Data transposition

It is immaterial which Fourier transformation is carried out first and which second (i.e., whether the function is first transformed with respect to the <1 or the /2 variable). Usually, it is more economical to transform individual FIDs (transformation with respect to 2) and then, after data transposition. 

There are actually two independent time periods involved, t and t. The time period ti after the application of the first pulse is incremented systematically, and separate FIDs are obtained at each value of t. The second time period, represents the detection period and it is kept constant. The first set of Fourier transformations (of rows) yields frequency-domain spectra, as in the ID experiment. When these frequency-domain spectra are stacked together (data transposition), a new data matrix, or pseudo-FID, is obtained, S(absorption-mode signals are modulated in amplitude as a function of t. It is therefore necessary to carry out second Fourier transformation to convert this pseudo FID to frequency domain spectra. The second set of Fourier transformations (across columns) on S (/j, F. produces a two-dimensional spectrum S F, F ). This represents a general procedure for obtaining 2D spectra. 

Data transposition is the process of changing the orientation of the data from a normalized structure to a non-normalized structure or vice versa. There are many definitions of normalization of data, and you should learn about normal forms and normalization. Here, in brief, normalization of data means the process of taking information out of the variable definitions and turning that information into row definitions/keys in order to reduce the overall number of variables. Normalized data may also be described as stacked, vertical, or tall and skinny, while non-normalized data are often called flat, wide, or short and fat. ... 

Graphically, the process of data transposition from normalized to non-normalized data looks like this ... 

There are two tools commonly used for performing data transpositions in SAS PROC TRANSPOSE, and a DATA step with ARRAY statements. PROC TRANSPOSE is a powerful tool that flips a data set with just a few lines of SAS code. On the other hand, DATA steps that employ arrays for data transposition are more flexible, in that they allow for more precise control of the transposition process. We will now examine PROC... 

The influence of skin effects in a multi-core cable is almost the same as that of a multiphase busbar system, discussed in Sections 28.7 and 28.8. However, unlike a busbar system, the resistance and inductive reactance for various sizes of cables can be easily measured and are provided by leading manufacturers as standard practice in their technical data sheets. To this extent, making an assessment of skin effects in cables is easy compared to a busbar system. Since all the phases in a cable, of a 3-core or 3 72-core are in a regularly twisted formation throughout the length of the cable, they represent the case of an ideal phase transposition (Section 28.8.4(3)) and almost nullify the effect of proximity. 

Transform) the content of a given column ( vector) can be mathematically modified in various ways, the result being deposited in the (N + 1) column. The available operators are addition of and multiplication with a constant, square and square root, reciprocal, log(w), Infn), 10 , exp(M), clipping of digits, adding Gaussian noise, normalization of the column, and transposition of the table. More complicated data work-up is best done in a spreadsheet and then imported. 

Figure 3.3 The mechanics of obtaining a two-dimensional NMR spectrum. As the l value is varied, the magnetization vectors are caught during detection at their various positions on the x /-plane. The value of the detection time l-i is kept constant. The first set of Fourier transformations across is followed by transposition of the data, which aligns the peaks behind one another, and a second set of Fourier transformations across t then affords the 2D plot.

In this example you can see that the transposition for subject 101 is incorrect because of the missing record for visit 2. In this case, the systolic blood pressure values are shifted down one slot so that visit 3 data are mistakenly placed in the visit 2 slot, and so forth for visit 4 and visit 5. To remedy this error, use an ID statement in PROC TRANSPOSE as follows ... 

There may be times when a DATA step with arrays is a better means to transpose data. This is true when the data to be transposed have more than one record per BY group variable or when there is a need to have the resulting data set include data that are not in the source data set. In clinical trials missing data is a very common issue. Let s look at a derivation of the previous systolic blood pressure transposition problem where visit 2 is always missing. 

Notice the missing column for visit 2. This is exactly what you would expect PROC TRANSPOSE to give you. PROC TRANSPOSE transposed the data that were present and could not be expected to know about visits that are not represented in the data. However, often in clinical trials reporting you want to report on all visits, treatments, or other expected parameters whether they are represented in the actual data or not. In this case, a DATA step with arrays is a better choice to transform the data. Here is an example of the previous transposition that includes all visits 1-5, regardless of which visits are included in the underlying data. 

PROC TRANSPOSE is an efficient way to transpose a SAS data set when the transposition process is simple. However, if the transposition process is more complicated, and involves transforming to a data set where all possible columns must be represented or where there are multiple records per BY group, then a DATA step with arrays is probably a better choice. 

From final report backwards to the original report and record of sample, the trail was found to be easy to follow. Copies of chromatograms appearing in the final report were matched with original chromatograms. Calculations of data were determined to be correct. However, an outstanding problem of transposition of data... 

The cyclization of the phosphorylated arylhydrazones, leading to compounds 168, presumably takes place through the initial formation of 3-phosphorylated indoles 69, which isomerize to compounds 168 in the course of the reaction. Such 3—>2 rearrangements are well-known [30, 180-182, 231]. The transposition of the phosphorus-containing substituent in indoles was first observed in [178, 179]. In the review [8] the data on the formation of 2-phosphorylindoles from the arylhydrazones of phosphorylpropionic aldehyde were considered proved, but the results on the cyclization of hydrazones of phosphorylacetaldehyde to the 2-isomers were placed under some doubt. 

Moreover, the radiative lifetime is not a constant for a given ion and a given electronic level. Indeed, there is a dependence on the refractive index, as clearly shown by eq. (14), so that transposition of a literature value to a specific compound cannot be made directly, which explains the wide range of rrad values reported for an individual Lnm ion. As an example, reported radiative lifetimes for Er111 range from 3 to 12 ms, even for relatively similar compounds (see table 19 below) Another hypothesis inherent to Judd-Ofelt theory is that 4f functions do not contain contributions from 5d orbitals, which is not quite the case for Pr111 and Tbm for instance. Selected data reported in the literature are listed in table 5. 

Mass spectrometry offers several advantages over classical methods for the characterization of non-covalent complexes rapidity, simplicity and ability to work on mixtures. One of the goals in this field is to transfer gas-phase data to the liquid phase. However, this transposition has to be done with caution. Indeed, some of the complexes observed are nonspecific associations formed in the gas phase or aggregates resulting from the ESI process itself. Also, some of the complexes present in the liquid phase might not be observed in the mass spectrum. 

Owing to the extremely large variety of solvents used in organic or organometallic chemistry, it is unlikely that all the pertinent electrochemical data can be found for a particular system and a particular solvent [30]. Thus the problem of the transposition of data obtained for one solvent to another frequently arises. As discussed for Ip or Aff, this should not be done without extreme precautions. Indeed, by substruction of the two equations, akin to Eq. (25), pertinent to each solvent, one obtains readily for a given O/R redox system... 

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