Transform Hartley

Weld Defects Recognition Using the Digital Hartley Transform. 

An invariant pattern recognition method, based on the Hartley transform, and applied to radiographic images, containing different types of weld defects, is presented. Practical results show that this method is capable to describe weld flaws into a small feature vectors, allowing their recognition automatically by the inspection system we are realizing. 

Economou, A., Fielden, P. R., and Packham, A. J., Deconvolution of overlapping chromatographic peaks by means of fast Fourier and Hartley transforms, Analyst, 121, 97, 1996. 

The identification of thirteen penicillins including amoxicillin by their UV and derivative UV spectra has been achieved [73,74], Similar spectra were differentiated by use of the Fast Hartley Transform. 

Azobenzene [103-33-3] M 182.2, m 68", pK 2.48. Ordinary azobenzene is nearly all in the transform. It is partly converted into the cw-form on exposure to light [for isolation see Hartley J Chem Soc 633 1938, and for spectra of cis- and /ran5-azobenzenes, see Winkel and Siebert Chem Ber 74B 6707947]. trans-Azobenzene is obtained by chromatography on alumina using 1 4 benzene/heptane or pet ether, and crystd from EtOH (after refluxing for several hours) or hexane. All operations should be carried out in diffuse red light or in the dark. 

From the authors experience not all real data sets can be transformed to constant variance using power transformations. Instrumentation imperfections in our laboratory resulted in data that had variable variances despite our attempts at transformation. The transformed chlorothalonil data set, as shown in Table III illustrates a set where the transformations attempted nearly failed to give constant variance across the response range in this case the Hartley criterion was barely satisfied. The replications at the 0.1 and 20. ng levels had excessively high variance over the other levels. An example where constant variance was easily achieved utilized data of the insecticide chlordecone (kepone) also on the electron capture detector. Table II shows that using a transformation power of 0.3 resulted in nearly constant variance. 

Transformation Power of Selected Data Sets. Hartley statistic values are shown in Tables I-III for fenvalerate, chlordecone, and chlorothalonil. In each case a power transformation was found of sufficient size at a 93% probability which satisfied the H criterion. For fenvalerate the power of 0.15 was satisfactory for constant variance. For chlordecone the whole range of powers from 0.30 to 0.10 satisfied the critical H value (listed in order of increasing transformation power). Despite apparent non-constancy of data for chlorothalonil shown in Table III, the critical H was satisfied for the range in power transformation from 0.23 to 0.10. 

The response transformation powers for all data sets studied for this work are given in Table V. The acceptable range, judged from the Hartley test, for each individual data set is listed. 

Table V Optimal and Acceptable Range of Response Transformation Power (a) Satisfying the Hartley Test for Data Sets Determined in Various Detectors.

Witkonton and Ercegovich (1972) studied the transformation of chlordimeform in six different fruits following foliar spray application. They found //-chloro-o-formotoluidide was the only major metabolite identified in apples, pears, cherries, plums, strawberries, and peaches. Chemical/Physical. Reacts with acids forming soluble salts (Hartley and Kidd, 1987). 

The interpretation of a spectrum from a dynamical point of view can also be applied to a spectrum containing a broad feature associated with direct and/or indirect dissociation reactions. From such spectra dynamics of a dissociating molecule can also be extracted via the Fourier transform of a spectrum. An application of the Fourier transform to the Hartley band of ozone by Johnson and Kinsey [3] demonstrated that a small oscillatory modulation built on a broad absorption feature contains information of the classical trajectories of the vibrational motion on PES, so-called unstable periodic orbits, at the transition state of a unimolecular dissociation. 

To apply ANOVA methods, we need to make a few assumptions concerning the populations under study. First, the usual ANOVA methods are based on an equal variance assumption. That is, the variances of the I populations are assumed to be identical. This assumption is sometimes tested (Hartley test) by comparing the maximum and minimum variances in the set with an F test (see Section 7B-4). However, the Hartley test is quite susceptible to departures from the normal distribution. As a rough rule of thumb, the largest s should not be much more than twice the smallest s for equal variances to be assumed. Transforming the data by working with a new variable such as or log x can also... 

Hartley et al. (1986) devised a nonradioactive probe, called probe-vector, which can, after hybridization, transform competent E. coli cells and, depending on the transformation efficiency, detect as little as 0.1 pg of target nucleic acid. The probe-vector molecules are linear, partially si DNA prepared by hybridizing individually prepared DNA strands. The ds region of the probe-vector encodes a phenotypic marker and origin of replication. The two terminal si... 

According to the above concept of ozone destruction, the troposphere is an inert medium concerning ozone chemistry. However, as Crutzen (1974) pointed out, there are several possible reaction steps for tropospheric 03. Thus ozone can be removed chemically from the air by transformation processes tabulated in Table 10. One reaction chain starts with the photolysis of 03, which is caused by radiations in the Hartley and Chappuis bands. The excited oxygen atoms, formed by Rl, are partly transformed to ground state atomic oxygen by R4. However, they also react with water vapour to give OH radicals (R5). The sum of reactions 1-5 can be written in the following way ... 

A camera model transforms the coordinates of a point in space (3D) to the coordinates of a point in an image (2D), i.e., explains the process of forming an image with a camera. In the first instance the Pinhole camera model is used. It is the most simple and specialized camera model, which represents an ideal camera distortion-free as shown by Tsai [1], Weng et al. [2] and Hartley et al. [3]. It will serve to explain other models. Taking into account that the equipment of study has telecentric optics, the affine camera model as shown by Hartley et al. [3] will be employed. In this model, the optical center is a point in the infinity. This camera model can be expressed by the following matrix expression ... 

Although sometimes longer samples were collected, only the first 15 min of observation each session were used for each animal. The inanimate object TFs were grouped together (most were to leaves and branches) for analysis and called substrate TFs here. Here and throughout the paper, a square root (+. 5) data transformation was used for all parametric tests if the variances differed significantly (Hartley s test). 

---