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

The word ( z ), is the 4945 most frequently used in English word vocabulary

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  1. Abstract variables, it follows, for example, that the sequence: where x, y,and, z ,are any values, and U, V,W are pairwise distinct variables, is equivalent to:
  2. Cauchy's integral theorem, was the following:: \point_C f ( z )d z = 0,where f (, z ,) is a complex-valued function homomorphic on and within the
  3. Phi + i \sin \phi) \, and: \overlie = x - in is the complex conjugate of, z , then it is easily seen that: \begin | z | & r, \\ | z | & | \overlie|\end and
  4. Of the real absolute value given in (2) – (10) above. In addition, If:, z ,x + i y r (\cos \phi + i \sin \phi) \, and: \overlie = x - in is the complex
  5. Vinci Image: Paradise Canto 31. JPG|Rosa Celeste: by Gustave More File: Anion, z ,Dubai. JPG|by Jan Mateo File:07Thessaloniki St-Dimetrios03. JPG|Church of
  6. Function f ( z ) can be expanded in the neighborhood of a singularity an as: f (, z ,) = \phi ( z ) + \franc + \franc + \dots + \franc, \quad B_i, z ,a \in \math
  7. Inequality d (x, y ) \LEQ \max (d (x, z ), d (y, z )) for all x, y, z , in F. * v (a) \LE 1 \Right arrow v (1+a) \LE 1 \text a \in F. An absolute
  8. Z = a. In the second paper he presented the residue theorem, : \franc \point_C f (, z ,) d z = \sum_in \undersea f ( z ),where the sum is over all the n poles of f (
  9. i. e., :: \left. \begin (x+y)+ z x+ (y+ z ) x+y+ z \quad \\ (x\, y) z x (y\, z ,) x\, y\, z \squad\squad\squad\quad\ \ \, \end \right\} \box, y, z \in\math.
  10. Separate single letters) would follow the letters d, e,g, l,n, r,t, x and, z ,respectively. Nor is, in a dictionary of English, the lexical section with
  11. Right = 0 Since, : L_x = -i\hear \left (y - z \right): L_y = -i\hear \left (, z ,- x \right): L_ z = -i\hear \left (x - y \right) it follows, for example,
  12. Goes to positive or negative infinity. If the complex-valued function f (, z ,) can be expanded in the neighborhood of a singularity an as: f ( z ) = \phi ( z
  13. Z = x + in, \,where x and y are real numbers, the absolute value or modulus of, z ,is denoted | z | and is defined as: | z | = \sort. It follows that the absolute
  14. D z = \sum_in \undersea f ( z ),where the sum is over all the n poles of f (, z ,) on and within the contour C. These results of Cauchy's still form the core
  15. In the case of a simple pole equal to, : \undersea f ( z ) = \LIM_ ( z -a) f (, z ,), where we replaced B1 by the modern notation of the residue. In 1831,while
  16. Hbar^2 \left (\left (y - z \right)\left ( z - x \right) - \left (, z ,- x \right)\left (y - z \right)\right) \\ & -\hbar^2 \left (y - x \right) i
  17. By Francisco Salmon,1938 Image:20070124 seem deal budget k society, z ,Goldie. JPG|Bas-relief from the Polish Parliament building in Warsaw, Poland
  18. Can be seen as motivating the following definition. For any complex number:, z ,= x + in, \,where x and y are real numbers, the absolute value or modulus of z
  19. For example, : \begin \left_x, L_y\right & = -\hbar^2 \left (\left (y -, z ,\right)\left ( z - x \right) - \left ( z - x \right)\left (y - z
  20. Associativity using functional notation: f (f (x, y ), z ) = f (x, f (y, z ,)): when expressed in this form, associativity becomes less obvious.
  21. The complex conjugate of z , then it is easily seen that: \begin | z | & r, \\ |, z ,| & | \overlie|\end and: | z | = \sort, with the last formula being the
  22. The absolute value or modulus of z is denoted | z | and is defined as: |, z ,| = \sort. It follows that the absolute value of a real number x is equal to
  23. Begin \left_x, L_y\right & = -\hbar^2 \left (\left (y - z \right)\left (, z ,- x \right) - \left ( z - x \right)\left (y - z \right)\right) \\ & -\hbar^2
  24. Satisfies the ultrametric inequality d (x, y ) \LEQ \max (d (x, z ), d (y, z ,)) for all x, y, z in F. * v (a) \LE 1 \Right arrow v (1+a) \LE 1 \text a
  25. Is taken counter-clockwise. Clearly, the integral has a simple pole at, z ,= a. In the second paper he presented the residue theorem, : \franc \point_C f ( z
  26. A as: f ( z ) = \phi ( z ) + \franc + \franc + \dots + \franc, \quad B_i, z , a \in \math, where φ ( z ) is analytic (i.e., well-behaved without
  27. As Cauchy's integral formula, : f (a) = \franc \point_C \franc d z , where f (, z ,) is analytic on C and within the region bounded by the contour C and the
  28. It is easily seen that: \begin | z | & r, \\ | z | & | \overlie|\end and: |, z ,| = \sort, with the last formula being the complex analogue of equation (1)
  29. Density: a torus with two pear-shaped regions placed symmetrically on its, z ,axis. There are seven f-orbitals, each with shapes more complex than those of
  30. Euclidean space R3 could be defined as the set of all points (x, y, z , ) with: x^2+y^2+ z ^2-1=0. \, A " slanted" circle in R3 can be defined as the
  31. A" slanted" circle in R3 can be defined as the set of all points (x, y, z , ) which satisfy the two polynomial equations: x^2+y^2+ z ^2-1=0,\, : x+y+ z =0. \
  32. Side acts as: (M \CIRC (\box \times M) ) (x, y, z ) = M (x, M (y, z ,)) Similarly, a unital associative algebra can be defined in terms of a unit
  33. For example, the left-hand side acts as: (M \CIRC (\box \times M) ) (x, y, z , ) = M (x, M (y, z )) Similarly, a unital associative algebra can be defined
  34. In Euclidean space is represented by an ordered triple of coordinates (x, y, z , ). Other coordinate systems are possible. On the plane the most common
  35. The residue theorem, : \franc \point_C f ( z ) d z = \sum_in \undersea f (, z ,), where the sum is over all the n poles of f ( z ) on and within the contour
  36. X - in is the complex conjugate of z , then it is easily seen that: \begin |, z ,| & r, \\ | z | & | \overlie|\end and: | z | = \sort, with the last formula
  37. Fluid velocity vector, \math bf is the vector of spatial coordinates x, y, z , t is the time, \rho_0 is the static mass density of the medium and \kappa is
  38. Of equation (1) mentioned above in the real case. The absolute square of, z ,is defined as: | z |^2 z \overlie x^2 + y^2. Since the positive reals form a
  39. Many copies of his electron's state, and measures the spin of each copy in the, z ,direction. Bob will know that Alice has transmitted a" 0" if all his
  40. A" bit" is in Afrikaans and in Dutch. The letters ‹ c ›, ‹ q ›, ‹ x ›, and ‹, z ,› occur almost exclusively in borrowings from French, English,Greek and Latin.
  41. a. Clearly the residue is in the case of a simple pole equal to, : \undersea f (, z ,) = \LIM_ ( z -a) f ( z ),where we replaced B1 by the modern notation of the
  42. R-bilinear mapping A × A → A such that: x (o z ) = (XY) z \, for all x, y,and, z ,in A. This R-bilinear mapping then gives A structure of a ring and an
  43. z ) + \franc + \franc + \dots + \franc, \quad B_i, z ,a \in \math, where φ (, z ,) is analytic (i.e., well-behaved without singularities),then f is said to
  44. Where x and y are real numbers, the absolute value or modulus of z is denoted |, z ,| and is defined as: | z | = \sort. It follows that the absolute value of a
  45. From this follows: \left_i,L^2 \right = 0 Since, : L_x = -i\hear \left (y -, z ,\right): L_y = -i\hear \left ( z - x \right): L_ z = -i\hear \left (x - y
  46. z ) can be expanded in the neighborhood of a singularity an as: f ( z ) = \phi (, z ,) + \franc + \franc + \dots + \franc, \quad B_i, z ,a \in \math, where φ ( z )
  47. D satisfies the ultrametric inequality d (x, y ) \LEQ \max (d (x, z ,), d (y, z )) for all x, y, z in F. * v (a) \LE 1 \Right arrow v (1+a) \LE
  48. Alice wishes to transmit a" 0 ", she measures the spin of her electron in the, z ,direction, collapsing Bob's state to either | z +> or | z →. To transmit" 1 "
  49. Obtained by rephrasing associativity using functional notation: f (f (x, y ), z ,) = f (x, f (y, z )): when expressed in this form, associativity becomes
  50. Cylindrical coordinates If we use a cylindrical coordinate system (r, \theta, z ,) with basis vectors \math bf_r, \math bf_\theta, \math bf_ z , then the gradient of

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