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Page "Population inversion" ¶ 22
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where and N
The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.
We have just observed that we can write Af where D is diagonalizable and N is nilpotent, and where D and N not only commute but are polynomials in T.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
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.
or under ' Four Stems ', I set off by asterisks cases where the combined N of stems Af was Af.
1 / N, where N is the scale or magnification of the image.
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.
The route has to be changed, which will require it to go through Rock Ridge, a frontier town where everyone has the last name of " Johnson " ( including a " Howard Johnson ", a " Dr. Samuel Johnson ", a " Van Johnson " and an " Olson N. Johnson ").
For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.
where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.
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
Under the administration of Félix Éboué, France's first black colonial governor, a military column, commanded by Colonel Philippe Leclerc de Hauteclocque, and including two battalions of Sara troops, moved north from N ' Djamena ( then Fort Lamy ) to engage Axis forces in Libya, where, in partnership with the British Army's Long Range Desert Group, they captured Kufra.
( V, T, P, S ), where N / V is the Non-terminal Variable, and Σ / T is the Terminal ) is context-sensitive if all rules in P are of the form
where A ∈ N ( i. e., A is a single nonterminal ), α, β ∈ ( N U Σ )* ( i. e., α and β are strings of nonterminals and terminals ) and γ ∈ ( N U Σ )< sup >+</ sup > ( i. e., γ is a nonempty string of nonterminals and terminals ).
The highest point is just east of where Connecticut, Massachusetts, and New York meet ( 42 ° 3 ' N ; 73 ° 29 ' W ), on the southern slope of Mount Frissell, whose peak lies nearby in Massachusetts.
where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.

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

where and 2
during the same period around sunrise, skywave transmission is declining, until at about 2 hours after sunrise it reaches a point where it becomes of little practical significance.
Class 2, stations operating on clear channels are required to cease operation or operate under nighttime restrictions beginning either at local sunset ( for daytime class 2, stations ) or sunset at the location of the dominant class 1, station where located west of the class 2, station ( for limited-time class 2, stations ).
Direct proportionality of the rate to the incident intensity has also been assumed in obtaining the value in the last column for the fourth sample of series 2, where the light intensity was reduced by use of a screen.
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 photocathode sensitivities S, phosphor efficiencies P, and anode potentials V of the individual stages shall be distinguished by means of subscripts 1, and 2, in the text, where required.
The mens rea for assault is simply " evil intent ", although this has been held to mean no more than that assault " cannot be committed accidentally or recklessly or negligently " as upheld in Lord Advocate's Reference No 2 of 1992 where it was found that a " hold-up " in a shop justified as a joke would still constitute an offence.
Their party was defeated ( 2 May 1182 ), but Andronikos Komnenos, a first cousin of Emperor Manuel, took advantage of these disorders to aim at the crown, entered Constantinople, where he was received with almost divine honours, and overthrew the government.
The standard for these progress reports is in 2: 46 – 47, where Luke describes the impact of the gospel on the new church in Jerusalem.
During his rookie season, he played in two games where he amassed a record of 5 passing attempts with 0 receptions and 2 interceptions.
The ability to run older versions of AIX as a WPAR keeps the opportunity to continue using 5. 2 where the hardware doesn't support it.
For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.
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 ).
In the Jewish Deuterocanonical book Second Maccabees, Chapter 2, " one finds in the records " that Jeremiah, having received an oracle of the Lord, ordered that the tent and the ark and the altar of incense should follow him to the mountain of God where he sealed them up in a cave, and he told those who followed him in order to mark the way ( but they could not find it ) " The place shall remain unknown until God gathers his people together again and shows his mercy, and then the Lord will disclose these things, and the glory of the Lord and the cloud shall appear, as they were shown in the case of Moses, and as Solomon asked that the place be specially consecrated.
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.
This view parted with the Jewish scriptures, where Israel offered praise with instruments by God's own command ( e. g.: 2 Chronicles 29: 25 ).
auxiliary regression is TR < sup > 2 </ sup >, where T is the sample size and R < sup > 2 </ sup > is the coefficient of determination.
The term ahimsa appears in the text Taittiriya Shakha of the Yajurveda ( TS 5. 2. 8. 7 ), where it refers to non-injury to the sacrificer himself.

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