Introduction to Superspace Groups. (Part 2. Composite Crystal).

Equivalence of superspace groups

An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be d...

Part 2 - Introduction

Introduction to biostatistics: Part 2, Descriptive statistics.

Descriptive statistics include measures of central tendency and variability. Measures of central tendency include mean, median, and mode. The mean is the arithmetic average of data from interval or ratio scales. The median reflects the 50th percentile score. The mode is the most frequently occurring value of a data distribution. Measures of variability include range, interquartile range, standa...

Introduction to Part Ii

In the following chapters we present the theory of bifurcations of dynamical systems with simple dynamics. It is difficult to over-emphasize the role of bifurcation theory in nonlinear dynamics the reason is quite simple: the methods of the theory of bifurcations comprise a working tool kit for the study of dynamical models. Besides, bifurcation theory provides a universal language to communica...

Introduction to arithmetic groups

Arithmetic groups are fundamental groups of locally symmetric spaces. We will see how they are constructed, and discuss some of their important properties. For example, although the Q-rank of an arithmetic group is usually defined in purely algebraic terms, we will see that it provides important information about the geometry and topology of the corresponding locally symmetric space. Algebraic ...