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Page "Cochran's theorem" ¶ 6
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Here and rank
Here a rank 1 tensor ( matrix product of a column vector and a row vector ) is the same thing as a rank 1 matrix of the given size.
Here ℓ is the rank of the covariance matrix.
Here χ is not a number as before but a tensor of rank 2, the electric susceptibility tensor.
Here he stepped at once into the foremost rank as a preacher, and his church was thronged with thoughtful men of all classes in society and of all shades of religious belief.
Here he established himself by rapidly rising through the ranks, and, after a military campaign against El Salvador, held the rank of colonel at the age of 28.
* Generic rank 2 distributions on 5-manifolds: Here G =
Here is a list of current-model CCM skates, as listed by rank of performance:
Here is a list of current-model CCM sticks, as listed by rank of performance
Here he threw himself heart and soul into the cause of the French Revolution, and took part under Dumouriez and Pichegru in the campaigns of 1792 and 1793, and was soon promoted to the rank of brigadier-general.
Here he followed revivalist principles by preaching to all people willing to listen, regardless of religious denomination or social rank ; attracting note as a populist pulpit orator, religious author and scholar, and a friendly counsellor.
Here, electors may rank all candidates in the order of their preference.
Here, the verb + has a rank of 0 0 0, the left argument has a rank of 0, and the right argument has a rank of 1 ( with a dimension of 3 ).

Here and Q
Here P represents the value of the stream in state P and Q the cost of operating the stage with conditions Q.
Here ΔG is change in Gibbs free energy, T is absolute temperature, R is the gas constant and Q is reaction quotient.
Here Qthe size of message block to be inserted ; N – the size ( in bits ) of one sample of the message file ( see figure The Fourth Protection Level Scheme ).
Here orthogonality is important not only for reducing A < sup > T </ sup > A = ( R < sup > T </ sup > Q < sup > T </ sup >) QR to R < sup > T </ sup > R, but also for allowing solution without magnifying numerical problems.
Here Q is the molar activation energy, R is the ideal gas constant, T is absolute temperature, and K < sub > 0 </ sub > is a material dependent factor.
Here Q < sub > Y | X </ sub >( y | x ), sometimes called a test channel, is the conditional probability density function ( PDF ) of the communication channel output ( compressed signal ) Y for a given input ( original signal ) X, and I < sub > Q </ sub >( Y ; X ) is the mutual information between Y and X defined as
( P + dP * Q / dQ ) can also be written as P ( 1 + dPQ / dQP ). Here, ( dP / dQ ) ( Q / P ) is 1 / E < sub > P </ sub >, where E < sub > P </ sub > is price elasticity of demand.
* Q Here Comes the Sun ( CD, 2005 )
Here, P ( Q ) denotes the power set of Q.
Here, is a vector in, the tangent space to the manifold Q at point q.
Here P serves as a price index, and Q serves as a quantity index of real value.
Here rational means that it is a purely transcendental extension of Q, generated by an algebraically independent set.
They played hundreds of dates, opened for acts as diverse as Graham Parker, Cheap Trick, Gang of Four and Morphine, and released three more records on Q ,: 1997's full-length No One Here Gets In For Free -- Rare and Unreleased 1989-1997 ; the 1998 hit single " Favorite ," produced by Denneen ; and 1999's full-length Silver Gorilla, also with Denneen, which amassed critical raves across the country, from Raygun to Entertainment Weekly.
and Duck Dodgers in the 24½th Century for Jones and Person to Bunny ( the final time Arthur Q. Bryan voiced Elmer Fudd ) and Here Today, Gone Tamale ( the only Speedy Gonzales cartoon he ever wrote ) for Freleng.
Here ‘ A ’ can be any letter of the Latin alphabet except I, O, Q, U and is treated as a base-22 digit ; ‘ 9 ’ can be any decimal digit.
Here, ζ ( s ) is the usual Riemann zeta function and L ( s, E ) is called the L-function of E / Q, which takes the form
Here at the new River Cottage H. Q., the team would film the 2006 series The River Cottage Treatment where Hugh would attempt to convert junk food lovers ' eating habits.
Q gave You Were Here 3 of 5 stars and called it " Lounge jazz, drum loops and lead guitar chops support a vocalist whose lyrical panache ... marks her out from the crowd.
Here is a game Reinfeld won against Marshall in New York City in 1941: 1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. cxd5 cxd5 5. Nc3 Nc6 6. Bf4 e6 7. e3 Bd6 8. Bxd6 Qxd6 9. Bd3 0-0 10. 0-0 e5 11. Nb5 Qe7 12. dxe5 Nxe5 13. Be2 Nxf3 + 14. Bxf3 Be6 15. Qe2 Rfc8 16. Rfd1 Rc5 17. Rd4 Rac8 18. Nc3 Rc4 19. Rad1 Rxd4 20. Rxd4 h6 21. h3 Rc5 22. Qd3 Qc7 23. g4 g5 24. Kg2 Qe5 25. b4 Rc4 26. Nxd5 Bxd5 27. Rxd5 Rc3 28. Rxe5 Rxd3 29. Ra5 b6 30. Rxa7 Nd7 31. Ra6 Kg7 32. Bc6 Ne5 33. Rxb6 Rd2 34. a4 Nc4 35. Rb7 Nxe3 + 36. Kf3 Nd1 37. Rd7 Rxf2 + 38. Kg3 Rf1 39. a5 Nc3 40. a6 Ne2 + 41. Kg2 Ra1 42. a7 Nf4 + 43. Kf3 Ra3 + 44. Ke4 Nxh3 45. a8 = Q Nf2 + 46. Kf5 1 – 0

Here and <
Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.
Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).
Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that
Here k is first-order rate constant having dimension 1 / time, ( t ) is concentration at a time t and < sub > 0 </ sub > is the initial concentration.
Here I < sub > 2 </ sub > is reduced to I < sup >–</ sup > and S < sub > 2 </ sub > O < sub > 3 </ sub >< sup > 2 –</ sup > ( thiosulfate anion ) is oxidized to S < sub > 4 </ sub > O < sub > 6 </ sub >< sup > 2 –</ sup >.
The simplest, and original, implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime and g is primitive root mod p. Here is an example of the protocol, with non-secret values in < span style =" color: blue "> blue </ span >, and secret values in < span style =" color: red "> boldface red </ span >:
Here is the center of the ellipse, and is the angle between the < math > X </ Math >- axis and the major axis of the ellipse.
Here C < sub > p </ sub > is the heat capacity at constant pressure and α is the coefficient of ( cubic ) thermal expansion
Here ( Z / 2Z ) is the polynomial ring of Z / 2Z and ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the equivalence classes of these polynomials modulo T < sup > 2 </ sup >+ T + 1.
Here the kets and columns are identified with the vectors of V and the bras and rows with the dual vectors or linear functionals of the dual space V < sup >*</ sup >, with conjugacy associated with duality.
Here, R < sub > ij </ sub > is the Ricci tensor.
# If A is a cartesian product of intervals I < sub > 1 </ sub > × I < sub > 2 </ sub > × ... × I < sub > n </ sub >, then A is Lebesgue measurable and Here, | I | denotes the length of the interval I.

2.266 seconds.