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.

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 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 ).

where 144 =

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.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

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.

t < sub > r </ sub > * BW = 0. 35, where t < sub > r </ sub > is rise time in seconds and BW is bandwidth in Hz.

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.

Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where ( x, y, z ) belongs to the subset if and only if f ( x, y ) = z.

The Boltzmann distribution is often expressed in terms of β = 1 / kT where β is referred to as thermodynamic beta.

Self-adjoint operators, where A = A < sup >†</ sup >, play an important role in quantum mechanics ; for example, an observable is always described by a self-adjoint operator.

where e = 2. 718 ....

where h ( 0 ) is the height at r = 0 ( the axis ).

where the convention B < sub > 1 </ sub > = + 1 / 2 is used.

where a = 0. 246 nm.

* Place (< span lang = grc > pou </ span >, where ) — examples: in a marketplace, in the Lyceum

The open-chain form of a monosaccharide often coexists with a closed ring form where the aldehyde / ketone carbonyl group carbon ( C = O ) and hydroxyl group (- OH ) react forming a hemiacetal with a new C-O-C bridge.

A simple electric circuit, where current is represented by the letter i. The relationship between the voltage ( V ), resistance ( R ), and current ( I ) is V = IR ; this is known as Ohm's Law.

where E = elastic modulus of the material, I < sub > min </ sub >

where r = radius of gyration of cross-section which is equal to the square root of ( I / A ), K = ratio of the longest half sine wave to the actual column length, and KL

P < sub > cr </ sub >/ A, where A = cross-sectional area of the column ), is greater than the proportional limit of the material, the column is experiencing inelastic buckling.

( Note: bandwidth is proportional to where = bit time ) Therefore, the bandwidth of the data signal is and the bandwidth of the spread spectrum signal is.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

where | v | = Rω is the magnitude of the velocity ( the speed ).

where it already is established that α = ρ.

* Within the region where radiative effects are important the description given by the idealized greenhouse model becomes realistic: The surface of the Earth, warmed to a temperature around 255 K, radiates long-wavelength, infrared heat in the range 4 – 100 μm.

It was expected that the reaction would be < sup > 253 </ sup > Es ( α, n ) < sup > 255 </ sup > Md, where < sup > 255 </ sup > Md was α-active with a t < sub > ½ </ sub > of 5 minutes and the corresponding α-energy.

The town of Pine Village lies about to the north of Williamsport where State Road 55 intersects State Road 26, near the northern edge of the county ; 255 people live in Pine Village.

* Lake Borrevannet is home to a national bird sanctuary where 255 different bird species have been observed ( 2003 numbers ).

He trained Carthaginian soldiers and led them into the battle of Tunis, where Carthaginian forces routed the Roman expeditionary force and captured the Roman consul Marcus Atilius Regulus in 255 BC.

The routes separate in Sunset Hills where US 50 migrates southeast bypassing St Louis by joining Interstate 255 to cross Mississippi River into Illinois.

By sequentially printing the characters 0 through 255 in all three areas, the program can simulate a graphics mode where each pixel can be set individually.

They could be defined by issuing the command DEF CHR $( n )=" HHHHHHHHHH " where n ranges from 252 to 255 and the H's are 10 hexadecimal digits ( 5 bytes ).

The trailer packet does only contain its packet id with no parameters where 255 equals the state of all bits set in the 8-bit packet id field ( 11111111 ).

If the RGB image is 24-bit ( the industry standard as of 2005 ), each channel has 8 bits, for red, green, and blue — in other words, the image is composed of three images ( one for each channel ), where each image can store discrete pixels with conventional brightness intensities between 0 and 255.

Abu Abdurrahman Ahmed ibn Shuaib ibn Ali ibn Sinan ibn Bahr ibn Dinar Al-Khurusani was born in the year 215 A. H as the Imam clearly states himself ( although some say 255 A. H or 214 A. H ) in the city of Nasa, situated in Western Asia known at that time as Khurusan which was a centre for Islamic Knowledge where millions of Ulama ' a were situated and Hadeeth and Fiqh was at its peak.

Kalamaria had a population of 14, 000 residents as recorded by an inventory in 1947, but this has considerably increased, as shown by the Greek census of 2001 where Kalamaria had a total of 87, 255 residents.