2D matrix

In Dynamic Spatial Reconstructor at the expense of use 2D matrix of detectors there was the opportunity to use a divergent cone beam of source emission. This system had a number of lacks. In particular the number of projections is rigidly limited by the number of x-ray sources. The dispersion of source emission results in errors of data collected.. However the system confirmed basic advantages of application of conic beams and 2D matrices of detectors for collecting information about 3D object. 

With long acquisition times and a correspondingly high resolution in F2, the experiment may be particularly useful in cases where the H spectrum is overcrowded. The corresponding "C spectra are usually well resolved and the separation of the cross peaks in FI of such 2D experiments can be used to extract the corresponding H subspectra (rows of the 2D matrix) which may then be analysed separately and allow to obtain H chemical shifts and H/ H coupling constants even for such demanding cases. 

In addition to the display functions offered in the buttons panel, the Display pulldown menu (Fig. 4.22) contains additional options for controlling the display of the 2D matrix and its related spectral elements. It is possible to display standard ID spectra, projections or slices on the Fl or F2 axis of a 2D plot together with the 2D spectrum. It is also possible to create additional expansion windows which can be moved, resized and deleted. 

In general, the page layout consists of these three individual windows, the Text window for the title, the Trace window for the 2D matrix, with space left for projections, and the Parameter window. 

To phase either the columns or rows, click on the appropriate button in the button panel. A cross-hair cursor appears in the display field, and the Chi button is highlighted indicating that the trace for the first channel is to be selected. The spectrum display area is internally divided into three parts, corresponding to three different channels (columns or rows) that can be chosen to perform the phase correction. Select appropriate columns or rows from the 2D matrix by moving the cursor to the desired position and clicking... 

With modern Bruker spectrometers the selective ID NOE experiment is usually performed in a pseudo 2D mode. The raw data is obtained as a 2D matrix with the individual rows (FIDs) corresponding to the different decoupler frequencies used for the selective perturbation plus one row where the decoupler frequency is set well away from any resonance line (reference FID). Consequently this 2D data matrix must first be decomposed into the individual 1D FIDs before the difference FIDs can be calculated. 

Here, the outlet of the chromatographic system is connected to an NMR detection cell. The NMR spectra are acquired continuously while the sample is flowing through the detection cell. The result is a set of one-dimensional (ID) NMR spectra which cover the whole chromatogram and are typically displayed as a two-dimensional (2D) matrix showing NMR spectrum against retention time, similar to an LC-diode array detection (DAD) plot. 

Global Alignment. In this approach (Needleman and Wunsch, 1970), a 2D matrix is constructed by comparing two sequences that are placed along the x- and the y-axes, respectively (Table 11.3). Cells representing identities are scored 1, and those with mismatches are scored 0 to populate the 2D array with 0 s and l s. 

The mechanics of addressing the three dimensions of the cube are shown in Figure 12.50. Because of the vast amount of data in a 3D data matrix, a lower digital resolution is used compared to a 2D matrix. Whereas a typical 2D data matrix might have 2048 columns and 1024 rows (about 2 million data values), a 3D matrix might have 256 columns, 256 rows... 

Fig. 3.13 The 2D matrix as combination of "scans" and "experiments". The acronym PS replaces the term pulse sequence. The phase cycling procedure for 2D quadrature detection is not implemented in the scheme.

In contrast to a ID experiment, at the beginning of a 2D experiment a serial file containing a fixed number of blank FID data files is generated in persistent memory. The two dimensional matrix consists of tdl files, with a size of TD with each file corresponding to one time increment in the 2D matrix. A pointer is used to instruct the computer to transfer the accumulated data for each time increment from temporary memory to the correct persistent file. The pointer is then incremented for the next element. This whole procedure is executed by the pointer command if 0. The zd command occurs after the if 0 command and deletes the buffer contents. The 2D loop is closed by the command lo to label. In this instance label is a number or a string that is entered in the first position of the line where the next time increment in the 2D matrix will be started. 

It has been a common practice that a 2D matrix is used to record the data of a weave (Li et al., 1988 Milasuis and Reklaitis, 1988 Chen et al., 1996). In the case of a singlelayer fabric, a 2D binary matrix is used to represent the weave, whose element values are either 0 or 1. 1 indicates a warp-over-weft crossover and 0 means a weft-overwarp crossover. The position of each element in the matrix is located by a coordinate (x,y) where x indicates the xth column from the left and y the yth row from the bottom. This approach is adopted in generating the weaves for hexagonal hollow structures (Chen et al., 2004). 

The weave for each fabric layer is recorded in a 2D matrix. The 2D weave matrix representing the overall weave for each area will be able to be generated by combining the 2D matrices of all fabric sections in the area concerned. Suppose there are n fabric layers in the area of concern. The weave for layer i is recorded in matrix M, ( = 1, 2,. .., n), and the element of this matrix at the xth warp and the yth weft is Mj x,y) (1 < X < r,g, 1 < y < rjp) where r,g is the number of warp ends in M, and the number of weft picks in M,. /, is the length of layer i. 

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