A doubling

Bredt s rule A double bond cannot be introduced at the bridgehead carbon of a bridged bicyclic or polocyclic system with small- or medium-sized rings. 

Linde process A high-pressure process for the production of liquid oxygen and nitrogen by compression to about 200 bar (20MN/m ) followed by refrigeration and fractionation in a double column. 

A comparison between the beam intensity before and after the flame provides a measurement of the quantity of photons absorbed and therefore the concentration of the atom being analyzed. The comparison can be made directly by a double beam analyzer. See Figure 2.7 in which the beam is divided into 2 branches one of which traverses the flame, the other serving as... 

The introduction of low quantities of surfactants (50 to 125 ppm) helps solve these two problems. The surfactant molecule has a lipophilic organic tail and a polar head that is adsorbed selectively on the metal walls of the admission system. These products have a double action ... 

A double time correlation among the 3 binary temporal sequences of a triplet of transducers are calculated. A maximum of 8 different but overlapping triplets can be predefined. 

The probes are assumed to be of contact type but are otherwise quite arbitrary. To model the probe the traction beneath it is prescribed and the resulting boundary value problem is first solved exactly by way of a double Fourier transform. To get managable expressions a far field approximation is then performed using the stationary phase method. As to not be too restrictive the probe is if necessary divided into elements which are each treated separately. Keeping the elements small enough the far field restriction becomes very week so that it is in fact enough if the separation between the probe and defect is one or two wavelengths. As each element can be controlled separately it is possible to have phased arrays and also point or line focussed probes. 

To find now the optimum excitation frequency, we calculate the first derivative of Equ. (3.1) to find the maximum value of the response field of cracks in different depths (Fig. 3,1). For example a crack (20 x 0.6 x 0,2 mm) in a depth of 9 mm in an aluminium sample (a = 20 MS/m) could be found with highest SNR when using a frequency of 260 Hz Here a double-D... 

Fig. 3.2 optimum excitation frequency for cracks in varing depths. The dotted line is for a sheet inducer and the solid one is for a Double-D coil. The indicated points represent the measured values. 

For the case of a double-D coil we multiply each matrix element with an element shifted by a constant distance of the same line. This is done in x- and y-direction. The distance between the two elements is the correlation length X for filtering in x-direction and a second correlation length for the movement in y-direction. Thus one gets two new matrices Ax and Ax for the filtering from the left to the right (positiv x-direction) and vice versa (negativ x-direction). 

In case of a gradiometric excitation with a double-D coil, this algorithm enhances the response of the crack, while other signals like artificial peaks and plateaus are supressed. The calculation can be done using different correlation lengths X in order to obtain additional information about the depth in wliich the crack is located. 

This is a double-channel flaw detector having their own microcomputer with 1 Mbyte memory to store data of the LMA and the LF channels for 800...2000 m of a rope under inspection. The instrument can be used in two modes as a tester for operative inspection or as a device for the inspection data storage. 

The computed CWT leads to complex coefficients. Therefore total information provided by the transform needs a double representation (modulus and phase). However, as the representation in the time-frequency plane of the phase of the CWT is generally quite difficult to interpret, we shall focus on the modulus of the CWT. Furthermore, it is known that the square modulus of the transform, CWT(s(t)) I corresponds to a distribution of the energy of s(t) in the time frequency plane [4], This property enhances the interpretability of the analysis. Indeed, each pattern formed in the representation can be understood as a part of the signal s total energy. This representation is called "scalogram". 

Another type of reaction that has been studied is that of the oxidation of a double bond. In the case of triolein, Mittelmann and Palmer [309] found that, on a dilute permanganate substrate, the area at constant him pressure hrst increased and then decreased. The increase was attributed to the reaction... 

This produces a double layer of charge, one localized on the surface of the plane and the other developed in a diffuse region extending into solution. 

Cationic surfactants may be used [94] and the effect of salinity and valence of electrolyte on charged systems has been investigated [95-98]. The phospholipid lecithin can also produce microemulsions when combined with an alcohol cosolvent [99]. Microemulsions formed with a double-tailed surfactant such as Aerosol OT (AOT) do not require a cosurfactant for stability (see, for instance. Refs. 100, 101). Morphological hysteresis has been observed in the inversion process and the formation of stable mixtures of microemulsion indicated [102]. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

The factor of 2 in the first tenn comes from spin. In the exchange temi, there is no extra factor of 2 because one can subtract off a double-counting tenn (see equation Al.3.19). The simnnations can be executed as per equation A 1.3.29 to yield... 

The gas phase reaction shows a double minimum and a small barrier along the reaction coordinate which is the difference between the two C-CL distances. The minima disappear in aqueous solution and this is accompanied by an increase in the height of the barrier. The behaviour in dimethyl fonnamide is intennediate between these two. 

The decrease in reactivity with increasing temperature is due to the fact that many low-energy ion-molecule reactions proceed tln-ough a double-well potential with the following mechanism [82] ... 

In essence, a guided-ion beam is a double mass spectrometer. Figure A3.5.9 shows a schematic diagram of a griided-ion beam apparatus [104]. Ions are created and extracted from an ion source. Many types of source have been used and the choice depends upon the application. Combining a flow tube such as that described in this chapter has proven to be versatile and it ensures the ions are thennalized [105]. After extraction, the ions are mass selected. Many types of mass spectrometer can be used a Wien ExB filter is shown. The ions are then injected into an octopole ion trap. The octopole consists of eight parallel rods arranged on a circle. An RF... 

Due to the rather stringent requirements placed on the monochromator, a double or triple monocln-omator is typically employed. Because the vibrational frequencies are only several hundred to several thousand cm and the linewidths are only tens of cm it is necessary to use a monochromator with reasonably high resolution. In addition to linewidth issues, it is necessary to suppress the very intense Rayleigh scattering. If a high resolution spectrum is not needed, however, then it is possible to use narrow-band interference filters to block the excitation line, and a low resolution monocln-omator to collect the spectrum. In fact, this is the approach taken with Fourier transfonn Raman spectrometers. 

As we have discussed earlier in the context of surfaces and interfaces, the breaking of the inversion synnnetry strongly alters the SFIG from a centrosynnnetric medium. Surfaces and interfaces are not the only means of breaking the inversion synnnetry of a centrosynnnetric material. Another important perturbation is diat induced by (static) electric fields. Such electric fields may be applied externally or may arise internally from a depletion layer at the interface of a semiconductor or from a double-charge layer at the interface of a liquid. 

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