Modern crystallography and its foundations

The Foundations of Modern

The X-ray Transform and its Application in Nano Crystallography

In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...

J. M. Bernardo. Modern Bayesian Inference: Foundations and Objective Methods MODERN BAYESIAN INFERENCE: FOUNDATIONS AND OBJECTIVEMETHODS

The field of statistics includes two major paradigms: frequentist and Bayesian. Bayesian methods provide a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods may be derived from an axiomatic system and provide a coherentmethodology which makes it possible to incorporate relevant initial information, and which solvesmany of the difficulties w...

Impact of Crystallography on Modern Science

Diffraction techniques represent the ideal tools for the determination of the structure of materials characterized by long range order; no spectroscopic technique can compete with them in terms of accuracy. However, when the long range is missing, because we are dealing with molecules, gases, liquids, amorphous solids, nanostructured materials etc... than the standard way of analyzing diffracti...

The Foundations of Modern Cryptography (

In our opinion, the Foundations of Cryptography are the paradigms, approaches and techniques used to conceptualize, deene and provide solutions to natural cryptographic problems. In this essay, we survey some of these paradigms, approaches and techniques as well as some of the fundamental results obtained using them. Special eeort is made in attempt to dissolve common misconceptions regarding t...