit ) showing that 2 is divisible by the square of a Gaussian prime ; it is the unique prime number with this property.

This additional ionization is referred to as non-sequential ionization for two reasons: One, there is no order to how the second electron is removed, and, two, an atom or molecule with a + 2 charge can be created straight from an atom or molecule with a neutral charge, so the integer charges are not sequential.

In mathematics, a ratio is a relationship between two numbers of the same kind ( e. g., objects, persons, students, spoonfuls, units of whatever identical dimension ), usually expressed as " a to b " or a: b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second ( not necessarily an integer ).

Enhancements included a faster 60x system bus ( 66 MHz ), larger L1 caches ( 32 KB instruction and 32 KB data ), a second integer unit, an enhanced floating point unit, and higher core frequency.

Imposing this regularity in the solution Θ of the second equation at the boundary points of the domain is a Sturm – Liouville problem that forces the parameter λ to be of the form λ = ℓ ( ℓ + 1 ) for some non-negative integer with ℓ ≥ | m |; this is also explained below in terms of the orbital angular momentum.

The first concerns Artin L-functions for a linear representation of a Galois group ; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies.

( If a is a positive integer, the independent solution is given by the appropriate Bessel function of the second kind.

Analogously, the first Chern class classifies smooth complex line bundles on a space, and the group of line bundles is isomorphic to the second cohomology class with integer coefficients.

All Fibonacci integer sequences appear in shifted form as a row of the Wythoff array ; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row.

LBA is a particularly simple linear addressing scheme ; blocks are located by an integer index, with the first block being LBA 0, the second LBA 1, and so on.

* Indeterminate equations ( Kuttaka ), integer solutions ( first and second order ).

The quadratic sieve algorithm ( QS ) is an integer factorization algorithm and, in practice, the second fastest method known ( after the general number field sieve ).

Given two integer parameters P and Q, the Lucas sequences of the first kind U < sub > n </ sub >( P, Q ) and of the second kind V < sub > n </ sub >( P, Q ) are defined by the recurrence relations:

where and are the mode numbers of the first and second ring respectively and they must remain as positive integer numbers.

In a two-story house, one unit may be installed in the basement to serve the first floor, another in the attic to cool the second.

In practical terms, the ampere is a measure of the amount of electric charge passing a point in an electric circuit per unit time with 6. 241 × 10 < sup > 18 </ sup > electrons, or one coulomb per second constituting one ampere.

The SI unit of charge, the coulomb, " is the quantity of electricity carried in 1 second by a current of 1 ampere ".

As the speed of light in meters per second ( c < sub > 0 </ sub >) is fixed in the International System of Units, this measurement of the speed of light in AU / d ( c < sub > AU </ sub >) also determines the value of the astronomical unit in meters ( A ):

The second incarnation was a much smaller unit the width of two 5¼ " floppy drives stacked on top of each other, and the third incarnation looked like a flattened Apple with a built-in keyboard.

They have the only embossers with staking unit and with Staple and fold Unit which produces books at a speed of 650 braille characters per second and a finished book.

Even adding a second execution unit ( see below ) does not improve performance much ; rather than one pathway being hung up, now two pathways are hung up and the number of unused transistors is increased.

Although the candela is now defined in terms of the second ( an SI base unit ) and the watt ( a derived SI unit ), the candela remains a base unit of the SI system, by definition.

The SI derived unit for measuring the catalytic activity of a catalyst is the katal, which is moles per second.

The SI unit for measuring the rate of flow of electric charge is the ampere, which is charge flowing through some surface at the rate of one coulomb per second.

The centimetre – gram – second system ( abbreviated CGS or cgs ) is a variant of the metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time.

The two systems differ only in the scale of two out of the three base units ( centimetre versus metre and gram versus kilogram, respectively ), while the third unit ( second as the unit of time ) is the same in both systems.

All these proteins share a catalytic mechanism of di-metal-ion-mediated nucleotide transfer, whereby two acidic residues located at the end of the first strand and between the second and third strands of the RRM-like unit respectively, chelate two divalent cations.

The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second.

Following this, an astronomical conference held in Paris in 1950 recommended " that in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900. 0, that the time reckoned in this unit be designated ephemeris time ", and gave Clemence's formula ( see Definition of ephemeris time ( 1952 )) for translating mean solar time to ephemeris time.

There had been a good second or two during which my muffler had been blowing out, and now I was certain I'd seen her somewhere before.

Their skin was covered with a thin coating of sweat and dirt which had almost the consistency of a second skin.

As for progress, the `` backward South '' can boast of Baton Rouge, which increased its population between 1940 and 1950 by two hundred and sixty-two percent, to 126,000, the second largest growth of the period for all cities over 25,000.

Nothing testifies more clearly to that cleavage than the peculiar editorial page appearing in a July issue of Life Magazine, the issue which also carried the second announcement of the candidacy.

The second involves something deeper, but its characteristic form focuses on a shift in policy for the community, not in the truth on which the community rests.

There is a second feature of the influences of literature, good literature, on emotional life which may have some special value for our time.

Upon second thought we were forced to realize that we have very few reliable historical benchmarks against which we might compare the present situation, and that conclusions that present-day students are `` more '' or `` less '' religious could not be defended on the basis of our data.

And the second requirement for convincing people without their knowledge is artistic talent to prepare the words and pictures which persuade by using the principles which the scientists have discovered.

The House was his habitat and there he flourished, first as a young representative, then as a forceful committee chairman, and finally in the post for which he seemed intended from birth, Speaker of the House, and second most powerful man in Washington.

When he came to Baltimore, he was leaving a team which was supposed to win the National League pennant, and he was joining what seemed to be a second division American League club.

In the second and third chapters of Revelation the new version retains, however, the old phrase `` angel of the church '' which Biblical scholars have previously interpreted as meaning bishop.

The 15th Street deposit is not to be confused with the nearby famous Mayflower Hotel cypress swamp on 17th Street reported in The Washington Post, August 2, 1955, which was probably formed during the second interglacial period and is therefore much younger.

The second great dilemma has been the morality of nuclear testing, a dilemma which has suddenly become acute because of the present series of Soviet tests.

The video signal is amplified and then switched, in synchronism with the three ultraviolet light sources which are sequenced by the rotating mirror so that during one-twentieth of a second only one wavelength, corresponding to red, green, or blue, is seen.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

the second requires that there be a line through P which meets **zg in Af points.

In the second, the fixed elements are the lines which join the vertex, P, to the two intersections of **zg and the plane of the pencil which do not lie on the multiple secant.

Continuing with the case in which **zg is a Af curve on a quadric Q, we first observe that the second regulus of Q consists precisely of the lines which join the two free intersections of **zg and the planes through any one of the multiple secants.

These differences in turn result from the fact that my Yokuts vocabularies were built up of terms selected mainly to insure unambiguity of English meaning between illiterate informants and myself, within a compact and uniform territorial area, but that Hoijer's vocabulary is based on Swadesh's second glottochronological list which aims at eliminating all items which might be culturally or geographically determined.

But in the second subtype, which I take to be the one more frequently applied, only the operating expenses and not the `` cost of capital '' or `` fair return '' are apportioned directly among the various classes of service.

The second productive period, the decade from 1910 to 1920, can be related to three events: the completion of The Dynasts in 1909, which left Hardy free of pressure for the first time in forty years ; ;