Two-channel calculation

This scheme may be viewed as a two-channel calculation procedure, where one channel corresponds to the filter in the normal way, and the other corresponds to the corrective part. This parallel computation will generate a corrective term (due to the bias estimation) that will affect the final results of the original normal filter. Since the state and parameter estimates are decoupled, the corrective term can be activated only when necessary, that is, when an anomaly occurs. 

The simplest type of shell-and-tube heat exchanger is shown in Eigure 3-1. The essential parts are a shell (1), equipped with two nozzles and having tube sheets (2) at both ends, which also serve as flanges for the attachment of the two channels or beads ( 3) and their respective channel covers (4). The tubes are expanded into both tube sheets and are equipped w nil transverse baffles (5) on the shell side for support. The calculation of the effective heat transfer surface is based on the distance between the inside faces of the tube sheets instead of the overall tube length. 

Conventional implementations of MaxEnt method for charge density studies do not allow easy access to deformation maps a possible approach involves running a MaxEnt calculation on a set of data computed from a superposition of spherical atoms, and subtracting this map from qME [44], Recourse to a two-channel formalism, that redistributes positive- and negative-density scatterers, fitting a set of difference Fourier coefficients, has also been made [18], but there is no consensus on what the definition of entropy should be in a two-channel situation [18, 36,41] moreover, the shapes and number of positive and negative scatterers may need to differ in a way which is difficult to specify. 

This map can have negative as well as positive features, and yet its calculation involves only that of the positive map qmi, thus avoiding the issue of extending the MaxEnt method to two-channel problems. 

C-labelled cholesterol was used to test the recovery of 5-100 pg of faecal sterols from seawater (labelled coprostanol not being available). The radioactivity of the samples and eluates was measured by a two-channel liquid scintillation counter. Percentage recovery was calculated on the basis of the amount of labeled material recovered in the acetone eluant. The results indicate that column extraction efficiency is not adversely affected by the salinity of the water samples, i.e., in the range 95-97%. 

A more detailed description of the working principle of the multichannel YI is given for a four-channel device (N = A). The distances between the channels have been chosen such that di2 k d23 i=- d34 / di3 =/= d24 / dl4. There are six possible different channel pairs corresponding to six different distances of dx2 = 60 pm, d23 = 80 pm, d34 = 100 pm, d13 = 140 pm, d24 = 180 pm, and d14 = 240 pm. These distances match the realized YI sensor structure described in Sect. 10.3. The final interference pattern will thus be a superposition of six two-channel interference patterns. The calculated interference pattern for the four-channel YI is shown in Fig. 10.6a. The amplitude spectrum (lower graph) and the phase spectrum (upper graph) of the Fourier-transformed interference pattern are presented in Fig. 10.6b. 

Fig. 10.10 (a) Response of the two channel YI sensor to refractive index changes caused by applying six different glucose concentrations of 0.0175%, 0.035%, 0.07%, 0.14%, 0.21%, and 0.28% (by weight) intermitted by pure water to the measuring channel of the device, (b) Phase change vs. the glucose concentration calculated (line), measured (filled square)), linear fit (dotted line)... 

Two different calculation methods were used for the simulations (1) the generalized Newtonian method as developed above, and (2) the three-dimensional numerical method presented in Section 7.5.1. The generalized Newtonian method used a shear viscosity value that was based on the average barrel rotation shear rate and temperature in the channel. The average shear rate based on barrel rotation (7ft) is provided by Eq. 7.52. Barrel rotation shear rate and the generalized Newtonian method are used by many commercial codes, and that is why it was used for this study. 

From a calculation to locate the energy minima of Xe in silicalite, three sets of four symmetry-equivalent minima were found, one in each of the two channel systems and one at the intersections. Pathways connect these minima via saddle points and in addition to pathways from a straight or sinusoidal channel minimum to an intersection minimum, there are pathways that are direct transitions between channel segments, circumventing the intersection minima. 

Bell et al. (81) presented forced diffusion calculations of butene isomers in the zeolite DAF-1. DAF-1 (82) is a MeALPO comprising two different channel systems, both bounded by 12-rings. The first of these is unidimensional with periodic supercages, while the other is three-dimensional and linked by double 10-rings. The two channel systems are linked together by small 8-ring pores. It is a particularly useful catalyst for the isomerization of but-l-ene to isobutylene (S3) its activity and selectivity are greater than those of ferrierite, theta-1, or ZSM-5. 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

The slow peak was associated with the dissociation channel that produces an H atom and an X(2) fragment, while the fast peak was identified with the channel that produces the I( 3/2) fragment. From the polarization measurements they could obtain the anisotropy parameter 3, and this along with the TOF spectra could be used to derive the branching ratio between the two channels as a function of wavelength. Combining this information with the measured extinction coefficients, they were able to derive the partial extinction coefficients to the upper states that correlate with each of the channels. A modified 6 approximation was then combined with all of this information to calculate the upper repulsive potential curves that lead to dissociation into these products. Four upper states are involved in the dissociation in this region. The symmetries of these four states are 3nx, fjl, 3no, and The first two states produce... 

We defined the parameters of our model and made numerical calculations of temperature dependent of two gaps. It is a qualitative agreement with experiments. We proposed a two channel scenario of superconductivity first a conventional channel (intraband gi) whichis is connected with BCS mechanism in different zone and a unconventional channel (interband gi) which describes the tunneling of a Cooper pair between two bands. The tunneling of Cooper pair also stabilizes the order parameters of superconductivity [9-12] and increases the critical temperature of superconductivity. 

Low energy positron-alkali atom scattering should therefore be considered as a two-channel process, although the positronium formation channel has been neglected in some calculations. 

Fig. 13.14 Numerical simulation of the velocity field behind an advancing liquid front, moving at constant speed inside a two-dimensional channel. Calculations were carried out with a standard, general purpose FEM program. [Reprinted by permission from H. Mavridis, A. N. Hrymak and J. Vlachopoulos, A Finite Element Simulation of the Fountain Flow, Polym. Eng. Set, 26, 449 (1986).]...

One common microarray data normalization method is to calculate a normalization factor on a per array basis or across an entire experiment. The primary assumption for using a singular normalization factor is that the volume of labeled sample is comparable across the two channels. Thus, due to the large population of labeled cDNA within the uniform volume it is assumed that the same number of labeled cDNAs exist in both samples. Ideally, the overall intensity in the two channels will be the same. Furthermore, any increases in labeled cDNAs, due to increases in mRNA, must result in decreases of some other labeled cDNAs. Typical methods include mean- or median-centering, where the mean/median values are centered within the data distribution, and z-score normalization which adds a scaling factor to mean-centering. 

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