Examples of the the word, exp , in a Sentence Context

The word ( exp ), is the 14879 most frequently used in English word vocabulary

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  1. P_X \right)=\text\left (X\right). \, Exponential trace Expressions like, exp ,(try (A) ), where A is a square matrix, occur so often in some fields (e.g.
  2. X to itself, taking the initial state u0 at time t 0 to the state u (t) =, exp ,(ta)u0 at time t. The operator A is said to be the infinitesimal generator of
  3. Diffeomorphisms arbitrarily close to the identity which are not in the image of, exp ,). Furthermore, some infinite-dimensional Lie algebras are not the Lie algebra
  4. Particle will have a lesser probability to be in state \script style|1\range by, exp ,(HE/T). In the distinguishable case, the particle distribution will be biased
  5. Above multiplication table, while exp ressions like cos (θ) + sin (θ) and, exp ,(θ) are not, and are (correctly) deemed physical. It should be clear that
  6. Counterclockwise rotation by one full turn which results in a multiplication by, exp ,(in). This phase factor here is called the mutual statistics. As for R, even
  7. Axis exp (−x22) after multiplication takes the form exp (−x12−x22) or, exp ,(−r2) and so is only dependent on distance from the origin. Alternatives
  8. It is the same as flipping a coin with probability proportional to p =, exp ,(HE/T) to land tails. The probability to land heads is 1/ (1 + p),which is
  9. Since it is not able to represent transcendental functions. The function, exp ,(x),for example, is transcendental and therefore cannot be exp ressed as a
  10. Leq \log \left (\sum_WNW_ix_i \right) By applying (strictly increasing), exp , function to both sides we get the inequality:: \prod_ANX_in \LEQ \sum_WNW_ix_i
  11. Is irrational. * The values of the exp onential, sine and cosine functions, exp ,(x),sin (x),cos (x),are known to be irrational for any rational value
  12. Of the unit n-ball. Examples For example, when n = 2 the normal distribution, exp ,(−x12) when exp anded over another axis exp (−x22) after multiplication
  13. Representation. This approach is due to T. J. Stilts (1894). Writing z! =, exp ,(P (z) ) where P (z) is: P (z) = p (z) + \log (2\pi)/2 - z + \left (
  14. In case u and v commute, this formula reduces to the familiar exp onential law, exp ,(u) exp (v) = exp (u + v). The exp onential map from the Lie algebra to
  15. One possible exception, infinitely often on V. Examples The function f (z), exp , ( 1/z) has an essential singularity at z0 0,but the function g (z) = 1/z3
  16. Energy to produce a pair of increases with temperature, being approximately, exp ,(LEG/kt),where k is Boltzmann's constant’T is absolute temperature and EG
  17. Frac\right)\right) \LN (x_n) and again, by continuity of the, exp ,function:: \LIM_\sort \ exp \left (\LIM_\franc\LN\left (
  18. Known derivatives of the elementary functions x2,x4,sin (x),LN (x) and, exp ,(x) = ex, as well as the constant 7,were also used. Derivatives in higher
  19. Is used to construct a number of elementary functions: the exp onential function, exp ,(z),also written EZ, is defined as the infinite series: \ exp (z):
  20. When (syntax-rules () (( when red exp exp ...) (if red (begin, exp , exp ...) )) )) Thus the syntax of Scheme can easily be extended.
  21. U and v commute, this formula reduces to the familiar exp onential law exp (u), exp , ( v) = exp (u + v). The exp onential map from the Lie algebra to the Lie
  22. A meaning must be given to the exp onential of ta. As a function of t, exp ,(ta) is a semigroup of operators from X to itself, taking the initial state
  23. 1977,2nd exp . ed. 1996,with Claire Parent). Trans. Dialogues (1987,2nd, exp , Ed. 2002). * Francis Bacon - Monique de la sensation (1981). Trans. Francis
  24. Or lengthy * if a function has no elementary antiderivative (for instance, exp ,(-x2) ), its definite integral can be approximated using numerical
  25. Et LES signs (1964,2nd exp . ed. 1976). Trans. Proust and Signs (1973,2nd, exp , Ed. 2000). * Nietzsche (1965). Trans. In Pure Immanence (2001). * Le
  26. Log-normal distribution with parameters μ and σ2,the standard deviation is (, exp ,(σ2) − 1) exp (2μ + σ2)1/2. Estimation One can find the standard deviation of
  27. Is equivalent to an average in space computed with the Boltzmann factor, exp ,(mph). This idea has been generalized by Sinai, Bowen,and Rule (SRB) to
  28. The special orthogonal group SO (2). An isomorphism is given by f (a + Z) =, exp ,(2πia) (see Euler's identity). *If G is the group of invertible 3 × 3 real
  29. When n = 2 the normal distribution exp (−x12) when exp anded over another axis, exp ,(−x22) after multiplication takes the form exp (−x12−x22) or exp (−r2)
  30. Pratique (1970,2nd ed. 1981). Trans. (1988). * Dialogues (1977,2nd, exp , Ed. 1996,with Claire Parent). Trans. Dialogues (1987,2nd exp . ed. 2002).
  31. Or, for real matrices A, : \math rm (A) = \log (\DET (\ exp (A) )). \, Here, exp , ( A) denotes the matrix exp onential of A, because every eigenvalue λ of A
  32. Exponential of A, because every eigenvalue λ of A corresponds to the eigenvalue, exp ,(λ) of exp (A). In particular, given any logarithm of A, that is, any
  33. On a heuristic level, the solution to this problem" ought" to be u (t), exp , ( ta)u0. However, for a rigorous treatment, a meaning must be given to the
  34. Trans. Kant's Critical Philosophy (1983). * Proust et LES signs (1964,2nd, exp , Ed. 1976). Trans. Proust and Signs (1973,2nd exp . ed. 2000). * Nietzsche (
  35. Expanded over another axis exp (−x22) after multiplication takes the form, exp ,(−x12−x22) or exp (−r2) and so is only dependent on distance from the
  36. A special case of the Lie algebra exp onential map. The identity exp (x+y) =, exp ,(x) exp (y) can fail for Lie algebra elements x and y that do not commute;
  37. Only Perl keywords (no literals or punctuation): not, exp ,logs rand xor sqq ex xor s x x length UC ORD and print CHR ORD for QC q join
  38. And no false branch. (define-syntax when (syntax-rules () (( when red, exp , exp ...) (if red (begin exp exp ...) )) )) Thus the syntax of Scheme
  39. Qq q xor int evil LC q m cos and print CHR ORD for QC y abs né open tied hex, exp ,ref y m xor scalars rand print HQ q xor int evil LC HQ y sort cos and print
  40. Impractical. Because nuclear reaction rates strongly depend on temperature (, exp ,(HE/kt) ), achieving reasonable energy production rates in terrestrial fusion
  41. This formula reduces to the familiar exp onential law exp (u) exp (v) =, exp ,(u + v). The exp onential map from the Lie algebra to the Lie group is not
  42. To the system (e.g. in the absence of a potential field, α=3/2),z is, exp ,(μ/kt) where μ is the chemical potential, Li is the poly logarithm, ζ is the
  43. U of the zero element of \Mather, such that for u, v in U we have: exp (u), exp , ( v) = exp (u + v + 1/2 u, v + 1/12 u, v,v − 1/12 u, v,u − ...) where the
  44. Element of \Mather, such that for u, v in U we have: exp (u) exp (v) =, exp ,(u + v + 1/2 u, v + 1/12 u, v,v − 1/12 u, v,u − ...) where the omitted
  45. Matrices is a special case of the Lie algebra exp onential map. The identity, exp ,(x+y) = exp (x) exp (y) can fail for Lie algebra elements x and y that do
  46. Not exist. For instance, it is known that the antiderivative of the functions, exp ,(x2),xx and sin x /x cannot be exp ressed in the closed form involving only
  47. U of the zero element of \Mather, such that for u, v in U we have:, exp ,(u) exp (v) = exp (u + v + 1/2 u, v + 1/12 u, v,v − 1/12 u, v,u − ...)
  48. A, because every eigenvalue λ of A corresponds to the eigenvalue exp (λ) of, exp ,(A). In particular, given any logarithm of A, that is, any matrix L
  49. State. So, such an interchange can generically result in a multiplication by, exp ,(in) (its absolute value is 1 because of unitary ...). This is called
  50. Or decrease) in the dependent variable. The function is often written as, exp ,(x),especially when it is impractical to write the independent variable as a

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