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 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.

where μ < sub > 3 </ sub > is the third moment about the mean μ, σ is the standard deviation, and E is the expectation operator.

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 >.

When they have 4 to 6 leaves and are thrifty little plants, it's time to set them out where they are to remain.

It will be seen that where the scope is similar, the Athabascan ratios come out somewhat higher ( as indeed they ought to with a total ratio of 2.8 as against 3.5 or 4: 5 ) except for verbs, where alone the Athabascan ratio is lower.

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.

When the shouting ended, the bill passed, 114 to 4, sending it to the Senate, where a similar proposal is being sponsored by Sen. George Parkhouse of Dallas.

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 ).

Subsequently, Roosa and Mitchell were recycled to serve as members of the backup crew after returning from Apollo 14, while Pogue and Carr were re-assigned to the Skylab program where they later flew on Skylab 4.

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.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

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

After multiple revisions, the show opened on Broadway on April 4, 1964 at the Majestic Theatre, where it closed after 9 performances and 12 previews, unable to overcome the generally negative reviews it had received.

* 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.

Two hours later the Duke, accompanied by the Dutch field commander Field Marshal Overkirk, General Daniel Dopff, and the Allied staff, rode up to Cadogan where on the horizon to the westward he could discern the massed ranks of the French army deploying for battle along the four mile ( 6. 4 km ) front.

Only from Spain did Louis XIV receive any good news where Das Minas and Galway had been forced to retreat from Madrid towards Valencia, allowing Philip V to re-enter his capital on 4 October.

Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.

* The land between Egypt and Canaan of the first Exodus was a " great and terrible wilderness, an arid wasteland " ( Deut 8: 15 ), but in this new Exodus, the land between Babylon ( Mesopotamia ) and the Promised Land will be transformed into a paradise, where the mountains will be lowered and the valleys raised to create level road ( Isa 40: 4 ).

He was a native of Cyprus, where he possessed land ( Acts 4: 36, 37 ), which he sold, giving the proceeds to the church in Jerusalem.

In large churches where they were celebrated the services were usually grouped ; e. g. Matins and Lauds ( about 7. 30 A. M .); Prime, Terce ( High Mass ), Sext, and None ( about 10 A. M .); Vespers and Compline ( 4 P. M .); and from four to eight hours ( depending on the amount of music and the number of high masses ) are thus spent in choir.

In some situations where 4NT is a quantitative invitation, especially where 4 is a jump, many partnerships use the Gerber convention by some analogy to the Blackwood family: 4 asks for the number of aces or key cards.

HTML (< u > H </ u > yper < u > t </ u > ext < u > M </ u > arkup < u > L </ u > anguage ) has been in use since 1991, but HTML 4. 0 ( December 1997 ) was the first standardized version where international characters were given reasonably complete treatment.