Facts about Integrals

The mechanism of ATP synthesis discussed here assumes that protons extruded during electron transport are in the bulk phase surrounding the inner mitochondrial membrane (intermembrane and extramitochondrial spaces). An alternative view is that there are local proton circuits within or close to the respiratory chain and complex V, and that these protons may not be in free equilibrium with the bulk phase (Williams, 1978), although this has not been supported experimentally (for references see Nicholls and Ferguson, 1992). The chemiosmotic mechanism is both elegant and simple and explains all the known facts about ATP synthesis and its dependence on the structural integrity of the mitochondria, although the details may appear complex. This mechanism will now be discussed in more detail. 

Comparison of integrated peak intensities in Figures 1.5(a), (b) shows that the peaks in the decoupled spectrum are in fact about 2.5 times greater than... 

Fascinating Facts About Integrated-Circuit Design... 

The following facts about definite integrals are frequently useful ... 

Fourier proved the following facts about Fourier series (1) Any Fourier series in X is uniformly convergent for all real values of x (2) the set of sine and cosine basis functions in Eq. (B-104) is a complete set for the representation of periodic functions of period 2L. This means that any periodic function obeying certain conditions such as integrability can be accurately represented by the appropriate Fourier series. It is not necessary that the function be continuous. 

Wlien Al MAS NMR spectra were first collected at moderate Bq with relatively slow MAS rates (<4 kHz) there was much confiision about the quantitative integrity of such spectra. In fact, provided the correct excitations are employed (i.e. and 1) all that is necessary to make MAS NMR spectra... 

Sometimes chemists have to analyze substances about which they know very little. A chemist may isolate an interesting molecule from a natural source, such as a plant or an insect. Under these conditions the chemical formula must be deduced from mass percentage data, without the help of an expected formula. A four-step procedure accomplishes this by using mass-mole conversions, the molar masses of the elements, and the fact that a chemical formula must contain integral numbers of atoms of each element. 

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