Triangular squared function

Fig. 15 Apodization, or the reduction of artifacts in the spectral line by the multiplication of the interferogram by a window function that tapers to zero at the end point of the interferogram. (a) Cosine interferogram of Fig. 13(a) multiplied by the triangular window function of Fig. 14(d). (b) Resulting spectral line, the sine-squared function.

Function generator — A function generator is an electronic device which generates a desired potential wave form (e.g., DC bias, steps, triangular, square, sinusoidal, and any desired combination thereof). Modern function generators are often interfaced with a computer which allows for a choice of user-selected and/or user-defined functions or combinations of functions. In electrochemical applications the function generator will provide the input for a -> potentiostat or... 

Figure 2.5 shows three examples of apodization functions and the corresponding ILS. It can be observed that the triangular and squared triangular apodization functions (green and red, respectively) present a reduced side lobe intensity. However,... 

Figure 13. Graphical constructions to show the convolution of two simple square pulses (e(t) and h(t) of Eq. 31) to yield a triangular function (f(t) of Eq. 31). Holding the first square function fixed, the second function is moved from left to right, and the two functions multiplied together, as shown in the shaded segments. Each point, a to e, of the convolution represents the area of the product shown at the lower left (see text).

Here in Chapter 1 we make the additional assumptions that the fluid has constant density, that the cross-sectional area of the tube is constant, and that the walls of the tube are impenetrable (i.e., no transpiration through the walls), but these assumptions are not required in the general definition of piston flow. In the general case, it is possible for u, temperature, and pressure to vary as a function of z. The axis of the tube need not be straight. Helically coiled tubes sometimes approximate piston flow more closely than straight tubes. Reactors with square or triangular cross sections are occasionally used. However, in most of this book, we will assume that PFRs are circular tubes of length L and constant radius R. 

Some other less important types of AC polarography may also be considered as sinusoidal ac techniques, as their theoretical treatment can be based on signals from a complex Fourier function in this context we confine ourselves to mentioning sawtooth or triangular wave48 superimposed on the dc ramp. Square-wave polarography is also of that type, but in view of its greater importance we shall treat it separately. 

Fig. 26 Fourier transform spectrum of v2 of ammonia. Trace (a) is a section of the infrared absorption spectrum of ammonia recorded on a Digilab Fourier transform spectrometer at a nominal resolution of 0.125 cm-1. In this section of the spectrum near 848 cm-1 the sidelobes of the sine response function partially cancel, but the spectrum exhibits negative absorption and some sidelobes. Trace (b) is the same section of the ammonia spectrum using triangular apodiza-tion to produce a sine-squared transfer function. Trace (c) is the deconvolution of the sine-squared data using a Jansson-type weight constraint.

Fig. 5.17 The binding energy per atom U as a function of the coordination number for aluminium. The crosses correspond to LDA predictions, whereas the curve is a least-squares fit of the form of eqn (5.72). The lattice types considered are the linear chain ( = 2), graphite ( = 3), diamond ( = 4), two-dimensional square mesh ( = 4), square bilayer ( = 5), simple cubic (x = 6), triangular mesh (x - 6), vacancy lattice (x — 8) and face centred cubic (x = 12). (After Heine eta/. (1991).)...

Fig. 11. The change in surface tension as a function of electrolyte concentration for (a) a square well interaction for anions, with d1 = 5 A and = 1 kT (b) a triangular well interaction for anions, with dl =...

Cross-sectional shapes other than circular are also obtainable, these include square, rectangular, triangular and D-sections. All such tubes are expensive and so should be bought and used only if their special dimensions and form are essential to the function of the apparatus in hand. 

Fig. 7-15. Left Nucleation rate in the binary system H2S04-H20 at 298 K as a function of relative humidity and with the H2S04 activity p/ps as a parameter [from calculations of Mirabel and Katz (1974)]. Right Steady-state H2S04 number density required for a nucleation rate of 1 particle/cm3 s as a function of relative humidity. The solid lines and the triangular point are from calculations of the authors indicated the squares with error bars were obtained experimentally by Boulaud et al. (1977).

Let us assume that P is the fraction of available sites on the alumina surface that are occupied by chromium ions. Multilayer adsorption will be excluded, so that each site may be occupied only once. If there are N chromium atoms on the surface, then the number of atoms in single, double, triple, and quadruple clusters denoted by 8, D, T, and Q, respectively, are given by the expressions listed in Table VI. Note that there are several types of triple and quadruple clusters. Formulae are presented for both a plane triangular lattice and a plane square lattice. The original article should be consulted for the derivation of these expressions (202). The actual arrangement of the alumina sites depends upon the exposed surface plane, and for our purposes either the triangular or the square lattice is an adequate approximation to the surface. The quantities SjN, DjN, TjN, and QjN are shown graphically in Fig. 36 as a function of the fraction P of the occupied sites. 

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