Download e-book for iPad: Analysis of superoscillatory wave functions by Calder M.S., Kempf A.

By Calder M.S., Kempf A.

Strangely, differentiable features may be able to oscillate arbitrarily speedier than theirhighest Fourier part might recommend. The phenomenon is named superoscillation.Recently, a realistic approach for calculating superoscillatory capabilities waspresented and it used to be proven that superoscillatory quantum mechanical wave functionsshould convey a couple of counter-intuitive actual results. Following up onthis paintings, we the following current extra normal equipment which permit the calculation ofsuperoscillatory wave capabilities with custom-designed actual houses. We giveconcrete examples and we end up effects in regards to the limits to superoscillatory behavior.We additionally provide an easy and intuitive new reason for the exponential computationalcost of superoscillations

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Extra resources for Analysis of superoscillatory wave functions

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In certain situations, the frictional contact problem stated above describes the material deformation quite accurately. In more complicated situations, such as when the contact zone is not prescribed a priori or when more realistic frictional contact laws are used, the frictional contact problem here can be viewed as an intermediate problem for a typical step in an iterative solution procedure for solving the more complicated contact problem. For a variational analysis of the problem, we need to introduce a function space and some functionals defined over the space.

Assume u E K.

59, 601 where the mathematical theory is motived by duality in natural phenomena with particular emphasis on mechanics. In this chapter, we review some basic notions and results on convex sets, convex functions and their properties as well as the duality theory. Detailed discussions and proofs of the stated results can be found in [49] or [159]. In the theory of convex analysis, it is convenient to consider functions that take on values on the extended real line E. Recall that a functional f : V + is said to be proper if f ( v ) > -cc b'v E V and f ( u ) < cx for some u E V.

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

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