Blackman function

A Lorentzian LBF was used in the deconvolution. A deconvolution factor of 100 was chosen in order to achieve a net amplification of 3.4. This value was chosen after trials with deconvolution factors of 50,100 and 1000 in the manner recommended by Kauppinen et al. (52). With a factor of 50, underdeconvolution is observed, while a factor of 1000 results in over-deconvolution and negative side lobes. The deconvolution function amplifies the noise as well, and in order to reduce the noise, apodisation with a Blackman function is performed in conjunction with the deconvolution over the fraction of the interferogram specified by a noise reduction factor. A noise reduction factor of 0.5 was chosen. While the intensities of the deconvolved peaks are higher than those in the original spectra, the relative peak intensities in the deconvolved spectra remain the same as in the original (57). 

The FWHH of this function is even wider than that of the Norton-Beer strong function and so in general is not recommended. (A similar function is the Blackman function that uses the first three terms instead of four, but the coefficients are different.)... 

Where Jf2x) is the Bessel function of zero order. This relation depends only on A and is valid for all t5 es of electron DP. For practical purposes the graph of the D(A) function (the Blackman curve ) is plotted (Fig. 4), and the values of A and thickness values t are determined for each D value according to (2). 

The experiments performed by Clark and Blackman [29] have shown that in the foam there is a fraction of bubbles the size of which remains constant for a certain period of time (Fig. 6.4). Results, confirming the existence of such a fraction have been reported in [29]. It should be emphasised that in spite of Manegold s statement [32], the existence of this fraction is not connected with the dependence of bubble vapour pressure on its radius. The slopes of the R(t) curves presented in Fig. 6.4, increase for certain foams while decrease for others. This reflects not only the inconstancy of permeability I = Dp(h + 2/i0), resulting from thickness decrease, but also the change in the average radius Rm resulting from the change in the bubble distribution function. 

The data of Clark and Blackman for the change with time of the part of the specific surface area attributed to a certain bubble fraction, Fig. 6.6, can serve as a qualitative verification of the validity of the predicted evolution of the bubble distribution function, given... 

Blackman, M. J. (2000). Proteases involved in erythrocyte invasion by the malaria parasite Function and potential as chemotherapeutic targets. Curr. Drug Targets 1,59-83. 

Figure 5.3. Various apodization functions (left) and the instrumental lineshape produced by them (right) (a) boxcar truncation (b) triangular (c) trapezoidal (d) Norton-Beer weak, medium, and strong (e) Happ-Gen-zel (f) Blackman-Harris 3-term and 4-term. The maximum retardation is set to / = 1. In the Fourier transform the FWHH of the main lobe is indicated.

The coefficient A, of the three functions Happ-Genzel, Blackman-Harris three term, and Blackman-Harris four term are summarized in Tab. 5.2. 

Table 5.2. Coefficients of the Happ enzel and Blackman-Harris apodization functions.

The variable depends on the photon flux density Iph as discussed in the previous section where the photosynthesis models of Jassby Platt and Blackman were introduced. Consequently, the specific growth rate fi can be written as a function of the photon flux density as illustrated in Fig. 16 ... 

Figure 16 Specific growth rate // of a microaiga as a function of photon flux density /ph. The specific growth rate is derived from a substrate baiance according to Pirt in combination with the photosynthesis modeis of Jassby and Piatt (solid line) or Blackman (dashed line). The insert illustrates the compensation point /ph,c where photosynthesis is compensated by maintenance-associated respiration m. Parameter values based on high-light acclimated Chlorella sorokiniana 0x=3.5 m moix s/ph,m = 0.10 mols molph qs , = 1.25 x 10 mols mof s y x/s = 0.625 moix mol nis = 3.0x 10 mols moix s M =24 g mol.

Figure 19 Specific rate of sugar production ql blue darkgray in the print version) lines) and the observable yield of sugar on photons absorbed n ph red dark gray in the print version) lines) as a function of photon flux density /ph- The solid lines follow the model of Jassby and Platt the dashed lines follow the Blackman model. Parameter values based on high-light acclimated Chlorella sorokiniana Ux=3.5 m mof T ph,m=0.10 molj fnolph qs,m = 1-25x 10 mols mol s /Mx=24 g moix .

Figure 26 Volumetric productivity of a photobioreactor Tx as a function of biomass concentration Cx according to Blackman red (dark gray in the print version) lines) and Jassby and Platt blue dark gray in the print version) lines). Solid lines represent resuits for /pi,(0) = 0.75 X 10 molph m s - dashed lines represent resuits for /ph(0) = 1.5 x 1 molph m s Photobioreactor d=0.03 m. Parameter values are based on high-light acclimated Chlorella sorokiniana and a sunlight spectrum Ox=3.33 m moixfor sunlight Vs/ph,m = 0.10 mols molph <7s,m = 1-25 x 10 mols moix s V x/s=0.625 moix mol i ms=3.0 x 10 mols moix" s .

In Fig. 26 the volumetric productivity is presented as a function of the biomass concentration for a photobioreactor with a 3-cm optical path. Results are shown both for the approach based on Blackman without spectral resolution and Jassby and Platt including spectral resolution. 

If the constant K is very small we simply have the Monod equation, but if is very small the discontinuous function of Blackman kinetics is achieved. Model discriminations have shown that in a given confidence region of experimental error, the rival models cannot be distinguished (e.g., Boyle and Berthouex, 1974). Model functions with a minimum number of parameters are therefore preferred. 

In this simple example the objective is to approximate the Blackman model for the specific growth rate (//) as a function of substrate concentration (S) ... 

Windows are weighting functions applied to data to reduce the order of the discontinuity at the boundary of the periodic extension. Harris [71] has given a comprehensive review of the properties of over 30 windowing functions and we illustrate their properties with reference to a Blackman window, W. ... 

Earlier, when we were looking at molecular solids (see section 1.5.1), we saw the mixture of Debyean and Einsteinian terms in the partition function of the same solid with degrees of vibration of the lattice and degrees of vibration within the molecule. We will now make broader use of this concept, which was developed by Bom and Blackman, on the subject of ionic compounds. 

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