where μ < sub > i </ sub > is the chemical potential per particle for an i-type particle, and N < sub > i </ sub > is the number of such particles.

where the index i denotes the ith species, c is the concentration ( mol / m < sup > 3 </ sub >), R is the universal gas constant ( J /( K mol )), T is the absolute temperature ( K ), and μ is the chemical potential ( J / mol ).

where μ < sub > 4 </ sub > is the fourth moment about the mean and σ is the standard deviation.

where μ is the location parameter, θ represents additional parameters, and is a function of the additional parameters.

where μ is the Möbius function and the sums extend over all positive divisors d of n. In effect, the original f ( n ) can be determined given g ( n ) by using the inversion formula.

The theorem follows because * is ( commutative and ) associative, and 1 * μ = i, where i is the identity function for the Dirichlet convolution, taking values i ( 1 )= 1, i ( n )= 0 for all n > 1.

If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )

where a sum over μ is performed according to the rules of Einstein notation.

The positive integer n is square-free if and only if μ ( n ) ≠ 0, where μ denotes the Möbius function.

The throughput can be analyzed mathematically by means of queueing theory, where the load in packets per time unit is denoted arrival rate λ, and the throughput in packets per time unit is denoted departure rate μ.

where μ < sub > α </ sub > and μ < sub > δ </ sub > are the components of proper motion in the R. A. and Declination, respectively, and δ is the Declination.

where the linear density μ is the mass per unit length of the string.

where μ < sub > i </ sub > is the chemical potential for the i-th component in the system.

where a is the semi-major axis, P is the orbital period, and μ is the geocentric gravitational constant, equal to approximately 398600. 4418 km < sup > 3 </ sup >/ s < sup > 2 </ sup >.

In this case the solutions are elliptically polarized electromagnetic waves with phase velocities ( where μ is the magnetic permeability ).

where μ = 255 ( 8 bits ) in the North American and Japanese standards.

where λ ' is the critical failure rate ( λ without the tick is the total failure rate ) and μ ' is the critical repair rate ( rate at which critical failures are repaired ).

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 >

These nodes are areas where the action potential is amplified using a high density of sodium ( Na < big >+</ big >) ions and is subsequently passed along the axon.

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

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

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.

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

where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

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

The Battle of Qarqar is mentioned in extra-biblical records, and was perhaps at Apamea where Shalmaneser III of Assyria fought a great confederation of princes from Cilicia, Northern Syria, Israel, Ammon, and the tribes of the Syrian desert ( 853 BC ), including Ahab ( A-ha-ab-bu < sup > mat </ sup >) ( Adad -' idri ).

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 ).

We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.

where p is a program in L < sub > 2 </ sub >.

In type 3, this general relationship is maintained peripherally but not centrally where the pulmonary vein follows a more independent path to the hilum as is the case throughout the lung in type 2.

The pictures of Figs. 3 and 4 show the cracking and peeling types of removal where the coating is detached by failure in a region at, or close to, the interface between coating and substrate.

This is particularly important for light, modern anchors designed to bury in the bottom, where ratios of 5 – 7 to 1 are common, whereas heavy anchors and moorings can use 3 to 1 or less.

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 is the star's luminosity distance in parsecs, wherein 1 parsec is approximately 3. 2616 light-years.

Arizona had postseason victories over the St. Louis Cardinals ( 3 – 2 in the NLDS ) and the Atlanta Braves ( 4 – 1 in the NLCS ) to advance to the World Series where, in the wake of the September 11 terrorist attacks in New York City, they beat the three-time reigning champions, the New York Yankees, 4 to 3, to become the youngest expansion franchise to win the World Series ( in just their fourth season of play ).

Strabo ( 7. 2. 1, 4 and 7. 3. 1 ) states that the Cimbri still live on the peninsula ( Jutland ) where they always did, even though some of them liked to wander.

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 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 ).

In Quebec City, municipal officials built a 3 metre ( 10 ft ) high wall around the portion of the city where the Summit of the Americas was being held, which only residents, delegates to the summit, and certain accredited journalists were allowed to pass through.

The large pillars called " Kose (' Mile ') Minar ", erected at intervals of two miles ( 3 km ) along the entire way between Agra and Ajmer mark the places where the royal pilgrims halted every day.

Paul, in an attempt to heal divisions in the Corinthian church, summarized Apollos ' role in his ministry in 1 Corinthians 3: 6, where he states " I planted, Apollos watered (.

gives the example of Groombridge 1830, where he estimates that the true position is displaced by approximately 3 arcminutes from the direction in which we observe it.

In this format, the sprite is referenced to one of 8 palettes, where each palette holds 3 assignable colors.

In general, this is the case where the Mach number in part or all of the flow exceeds 0. 3.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

At the point where the Arno leaves the Apennines, flow measurements can vary between 0. 56 m³ / s and 3, 540 m³ / s.

The first occurrence of the phrase blue law so far found is in the New-York Mercury of March 3, 1755, where the writer imagines a future newspaper praising the revival of " our Connecticut's old Blue Laws ".

* A double play where the second baseman fields, throws to the shortstop covering second base, who throws to the 1st baseman is recorded as a 4 – 6 – 3 double play.

The simplest type of carbohydrate is a monosaccharide, which among other properties contains carbon, hydrogen, and oxygen, mostly in a ratio of 1: 2: 1 ( generalized formula C < sub > n </ sub > H < sub > 2n </ sub > O < sub > n </ sub >, where n is at least 3 ).

If the maximum gain is 0 dB, the 3 dB gain is the range where the gain is more than-3dB, or the attenuation is less than + 3dB.

The convention for a nucleic acid sequence is to list the nucleotides as they occur from the 5 ' end to the 3 ' end of the polymer chain, where 5 ' and 3 ' refer to the numbering of carbons around the ribose ring which participate in forming the phosphate diester linkages of the chain.