Multidimensional arrays

Data collected by modern analytical instalments are usually presented by the multidimensional arrays. To perform the detection/identification of the supposed component or to verify the authenticity of a product, it is necessary to estimate the similarity of the analyte to the reference. The similarity is commonly estimated with the use of the distance between the multidimensional arrays corresponding to the compared objects. To exclude within the limits of the possible the influence of the random errors and the nonreproductivity of the experimental conditions and to make the comparison of samples more robust, it is possible to handle the arrays with the use of the fuzzy set theory apparatus. 

Figure 15.3 Separation of tricyclic antidepressants by using multidimensional LC-LC. Peak identification is as follows DOX, doxepin DES, desipramine NOR, noitryptylene IMI, imipramine AMI, amiti yptyline. Adapted from Journal of Chromatography, 507, J. V. Posluszny et al., Optimization of multidimensional high-performance liquid cliromatography for the deterTnination of drugs in plasma by direct injection, micellar cleanup and photodiode array detection , pp. 267 - 276, copyright 1990, with permission from Elsevier Science.

In this section we represent wave packets as vectors v and refer to the individual components of v in the computer-friendly form of multidimensional arrays with indices, for example, v i,j,k), where the indices i,j, and k refer to the various degrees of freedom. These vectors may be real, such as the real vector V of the previous sections, or they may be complex representations of the... 

A DATA NULL step is used as the reporting tool of choice here primarily because the output format required is too complex for anything else. Because the CrossTabFreqs data set from PROC FREQ does not have all of the necessary items on the same observation, a multidimensional array called values is used to load and retain all data elements for the given week. The first dimension of the array represents rows and the second dimension represents columns. 

Parallel synthesis is the term loosely applied to the preparation of discrete compounds in the format of a spatially addressable array. It is often used in contrast to "mixture-based" combinatorial synthesis. While it is hue that the term "parallel synthesis" may encompass the preparation of a fully combinatorial multidimensional array of compounds, in practice, it most... 

Most of the detectors permit peak recognition but provide no structural information, which can be particularly important for identification of unknown compounds. From this point of view, the spectro-metric detectors, specifically mass spectrometer and photodiode array detectors, add a third dimension to the multidimensional system and give additional information useful in components identification. 

To a frog with its simple eye, the world is a dim array of grays and blacks. Are we like frogs in our limited sensorium, apprehending just part of the universe we inhabit Are we as a species now awakening to the reality of multidimensional worlds in which matter undergoes subtle reorganizations in some sort of hyperspace ... 

The application of this concept to liquid samples is what we already refer to electronic tongue . It entails the use of multidimensional information coming from an array of chemical sensors, mimicking the animal sense of taste. As several possibilities exist on the side of which sensors form the array, the general response shown by the different sensors used is of paramount importance that is, cross-selectivity features are needed in order to profit from the multidimensional aspects of the information [7]. The performance of electronic tongues can be suited not only to qualitative purposes like identification of species and classification of sample varieties, but also to quantitative uses, normally the multidetermination of a set of chemical species, an interesting objective for process control. A more bioinspired trend is the artificial taste [8] in order to perform automated taste perception, especially in the industrial field. 

New machine architectures are performing remarkably, provided the software can be written to use the architecture. Hypercube computers available commercially are multidimensional arrays of hundreds of computers, each with the power of a microvax. 

We are now in a positicm to prc am the computer to evaluate the multidimensional array c(n) with the following iterative expressions ... 

Arrays can be multidimensional. Excel permits arrays with up to 60 dimensions one-, two- and three-dimensional arrays are common. To create a 2-D array with dimensions 2 x 500, use the statement... 

Since multidimensional arrays such as the one above can use up significant amounts of memory, it s important to define the data type of the variable. The complete syntax of the Dim statement is... 

But, there s a limitation. Only the upper bound of the last dimension of a multidimensional array can be changed. Thus, the following code is valid ... 

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