Curve Smoothed

X is an acidity function based on the first-order approximation, Eq. (8-92). Values of X have been assigned by an iterative procedure. The data consist of values of Cb/cbh+ as functions of Ch+ for a large number of indicators. For each indicator an initial estimate of pXbh+ and m is made and X is calculated with Eq. (8-94). This yields a large body of X values, which are fitted to a polynomial in acid concentration. From this fitted curve smoothed X values are obtained, and Eq. (8-94), a linear function in X. allows refined values of pXbh + and m to be obtained. This procedure continues until the parameters undergo no further change. Table 8-20 gives X values for sulfuric and perchloric acid solutions. ... 

What was said above is illustrated by Fig. 1.29 and Fig. 1.30 corresponding to the cases p > pc and p < pc respectively. To make the presented kinetic curves smooth, in these calculations the transformation rate A — B was taken to be finite. To make results physically more transparent, the effective reaction rate K (t) of the A —> B transformation is also drawn. The standard chemical kinetics would be valid, if the value of K (t) tends to some constant. However, as it is shown in Fig. 1.30, K(t) reveals its own and quite complicated time development namely its oscillations cause the fluctuations in particle densities. The problems of kinetic phase transitions are discussed in detail in the last Chapter of the book. 

Figure 3.95. The normalized initial time dependence of the delayed fluorescence from anthracene (3 x 1CT5M) in MCH/MCP at 115 K ( ). The theoretical curve (smooth line) was calculated with p = 2 x 1010,y = 0.0125, D/R T = 6.4 x 103 s-1. The weighted residuals are shown below. (From Ref. 262.)...

Conchoidal produces curved smooth surfaces or concentric ridges (glass, quartz, garnets, obsidian)... 

Fracture Fracture describes the way a substance breaks when it neither cleaves nor parts (breaks along plane of weakness). The most common kind of visible fracture is conchoidal, which produces curved, smooth surfaces (glass, quartz). Freshwater pearl one that occurs in a freshwater (non-marine) mollusk. Gem a general term used to describe precious and semi-precious stones, usually after they have been cut and polished. In archaeology, it refers only to engraved stones (cameo, intaglio, seals, etc.). 

The total amount of radioactivity involved and the amounts bound to the antibody were measured for 2 min on a well-type gamma counter. The found values were corrected for non-specific binding and the concentrations of APS-314d in samples were obtained from the calibration curve smoothed by a 4-PL model. 

The spline must curve smoothly about each point with no sharp bends or kinks, so the slope of each segment where they connect must be similar. To achieve this the first derivatives of the spline polynomials must be equal at the measured points. 

Electronic integration zero 0.1 very good (depending on the algorithm for curve smoothing, peak detection, and baseline drift) suited... 

Fig. 10.22 Fluorescence decay of oxazine adsorbed on SnS2. This measurement was performed in a dry atmosphere after the dye had been adsorbed. The upper curve (smooth line) was obtained with oxazine adsorbed on tape. For comparison, the signals obtained with SnS2 were multiplied by 125. For details. see text. (After ref. [48])...

Fig. 16. Comparison of calculated (dashed curve) and measured (full curve) smoothed cross sections at three different energies, showing the improvement obtained by including rotational coupling. Upper pictures without rotational coupling [/f12(/ c) = 005eV L12 = 0] and lower pictures with rotational coupling [H 12(/ c) = 0-065 eV L12 = 0-04/i]. Notice the different vertical scales.

The use of integral distribution functions is common for two reasons first, these distribution functions have simpler shape and thus are more suitable for curve smoothing second, they allow for an easier determination of the fraction of particles belonging to a particular finite size range, Ar, as a simple difference between corresponding values, q(r + Ar) - q(r). 

The hardware used consists of an AD converter connected to an amplifier, a relay switch (operated by the microprocessor) for tltrant portioning and a DAC unit for decoding of data obtained and stored by the microprocessor. The microcomputer assembled by Betteridge et aL for this purpose consisted of 1 kb ROM, 2kb RAM and a digital I/O unit. The main functions of the software are data collection and display, derivation, curve smoothing, peak detection, Interpolation (determination of the maximum slope of the titration curve by calculation) and result delivery (display). 

Fig. 1.5g. Polarographic waves for a reversible (—— and an irreversible ( --- process. (Curves smoothed to remove oscillations)...

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