Differentiation width

Elemental area of any length z to infinitely long parallel strip of differential width plane containing element does not intersect strip... 

Strip of finite length and of differential width, to differential strip of same length on parallel generating line... 

Examples of these curves are presented in Figs. 5.54 5.56. The main features of profiling curves such as differentiation, width of the intermediate zone, are similar to those in the second case. Although the vertical response of the probe becomes better with an increase of a frequency, a value of apparent conductivity essentially differs from that corresponding to a medium with conductivity even for large values of n2- For example, if 0 /g2 = 1/16, H/L — 0.5 and ri2 = 0.16 ratio Oa/G = 2.5. Determination of thickness of such beds is also difficult. If // < 1/4L and oi/a 1/8, distinguishing such a bed is practically impossible with a two coil induction probe. 

Similar to the smoothing width in polynomial smoothing operations, the differentiation width h = Ax = AA) has an influence on the noise and therefore also on the SNR. The greater the differentiation width (h), the smaller the noise and the higher the SNR (Fig. 3-52). In analogy to the smoothing ratio r, the differentiation ratio f can be defined as the ratio of the differentiation width to the half width of a band ... 

For mathematical reasons, the beginning and the end of the differentiated data are never computed correctly, which also holds time for other polynomial algorithms, but this can easily be taken into consideration (see also Sect. 3.6.4.1) and completely compensated for. If the polynomial has a differentiation width of n = 2 m- points, the first and the last m of the computed new data must be deleted, i. e., w AA at both the low and the high site of the spectrum. This disadvantage also exists in all smoothing operations. However, if the PP differentiation method is used, only the step width AA at the beginning of the spectrum is lost. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

In general, once the curtain of filaments has been produced, it is necessary to attenuate the filaments in order to provide strength and resistance to deformation. The most commonly practiced approach is to utilize a single slot, which is at least the width of the curtain, at a point below the spinning plate and above the laydown screen. There are two practical approaches taken. The first utilizes the injection of low pressure air at a point above the slot so that the fibers attain sufficient acceleration in the slot to provide adequate draw (22) (Fig. 7). The second utilizes a low pressure vacuum below a venturi to provide the pressure differential requited for sufficient acceleration and resulting attenuation (30). 

For gradual changes in channel cross section and hquid depth, and for slopes less than 10°, the momentum equation for a rectangular channel of width b and liquid depth h may be written as a differential equation in the flow direction x. 

Starting with the Poisson form of the elution equation, the peak width at the points of inflexion of the curve (which corresponds to twice the standard deviation of the normal elution curve) can be found by equating the second differential to zero and solving in the usual manner. Thus, at the points of inflexion, ... 

The ability of a GC column to theoretically separate a multitude of components is normally defined by the capacity of the column. Component boiling point will be an initial property that determines relative component retention. Superimposed on this primary consideration is then the phase selectivity, which allows solutes of similar boiling point or volatility to be differentiated. In GC X GC, capacity is now defined in terms of the separation space available (11). As shown below, this space is an area determined by (a) the time of the modulation period (defined further below), which corresponds to an elution property on the second column, and (b) the elution time on the first column. In the normal experiment, the fast elution on the second column is conducted almost instantaneously, so will be essentially carried out under isothermal conditions, although the oven is temperature programmed. Thus, compounds will have an approximately constant peak width in the first dimension, but their widths in the second dimension will depend on how long they take to elute on the second column (isothermal conditions mean that later-eluting peaks on 2D are broader). In addition, peaks will have a variance (distribution) in each dimension depending on... 

ATBN - amine terminated nitrile rubber X - Flory Huggins interaction parameter CPE - carboxylated polyethylene d - width at half height of the copolymer profile given by Kuhn statistical segment length DMAE - dimethyl amino ethanol r - interfacial tension reduction d - particle size reduction DSC - differential scanning calorimetry EMA - ethylene methyl acrylate copolymer ENR - epoxidized natural rubber EOR - ethylene olefin rubber EPDM - ethylene propylene diene monomer EPM - ethylene propylene monomer rubber EPR - ethylene propylene rubber EPR-g-SA - succinic anhydride grafted ethylene propylene rubber... 

The quantitative determination of a component in gas chromatography using differential-type detectors of the type previously described is based upon meas urement of the recorded peak area or peak height the latter is more suitable in the case of small peaks, or peaks with narrow band width. In order that these quantities may be related to the amount of solute in the sample two conditions must prevail ... 

The peak-shaped response of differential-pulse measurements results in unproved resolution between two species with similar redox potentials, hi various situations, peaks separated by 50 mV may be measured. Such quantitation depends not only upon the corresponding peak potentials but also on the widths of the peak. The width of the peak (at half-height) is related to the electron stoichiometry ... 

The laser we use in these experiments is an exclmer laser with a pulse width of approximately 20 nsec. In this time regime the laser heating can be treated using the differential equation for heat flow with a well defined value for the thermal diffusivity (k) and the thermal conductivity (K) (4). 

The interfacial capacity is then obtained by calculating the profiles for various potential drops A0 and subsequent differentiation. Figure 7 shows several examples of capacity-potential characteristics for several widths of the interface. Obviously, the wider the interface, the higher the capacity. In all cases investigated it was higher than that calculated from the Verwey-Niessen model, in which ... 

FIG. 13 Differential pulse voltammograms for Au electrode modified with el6S-tl9-T12Fc ternary complex (filled circle) and el6S-ml9-T12Fc mismatch complex (open circle). Pulse amplitude, 50 mV pulse width, 50 ms pulse period, 200 ms. Other conditions are the same as those in Fig. 12. 

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