The expected value of F is ( where n is the treatment sample size )

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.

where X is the energy level corresponding to the principal quantum number n, type is a lower-case letter denoting the shape or subshell of the orbital and it corresponds to the angular quantum number l, and y is the number of electrons in that orbital.

The quantum number n first appeared in the Bohr model where it determines the radius of each circular electron orbit.

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

where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.

where < big ></ big > is the number of degrees of freedom divided by two, R is the universal gas constant and n is the number of moles in the system ( a constant ).

Lookup, insertion, and deletion all take O ( log n ) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation.

In Analytical Geometry a section of a line can be given by the formula where ( c, d )&( e, f ) are the endpoints of the line & m: n is the ratio of division

where n < sub > d </ sub >, n < sub > F </ sub > and n < sub > C </ sub > are the refractive indices of the material at the wavelengths of the Fraunhofer d -, F-and C-spectral lines ( 587. 6 nm, 486. 1 nm and 656. 3 nm respectively ).

where m and n are nonnegative integers with, is the azimuthal angle in radians, and is the normalized radial distance.

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.

Subsequently, the accelerative force on any given ion is controlled by the electrostatic equation, where n is the ionisation state of the ion, and e is the fundamental electric charge.

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.

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.

He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.

Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.

The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.

Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >

functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

It lacks the NH < sub > 2 </ sub > group because of the cyclization of the side-chain and is known as an imino acid ; it falls under the category of special structured amino acids .</ ref > where R is an organic substituent known as a " side-chain "); often the term " amino acid " is used to refer specifically to these.

½ ( pKa < sub > 1 </ sub > + pKa < sub > R </ sub >), where pKa < sub > R </ sub > is the side-chain pKa.

## < tt > SubBytes </ tt >— a non-linear substitution step where each byte is replaced with another according to a lookup table.

## < tt > ShiftRows </ tt >— a transposition step where each row of the state is shifted cyclically a certain number of steps.

The < tt > MixColumns </ tt > function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes.

It was built on a raised plateau overlooking the east bank of the river Strymon where it emerged from Lake Cercinitis, about 3 m. from the Aegean Sea.

), where heights of 1800 m to 2400 m ( 6000 to 8000 ft ) are reached.

where m is the slope of the line.

where R < sub > i </ sub > is the position vector of particle i from the reference point, m < sub > i </ sub > is its mass, and V < sub > i </ sub > is its velocity.

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

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

where α > − 1, δ < sub > m, n </ sub > is the Kronecker delta, and u < sub > α, m </ sub > is the m-th zero of J < sub > α </ sub >( x ).

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.

For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.

There are two forces ; one is the force of gravity vertically downward through the center of mass of the ball mg where m is the mass of the ball and g is the gravitational acceleration ; the second is the upward normal force exerted by the road perpendicular to the road surface ma < sub > n </ sub >.

where m is the mass of the molecule and v is its velocity.

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.

Cohen ( 1992 ) suggests effect sizes for various indexes, including ƒ ( where 0. 1 is a small effect, 0. 25 is a medium effect and 0. 4 is a large effect ).

The standard structure is where is the set of natural numbers, is the successor function and is naturally interpreted as the number 0.

where E < sub > 0 </ sub > is an infinite negative constant.

In an adiabatic irreversible process, dQ = 0 is not equal to TdS ( TdS > 0 ) where Q is thermal energy, T is temperature, and S is entropy.

The value of in the color code ranges from 0. 0 to 1. 0, where 0. 0 represents a fully transparent color, and 1. 0 represents a fully opaque color.

During his rookie season, he played in two games where he amassed a record of 5 passing attempts with 0 receptions and 2 interceptions.

This is in contrast to an insertion where a rotation resulting in a balance factor of 0 indicated that the subtree's height has remained unchanged.

The terms of the Artistic License 1. 0 were at issue in a 2007 federal district court decision in the US which was criticized by some for suggesting that FOSS-like licenses could only be enforced through contract law rather than through copyright law, in contexts where contract damages would be difficult to establish.

More technically, the law is concerned with the speedup achievable from an improvement to a computation that affects a proportion P of that computation where the improvement has a speedup of S. ( For example, if an improvement can speed up 30 % of the computation, P will be 0. 3 ; if the improvement makes the portion affected twice as fast, S will be 2.

where F ' and C ' are the blue and red cadmium lines at 480. 0 nm and 643. 8 nm, respectively.

This explains the dipole moment of 0. 8 D for this compound ( cis-isomer 0. 4 D ) where a value of zero is expected.