Read e-book online Analysis of superoscillatory wave functions PDF

By Calder M.S., Kempf A.

Unusually, differentiable capabilities may be able to oscillate arbitrarily swifter than theirhighest Fourier part may recommend. The phenomenon is named superoscillation.Recently, a pragmatic strategy for calculating superoscillatory features waspresented and it used to be proven that superoscillatory quantum mechanical wave functionsshould convey a few counter-intuitive actual results. Following up onthis paintings, we the following current extra common equipment which permit the calculation ofsuperoscillatory wave features with custom-designed actual houses. We giveconcrete examples and we turn out effects concerning the limits to superoscillatory behavior.We additionally supply an easy and intuitive new reason behind the exponential computationalcost of superoscillations

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On the other hand, contours of malignant tumors were typically modeled with a large number of narrow parabolas and few flat sections. The method was not extended to provide a reconstructed model of the original contour. Ventura and Chen [36] presented an algorithm to segment 2D curves in which the number of segments is prespecified to initiate the process, in relation to the complexity of the shape. This may not be a desirable step, depending on the application. Rangayyan et al. [14] proposed a polygonal modeling procedure that eliminates this limitation of the method of Ventura and Chen [36].

The procedure for joining two segments is described in Rule 1. The threshold Smin represents the relevance of a segment and θmax indicates the relevance of the turning angle between the two adjacent segments of the contour being analyzed. The relevance of the segment is related to the resolution of the image and the requirements of the application. A high value for θmax means that when the internal angle between the two adjacent segments is large, then the segments should be joined. The procedure stops when no segments are joined in an iteration.

The contour is partitioned into N linear segments, Si = {(xij , yij )}, j = 1, 2, . . , Mi , i = 1, 2, . . , N, with M = M1 + M2 + . . + MN , and Sk ∩ Sl = ∅ ∀(k, l), k = l. The next step is to reduce the influence of noise while maintaining the semantically (or diagnostically) relevant characteristics of the given contour, and attempting to reduce, in each iteration of the algorithm, the number of linear segments in the original contour, as well as to increase the 12 2. POLYGONAL MODELING OF CONTOURS number of points in each new linear segment.

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Analysis of superoscillatory wave functions by Calder M.S., Kempf A.

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