# Examples of the the word, f , in a Sentence Context

The word ( f ), is the 2085 most frequently used in English word vocabulary

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1. Mills (c),malt house (d). Facing the west are the stables (e),ox-sheds (, f ,), goatstables (GL, piggeries (h),sheep- f olds (i),together with the
2. Axiom can thus be expressed as:: There is a set A such that f or all f unctions, f ,(on the set o f non-empty subsets o f A),there is a B such that f (B) does
3. Where φ (z) is analytic (i.e., well-behaved without singularities),then, f ,is said to have a pole o f order n in the point a. I f n = 1,the pole is called
4. Function, the expression should be written as ~ f (\omega)=\ f ranc\int, f ,(t) \exp (i\omega t) t; however, it is assumed that the shape o f the
5. F, de f ined on a collection X o f nonempty sets, such that f or every set s in X, f ,(s) is an element o f s. With this concept, the axiom can be stated:: For any
6. Which there is a f unction f f rom the real numbers to the real numbers such that, f ,is not continuous at a, but f is sequentially continuous at a, i. e., f or any
7. Associativity using f unctional notation: f ( f (x, y ), z ) = f (x, f ,(y, z )): when expressed in this f orm, associativity becomes less obvious.
8. He presented the residue theorem, : \ f ranc \point_C f (z) dz = \sum_in \undersea, f ,(z),where the sum is over all the n poles o f f (z) on and within the
9. More generally, given f our sets M, N,P and Q, with h: M to N, g: N to P, and, f , : P to Q, then:: ( f \CIRC g)\CIRC h f \CIRC (g\CIRC h) f \CIRC g\CIRC h: as
10. Perspective is obtained by rephrasing associativity using f unctional notation:, f ,( f (x, y ), z ) = f (x, f (y, z )): when expressed in this f orm
11. Functions f (on the set o f non-empty subsets o f A),there is a B such that, f ,(B) does not lie in B. Restriction to f inite sets The statement o f the axiom
12. z) dz = \sum_in \undersea f (z),where the sum is over all the n poles o f , f ,(z) on and within the contour C. These results o f Cauchy's still f orm the
13. Y, z\in\math\boxy\ne0,z\ne0.:: ( f \, x \, y ) = ((, f ,\, x ) \, y ): This notation can be motivated by the currying isomorphism.
14. Axes. Additionally, as is the case with the s orbitals, individual p, d, f , and g orbitals with n values higher than the lowest possible value, exhibit an
15. Each with shapes more complex than those o f the d-orbitals. For each s, p,d, f ,and g set o f orbitals, the set o f orbitals which composes it f orms a
16. Speaking, such an expression requires that ~ f =0 ~; even i f f unction ~, f ,~ is a sel f -Fourier f unction, the expression should be written as ~ f (
17. As Cauchy's integral theorem, was the f ollowing:: \point_C f (z)dz = 0,where, f ,(z) is a complex-valued f unction homomorphic on and within the
18. In the f irst he proposed the f ormula now known as Cauchy's integral f ormula, :, f , ( a) = \ f ranc \point_C \ f ranc dz, where f (z) is analytic on C and within the
19. Can be stated:: For any set X o f nonempty sets, there exists a choice f unction, f ,de f ined on X. Thus the negation o f the axiom o f choice states that there exists
20. Statement is true. *There exists a model o f AFC in which there is a f unction, f , f rom the real numbers to the real numbers such that f is not continuous at a
21. Is obtained by rephrasing associativity using f unctional notation: f (, f ,(x, y ), z ) = f (x, f (y, z )): when expressed in this f orm, associativity
22. Maximum o f two electrons. The simple names s orbital, p orbital’d orbital and, f ,orbital re f er to orbitals with angular momentum quantum number l = 0,1,2 and
23. At z = a. In the second paper he presented the residue theorem, : \ f ranc \point_C, f ,(z) dz = \sum_in \undersea f (z),where the sum is over all the n poles o f
24. It is assumed that the shape o f the f unction (and even its norm \int |, f ,(x)|^2 x) depend on the character used to denote its argument. I f the Greek
25. Is in the case o f a simple pole equal to, : \undersea f (z) = \LIM_ (z-a), f , ( z),where we replaced B1 by the modern notation o f the residue. In 1831
26. Function goes to positive or negative in f inity. I f the complex-valued f unction, f ,(z) can be expanded in the neighborhood o f a singularity an as: f (z) = \phi
27. Between the graphs o f two f unctions is equal to the integral o f one f unction, f ,(x),minus the integral o f the other f unction, g (x). *an area bounded by a
28. X/y/z= (x/y)/z\squad\squad\quad\box, y,z\in\math\boxy\ne0,z\ne0.:: (, f ,\, x \, y ) = (( f \, x ) \, y ): This notation can be motivated by the
29. At di f f erent levels.: S_ = S_ + S_\, \! So, the number o f degrees o f f reedom, f ,can be partitioned similarly and speci f ies the chi-squared distribution
30. The same name to the f unction and to its Fourier trans f orm:: ~ f (\omega)=\int, f ,(t) \exp (i\omega t) t. Rigorously speaking, such an expression requires
31. Mode o f the wave. As with s orbitals, this phenomenon provides p, d, f , and g orbitals at the next higher possible value o f n ( f or example,3p
32. Called simple. The coe f f icient B1 is called by Cauchy the residue o f f unction, f ,at a. I f f is non-singular at a then the residue o f f is zero at a. Clearly the
33. Homestead Society in Brant f ord, Ontario; * The http://maps.google.com/maps?, f ,q&source s_OHL geocode HQ %22Alexander+Graham+Bell+%22,+Cambridge
34. Function density) at the center o f the nucleus. All other orbitals (p, d, f , etc.) have angular momentum, and thus avoid the nucleus (having a wave node
35. That Hume thinks gives us warrant to doubt any given testimony, and that is, f ,) i f the propositions being communicated are miraculous. Hume understands a
36. Is sequentially continuous at a, i. e., f or any sequence converging to a, limn, f , ( in)= f (a). *There exists a model o f AFC which has an in f inite set o f real
37. Known as Cauchy's integral f ormula, : f (a) = \ f ranc \point_C \ f ranc dz, where, f , ( z) is analytic on C and within the region bounded by the contour C and the
38. O f Compton scattering. Einstein concluded that each wave o f f requency, f ,is associated with a collection o f photons with energy h f each, where h is
39. The real numbers to the real numbers such that f is not continuous at a, but, f , is sequentially continuous at a, i. e., f or any sequence converging to a, limn
40. By rephrasing associativity using f unctional notation: f ( f (x, y ), z ) =, f ,(x, f (y, z )): when expressed in this f orm, associativity becomes less
41. A choice f unction. Which is equivalent to: For any set A there is a f unction, f ,such that f or any non-empty subset B o f A, f (B) lies in B. The negation o f
42. Theory with interesting consequences. Statement A choice f unction is a f unction, f , de f ined on a collection X o f nonempty sets, such that f or every set s in X, f
43. The residue o f f unction f at a. I f f is non-singular at a then the residue o f , f ,is zero at a. Clearly the residue is in the case o f a simple pole equal to,
44. At a. Clearly the residue is in the case o f a simple pole equal to, : \undersea, f ,(z) = \LIM_ (z-a) f (z),where we replaced B1 by the modern notation o f
45. Somewhat f rom other Scots dialects most noticeable are the pronunciation, f , f or what is normally written WH and EE f or what in standard English would
46. By Cauchy, now known as Cauchy's integral theorem, was the f ollowing:: \point_C, f ,(z)dz = 0,where f (z) is a complex-valued f unction homomorphic on and
47. For any set A there is a f unction f such that f or any non-empty subset B o f A, f ,(B) lies in B. The negation o f the axiom can thus be expressed as:: There is
48. The coe f f icient B1 is called by Cauchy the residue o f f unction f at a. I f , f ,is non-singular at a then the residue o f f is zero at a. Clearly the residue is
49. From the total number o f electrons which occupy a complete set o f s, p,d and, f ,atomic orbitals, respectively. Introduction With the development o f quantum
50. Function f (z) can be expanded in the neighborhood o f a singularity an as:, f ,(z) = \phi (z) + \ f ranc + \ f ranc + \dots + \ f ranc, \quad B_i, z,a \in

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