This phase problem
approach seems to me to have promise, using nanofabrication techniques to create cellular optical device encryption surfaces (or CODES) on the surface of banknotes in order to generate unique optical features which are very difficult to invert or counterfeit--in other words a secure easily recognizable physical one-way function.
The period of the interfering signal that is causing the phase problem
can be calculated from this display.
If one could minimize the value of this complicated expression containing thousands of variables, one could solve the phase problem
The main purpose of the book is to introduce the reader to principles of crystallographic symmetry, to discuss some traditional, as well as modern, experimental techniques, to formulate the phase problem
of crystallography, and present in some detail the methods for its indirect and direct solution which are indispensable for further work.
Part A covers the theoretical basis and such experimental techniques as principles of x-ray diffraction, solutions for the phase problem
and time-resolved x-ray crystallography.
In this study, a problem is considered to be a transfer problem if the solution of the problem uses the application of previous knowledge to solve a problem in a new situation, the validators classified them as transfer problems and the items are not similar to the acquisition and evaluation phase problems
and the nature of a proper sound-stage presentation are only part of the ongoing debate about microphones and their placement for two-channel recordings.
Dedicated to providing a complete, basic presentation of the subject that does not assume a background in physics or math, the book's content flows logically from basic principles to methods, such as those for solving phase problems
, interpretation of Patterson maps and the difference Fourier method, the fundamental theory of diffraction and the properties of crystals, and applications in determining macromolecular structure.
Done with skill, multi-microphone use can greatly reduce the kinds of phase problems
disliked by the coincident-source proponents, while still allowing the kind of control over the resulting sound mix that some recording engineers can feel comfortable with -- particularly if they have to re-master later on for a DVD-audio version.
The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems
, and even to multiscale analyses.