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Page "Eiffel (programming language)" ¶ 41

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Alphabets: Armenian alphabet | Armenian , Cyrillic | Cyrillic , Georgian alphabet | Georgian , Greek alphabet | Greek , Latin script | Latin , Latin ( and Arabic script | Arabic ) , Latin and Cyrillic Abjads: Arabic script | Arabic , Hebrew alphabet | Hebrew Abugidas: Indic scripts | North Indic , Indic scripts | South Indic , Ge ' ez script | Ge ' ez , Tāna , Canadian Aboriginal syllabics | Canadian Syllabic and Latin Logographic + syllabic: Pure logographic , Mixed logographic and syllabaries , Featural-alphabetic syllabary + limited logographic , Featural-alphabetic syllabary

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When certain ionic compounds containing bromine are mixed with potassium permanganate ( KMnO 4 ) and an acidic substance, they will form a pale brown cloud of bromine gas.

Solutions of iodine in strong donor solvents such as acetone, tetrahydrofuran, pyridine appears brown or yellow ( λ max = 460-480 nm ), while in solvents of weaker donors such as dichloromethane it appears crimson red, in aromatic hydrocarbons such as benzene and toluene it appears pink or reddish-brown.

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For example, the Hom functor is of the type C op × C → Set.

This defines a functor to Set which is contravariant in the first argument and covariant in the second, i. e. it is a functor C op × C → Set.

For example, < tt > ADD $ 0 ,$ 1, 3 </ tt > means " Set $ 0 to the sum of $ 1 and 3.

Moreover this isomorphism is natural in A and F when both sides are regarded as functors from Set C x C to Set.

An important special case of Yoneda's lemma is when the functor F from C to Set is another hom-functor h B .

Mapping each object A in C to its associated hom-functor h A = Hom ( A ,–) and each morphism f: B → A to the corresponding natural transformation Hom ( f ,–) determines a contravariant functor h – from C to Set C , the functor category of all ( covariant ) functors from C to Set.

The meaning of Yoneda's lemma in this setting is that the functor h – is fully faithful, and therefore gives an embedding of C op in the category of functors to Set.

The forgetful functor Met c → Set lifts finite limits but does not lift them uniquely.

To prove that every epimorphism f: X → Y in Set is surjective, we compose it with both the characteristic function g 1 : Y →

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Set x to VΣ + U T b.

# The category Set op can be embedded into Rel by representing each set as itself and each function f: X → Y as the relation from Y to X formed as the set of pairs ( f ( x ), x ) for all x ∈ X ; hence Set op is concretizable.

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* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x i − X ) 2 of the residuals.

The numerical value of K a 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 +.

As the speed of light in meters per second ( c 0 ) is fixed in the International System of Units, this measurement of the speed of light in AU / d ( c AU ) also determines the value of the astronomical unit in meters ( A ):

Neither G nor M ☉ can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets ( Kepler's Third Law expressed in terms of Newtonian gravitation ).

Since n grows faster than log 2 ( n ), there must exist a value n 0 such that

The U. S. survey acre is about 4, 046. 872 609 874 252 square metres ; its exact value ( m 2 ) is based on an inch defined by 1 metre = 39. 37 inches exactly, as established by the Mendenhall Order.

The value V d is given by

) Then X i is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ i and variance σ i 2 for all times i. Then the definition of the autocorrelation between times s and t is

Because of this keyword stropping, it was possible for AA to allow spaces in variable names, such as < code > integer previous value </ code >.

Thus, all the antiderivatives of x 2 can be obtained by changing the value of C in F ( x ) = ( x 3 / 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 − 27 kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.

Between 70 K and room temperature, berkelium behaves as a Curie – Weiss paramagnetic material with an effective magnetic moment of 9. 69 Bohr magnetons ( µ B ) and a Curie temperature of 101 K. This magnetic moment is almost equal to the theoretical value of 9. 72 µ B calculated within the simple atomic L-S coupling model.

Small could mean less than 3 dB below ( i. e., power output < 1 / 2 or voltage output < 0. 707 of ) the maximum value, or more rarely 10 dB below, or it could mean below a certain absolute value.

Most commonly, bandwidth refers to the 3-dB bandwidth, that is, the frequency range within which the spectral density ( in W / Hz or V 2 / Hz ) is above half its maximum value ( or the spectral amplitude, in V or V / Hz, is more than 70. 7 % of its maximum ); that is, above − 3 dB relative to the peak.

* BCS theory predicts the dependence of the value of the energy gap E at temperature T on the critical temperature T c .

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